equilibrium models in an applied framework: industrial structure and transformation

Lecture Notes in Economicsand Mathematical Systems 667

Founding Editors:

M. BeckmannH.P. Künzi

Managing Editors:

Prof. Dr. G. FandelFernUniversität HagenHagen, Germany

Prof. Dr. W. TrockelMurat Sertel Institute for Advanced Economic ResearchIstanbul Bilgi UniversityIstanbul, Turkey

Institut für Mathematische Wirtschaftsforschung (IMW)Universität BielefeldBielefeld, Germany

Editorial Board:

H. Dawid, D. Dimitrow, A. Gerber, C-J. Haake, C. Hofmann, T. Pfeiffer,R. Slowiński, W.H.M. Zijm

For further volumes:http://www.springer.com/series/300

Ronny Noren

Equilibrium Models in anApplied Framework

Industrial Structure and Transformation

Dr. Ronny NorenMid Sweden UniversityDepartment of Social SciencesOstersundSweden

ISSN 0075-8442ISBN 978-3-642-34993-5 ISBN 978-3-642-34994-2 (eBook)DOI 10.1007/978-3-642-34994-2Springer Heidelberg New York Dordrecht London

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Preface

The models and the discussion presented in this book focus on two important

foundations in economics: the interdependence within the economic activity and

the desire to come to a state of economic balance (equilibrium). Perhaps the state of

economic balance will not be achieved in practice, but it is essential that the

economic system possesses a strong mechanism to achieve it. Equilibrium, in that

sense, can be described as a “moving target” in economics.

In a changing world, it is essential to be competitive. To reach competitiveness,

we must be prepared for a challenge. This challenge cannot be met in a state of rest;

there is always a demand for continuous change, i.e., economic transformation.

With no transformation, the economy will become stagnant, and in the longer run, a

fall in the long-term growth will be observed. With the help of economic models of

industrial structure and transformation, this situation can perhaps be avoided. This

book is a presentation and discussion of these kinds of models.

This book consists of eight chapters. It contains an accessible analytical survey

of economic equilibrium models, including multi-sector programming models

(linear and quadratic) and the computable general equilibrium (CGE) model. The

presentation is focused on the theoretical and applied structure of these models. In

addition, the importance of disinvestment activities is emphasised by the presenta-

tion of a specific equilibrium model of economic transformation. Finally, the

globalisation process of the production system is put in focus.

The idea for this book arose when I was working with the lectures in my course

in applied equilibrium models. The purpose is to provide an interesting and

understandable analytical framework for applied equilibrium models of structure

and transformation, and also provoke a curiosity of further development in the field.

This book is directed primarily to advanced undergraduate and beginning grad-

uate students. Whilst the text of this book is couched in mathematical terminology,

the level of the mathematics is easy to grasp. In other words, the equilibriummodels

and the experiments introduced in this book are presented using convenient and

reliable techniques in order to facilitate an easy understanding of the subject. Thus,

the intention is to provide a clear and lucid interpretation of techniques and

applications.

v

The CGE model presented and used in this book is distributed with the GAMS

computer system. The unlicensed GAMS distribution is available on the Internet

free of cost. Thus, with the access to a computer, the reader can take part in the CGE

computations presented here.

I am indebted to colleagues and my students, graduate and undergraduate, for

helpful comments when writing the proposal, whose response has guided the

organisation of this book. Different versions have been suggested and used in my

teaching. The students’ encouragement has been just as important as their criticism.

I would also like to thank Thomas Quayle for his skilful and diligent review of my

English. Finally, I also wish to express my gratitude to the publisher for the edition

of this book. Of course, the usual disclaimer should be added absolving all of these

from any responsibility for errors and opinions expressed herein.

Sweden 2012 Ronny Noren

vi Preface

Contents

1 The Input–Output Model: A Study of the Interindustry

Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 The Basic Input–Output Structure . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 A Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 The Outlook of the Sovereign Planner: The Linear Activity

Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1 Commodities and Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Producers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Consumers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4 Feasible Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.5 The Programming Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 12


References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3 The Planner and the Market: The Takayama Judge Activity

Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1 The Quadratic Programming Problem . . . . . . . . . . . . . . . . . . . . . 22

3.2 Specification of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2.1 The Introduction of Foreign Trade . . . . . . . . . . . . . . . . . . 29

3.3 The Programming Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.4 A Temporary Equilibrium Specification . . . . . . . . . . . . . . . . . . . 35

3.5 Empirical Findings: Applications . . . . . . . . . . . . . . . . . . . . . . . . 37

3.6 Comparative Advantages? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41


Appendix 1: The Reformulation of the Walras-Cassel Model . . . . . . . . 43

Appendix 2: Tables 3.2, 3.3, 3.4, 3.5, and 3.6 . . . . . . . . . . . . . . . . . . . . 47

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

vii

4 A Market with Autonomous Economic Decision Makers:

Features of the CGE Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.1 The Basic Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.2 The Construction of a Simple CGE Model . . . . . . . . . . . . . . . . . . 58

4.3 Foreign Trade: The CES and CET Specification . . . . . . . . . . . . . 63


Appendix: A Summary of Models Presented . . . . . . . . . . . . . . . . . . . . 69

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5 An Applied Model: The CGE Mini Model . . . . . . . . . . . . . . . . . . . . 73

5.1 The Basic Structure of the CGE Model . . . . . . . . . . . . . . . . . . . . 73

5.2 The Numerical Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.2.1 Capital Stock Subject to Physical Deterioration . . . . . . . . . 79

5.2.2 A Change in the Real Exchange Rate . . . . . . . . . . . . . . . . 81

5.2.3 Growth in the Domestic Capital Stock . . . . . . . . . . . . . . . 83


Appendix 1: The Mathematical Equations of the Model . . . . . . . . . . . . 86

Appendix 2: Some Parameters Assignments of the Model . . . . . . . . . . . 96

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

6 A Suggested Model of Economic Transformation . . . . . . . . . . . . . . . 99

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

6.2 Outline of the Transformation Model . . . . . . . . . . . . . . . . . . . . . 100

6.3 The Process Towards Steady-State . . . . . . . . . . . . . . . . . . . . . . . 104

6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

7 Back to the CGE Mini Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

7.1 The New Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

7.2 Re-computations of Numerical Experiments . . . . . . . . . . . . . . . . 110

7.2.1 A Change in the Real Exchange Rate . . . . . . . . . . . . . . . . 112


References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

8 Globalisation and Intermediate Activity . . . . . . . . . . . . . . . . . . . . . . 119

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

8.2 Calculation Methodology and Results . . . . . . . . . . . . . . . . . . . . . 121

8.3 Questions of Economic Strategy . . . . . . . . . . . . . . . . . . . . . . . . . 124

Appendix 1: 2000 and 2005 SNA Statistics . . . . . . . . . . . . . . . . . . . . . 126

Appendix 2: Sector Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

A Final Word . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

viii Contents

Introduction

The Issue of Industrial Structure and Transformation

Economic transformation is a continuous process, in which commodities and

methods of production are renewed or replaced all the time.1 A common character-

istic in many economies is the failure to meet the demands for structural transfor-

mation in the industrial sector of the economy. Economic disequilibrium will arise

in both developed and underdeveloped economies. Often they are faced with

changes in external conditions that will require major adjustments. The structural

lack of equilibrium will accentuate the problems facing stabilisation policy (rising

inflation and unemployment). In a broader perspective, the industrial sector

contracts and the problem of external balance may become permanent. Moreover,

the increased mobility of capital, skills, and entrepreneurship, now as the core of the

process of globalisation, has become even more important as a vehicle for interna-

tional transactions. Increasing technological achievements, the adoption of invest-

ment liberalisation policies by many countries, privatisation, and the switch of

emphasis by firms to geographical diversification are some of the more important

explanations to the strong expansion in structural transformation that are recorded

in the past two decades. A natural question in this situation concerns the elaboration

of an economic policy necessary to increase the adaptability of the industrial sector

to meet the demand for economic transformation.

For a country where international trade represents a significant proportion of the

economic activity, the equilibrium of the domestic economy is to a great extent

determined by the conditions given abroad. Against that background, a crucial

factor for each individual country is to the extent the industry sector can adjust to

changes in foreign market conditions. To provide the formal link between changes

in foreign market conditions and changes in domestic production capacity, the

1 The term “structural transformation” refers primarily to arrangements affecting the allocation of

resources, and the patterns of domestic production and trade resulting from their allocation.

Structural transformation is thus a process of major change in a country’s economy.

ix

adjustment process must also include economic transformation, i.e., transferring

resources from uncompetitive to more expansive sectors of the economy.

The models and the discussion presented in this book focus on two important

foundation stones in economics: the interdependence in the economic activity and

the desire to come in a state of economic balance (equilibrium). Perhaps the state of

economic balance will not be achieved, but it is essential that the economic system

possesses a strong mechanism to achieve it. Equilibrium, in a strategic meaning,

can be described as a “moving target” in economics.

In a changing world, it is essential to be competitive. To reach competitiveness,

we must always be prepared for a challenge. This challenge cannot be met in a state

of rest; there is always a demand for a continuous change, i.e., an economic

transformation. With no transformation, the economy will become stagnant, and

in the longer run, a fall in the long term-growth will be observed. With the help of

economic models of economic structure and transformation, this situation can

perhaps be avoided. This book is a presentation and discussion of these kinds of

models.

This book contains an accessible analytical survey of economic models of

economic structure and transformation, including multi-sector programming

models (linear and quadratic) and the computable general equilibrium (CGE)

model. The presentation is focused on the theoretical and applied structure of

these models. In addition, the importance of disinvestment activities is emphasised

by the presentation of a specific equilibrium model of economic transformation.

Finally, the globalisation process of the production system is put in focus.

Statement of the Problem

If two countries engage in trade, each is assumed to have incentives to increase

domestic production, and reduce consumption, of commodities in which it has the

lower relative marginal cost prior to trade than the other.2 In a free trade equilib-

rium, each country will export such commodities. In the theory of international

trade, free trade raises the level of potential welfare (measured in terms of

commodities) for a country above the level reached in autarchy. The increase in

potential welfare can be subdivided into the gains from exchange that will result

when commodities are obtained at lower prices from abroad and the gains in

domestic production from specialisation in the commodities in which the country

has a comparative advantage.3 Technically, this problem involves the choice

between domestic production and imports, and between production for the

2We make the usual assumption that the agents are countries. This is a fiction. Except in centrally

planned economies, trade is conducted by individual actors rather than by governments.3 Ricardo (1817) developed the doctrine of comparative advantage which showed that all nations

can benefit from trade whatever their cost structure.

x Introduction

domestic market or exports in different sectors of the economy. Only by evaluation

of the economic efficiency of the industrial choices, using the opportunity cost of

resources, can an economic choice be made. From a formal point of view, mathe-

matical programming, and particularly, computable general equilibrium (CGE)

models, provide a detailed and consistent mode of analysis where partial equilib-

rium models are insufficiently comprehensive.

In close connection to the problem mentioned above, is the problem of structural

transformation.4 In fact, structural transformation is more or less ubiquitous in an

economy with free trade, and possibility to domestic specialisation. The problem of

structural transformation has two interrelated aspects. One is the need to close down

uncompetitive capacity. The other is the lack of expansion in potentially competi-

tive parts of industry. To be solved only by transferring resources from uncompeti-

tive to more expansive sectors of the economy. However, under the conditions of

structural disequilibrium, existing prices form an imperfect guide to resource

allocation. Strictly speaking, the existing price structure must be either modified

or discarded as a tool of resource allocation.

With the creation of the European Monetary Union (EMU) and the rules on fiscal

policy in the Eurozone, the questions of structural transformation have regained its

importance in the discussion of economic policy. The monetarist intellectual

influence in economics and the strategic position of Germany (Bundesbank) in

the process towards EMU5 explain the construction of the Eurosystem. This has led

to the creation of a European Central Bank (ECB) with a strong mandate for price

stability and a week responsibility for stabilising output and employment

fluctuations.6 In other words, ECB cannot do much to stabilise the economy. The

best thing is to stabilise the price level. According to the monetarist view, this will

have the incidental effect of producing the best possible outcome in terms of

stability of the economic cycle. Traditional Keynesian policy will only end up

with more inflation. This policy is supported by the real business cycle theory,

which says that the sources of economic cycles are shift in technology and changes

in preferences. There is very little the central bank can do about these movements.

Once again, the best is a stable price level. The medium- and long-term policies of

the union are to raise economic growth through higher labour market innovations,

4Methods to investigate structural transformation in production are not scare in applied econom-

ics. One method is to use a production function, there the factors of production with the utilisation

of new techniques can be analysed. Another method is to derive a Salter curve (Salter 1960). The

Salter curve forms a supply curve, similar to that employed to relate the supply curve of an industry

to the cost curves of individual firms which earn rents (quasi-rents). By comparing Salter curves

from different periods of time, structural change may be illustrated.5 The fiscal rules of the EMU countries are laid down in the Treaty of Maastricht and reiterated in

the Stability and Growth Pact (STP). The Maastricht convergence criterion would ensure that only

countries with a budgetary discipline would enter EMU. The aim of the STP is to ensure a policy

framework based on low inflation and stability of the public finances.6 The study of the construction and workings of the European Monetary Union, see further De

Grauwe (2007).

Introduction xi

which will be a boost to innovation and entrepreneurship. Education policy,

research, competition policy, and rigidities in labour market are focused on.

Hence, supply policy is the answer to raise flexibility and strengthen competitive-

ness. However, the economic performance of the EMU member countries has been

disappointing. Growth has been low and unemployment has remained very high. A

persistently high unemployment, and thus, the emergence of long-term unemploy-

ment above the natural rate, is likely to be associated with less and less downward

pressure on inflation. This situation would lead to an increase in the natural rate of

unemployment.7 This would further decrease the growth rate of the country.

Structural rigidities are often related with problems in the economic transformation

process. It means that we must study the principles of that process more closely.

The core around which the equilibrium models in this study of economic

structure are applied is usually the Leontief input–output model. The essence of

the Leontief input–output model is that it captures the crucial element of the

interrelatedness of production arising through the flow of intermediate commodities

among sectors. The essence of the equilibrium model is that it incorporates the

fundamental equilibrium links among production structure, incomes of various

groups, and the pattern of demand. In the computable general equilibrium (CGE)

model, the endogenous price and quantity variables are allowed to interact so as to

simulate the working of decentralised markets and autonomous economic decision

makers. This implies that we have the possibility to specify substitution in produc-

tion, foreign trade, and demand.

However, economic adjustment does not imply economic transformation and

long-term growth effects, if the model does not incorporate the specification of an

endogenous response in the change of the capital stock. The change of the capital

stock is a dynamic process in a dual sense, i.e., dismantling of old investments

subject to physical or economic deterioration and investment in new and more

efficient machines brought into production. Needless to say, both components of

this process must be taken into consideration when the effects of long-term policy

measures are under discussion.

The exchange rate, factor prices, and the value of output are important variables

in the context of the transformation process. For example, undervalued currency

increases competitiveness, raises the profit rates, and thus, there is a risk that

necessary cost reductions will not be realised. Hence, the incentives to dismantling

old investments on obsolescence diminish. On the other hand, an overvaluation of

the domestic currency can imply, due to decreasing competitiveness and falling

profit rates, a risk of exaggerated cost cuts. Logically, the incentives to dismantling

old investments on obsolescence increase. These two examples are simple but

provide a strong argument for acknowledging the disinvestment (dismantling of

capital stock) process in the economic analysis. Indeed, this leads to the question of

7Also known as hysteresis in macroeconomics. See, e.g., Nickell (1997) for discussions of

European unemployment.

xii Introduction

finding the appropriate balance between competitiveness and an efficient transfor-

mation in the economy to sustain a desirable growth path in the economy.

In the earlier national period, labour, capital, and management were all bundled

together, bound to the same place. Unbundling means that people, capital, and

commodities can be moved from place to place. Unbundling is now very important

in the global industrial activity. It affects tasks within the production chain. Since

we here discuss structural matters, we must focus on intermediate commodities.

Changes in the composition in the flow of intermediate commodities affect the

production structure in a various degree.

As now realised by the reader, the contribution in this book is, a presentation and

discussion of different types of applied equilibrium models, the explicit recognition

of the importance of endogenous disinvestment activities (the transformation pro-

cess), and the implications of unbundling in the global industrial activity.

Outline of Chapters

This book, organised in eight chapters, is designed as an introductory textbook in

equilibrium modelling of industrial structure and transformation. The analyses start

and end with an economic equilibrium. The equilibrium at the end is often different

from the equilibrium in the initial position. The explanation is that we have passed

through an economic change in economic policy or in the structure of the economy.

In the analyses of this change, computable general equilibrium (CGE) models are

often used. CGE models trace their linkage back to mathematical programming or

activity analysis and the literature on input–output models. Existing applied general

equilibrium models have often retained the description of the economic productions

system in terms of mutually interrelated, simultaneous flows of commodities,

technically described in a Leontief input–output model.

Hence, the purpose of Chap. 1 is to present the input–output model and the

technique used for calculation with the help of a numerical example. However, it is

important to remember that input–output analysis is a question of balancing supply

(output) and demand in terms of technical input–output relationships, representing

interindustry dependence, rather than a description of Walrasian type of market

equilibrium.

The model presented in Chap. 2 is essentially a Leontief type of input–output

model, extended with foreign trade activities and resource constraints, with the

objective of finding the welfare optimum. The programming formulation of the

Leontief input–output model, established as the linear activity analysis model,

represents an advancement in the construction of applied general equilibrium

models, because it introduces a great deal of flexibility into the basic linear

input–output structure. To provide the link to economic theory, the concept of

welfare optimum (Pareto efficiency) and its logical relation to competitive equilib-

rium is used as a connecting thread between the concept of economic equilibrium

Introduction xiii

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and the mathematical programming formulation. The role of shadow prices and

their relation to market prices in a competitive market is described.

Technically, this problem involves the choice between domestic production and

imports, and between production for the domestic market or exports in different

sectors of the economy. Only by evaluation of economic efficiency of the industrial

choices, using the opportunity cost of the resources, can an economic choice be

made. This study is an attempt to set up a formal equilibrium model for the

computation of this choice, based on mathematical programming and input–output

analysis. This provides the framework that will be used to examine the need for

structural transformation of domestic resources, when the resources are assumed to

follow the principles of adjustment to efficiency in domestic production and trade.

Given this formulation, the mathematical programming model will follow the

traditional framework emphasised in pure trade theory. However, the shadow prices

cannot be interpreted as market-clearing prices of general equilibrium theory,

because endogenous prices and general equilibrium interaction to simulate com-

petitive market behaviour cannot be achieved using the linear programming speci-

fication. Thus, without representing a realistic price system in which endogenous

price and quantity variables are allowed to interact, the interplay of market forces

cannot be described properly.

The next chapter, Chap. 3, extends the linear model by the direct inclusion of the

pricing mechanism endogenously in the programming model. The model is a

linearised version of the Walras–Cassel general equilibrium model (linearised

factor supply and commodity demand functions) which also utilises the basic

Leontief input–output structure as a production relationship. Given the linearised

factor supply and commodity demand functions, both the prices and quantities are

determined endogenously. In technical terms, the shadow prices are incorporated in

the objective function; in other words, the quadratic programming model, a

straightforward extension of the linear programming model, has been developed.

The solution of the quadratic programming problem can be characterised as a

simulation of market behaviour under the assumption of competition, but still, in

a model where the central planner is assumed to be the only maximising actor.

In applied form, the quadratic programming model is used for evaluation of the

pattern of domestic production and trade of the Swedish economy. The evaluation

of the pattern of comparative advantages of the Swedish economy is carried out as

an analysis of the choice between import and domestic production in a temporary

equilibrium framework with exogenously given world market prices, exports, and

domestic production capacities.

In Chap. 4, the nonlinear, price endogenous (CGE) model is presented. Alterna-

tive to the standard linear (and quadratic) programming model, where the central

planner is the only maximising actor, the CGE model has been developed to capture

the endogenous role of prices and the workings of the market system. In the CGE

model, the essence of the general equilibrium problem is the reconciliation of

maximising decisions made separately and independently by various actors,

xiv Introduction

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specified in terms of optimisation or market simulation.8 The equations of a CGE

model tend to be neo-classical in spirit, but we must remember that most CGE

models conform only in a loose manner to the theoretical general equilibrium

paradigm in economics. The general overview of the features of CGE model is

given in this chapter. Since the possibility to specify substitution in production,

foreign trade and demand is very essential in the CGE modelling approach, the

technique that is in this chapter presented more closely.

In Chap. 5, a CGE model (the CGE mini model9) is presented. The model is

simple enough to be presented in a few pages and yet complicated enough to

demonstrate the application of the general CGE structure. In short, the focus of

this chapter is to provide examples of structural adjustment in an open economy.

The numerical applications of this chapter will be an examination of the sensitivity

of the model to systematic variation in key variables of the adjustment process.

Here we emphasise the effect of changes (government intervention) in the fixed rate

of real exchange and growth in the capital stock. Readers who have access to a

computer and the GAMS program can take an active part of the model developed.

Full information of this facility is given in the appendix to this chapter.

Chapter 6 discusses the fundamental structure of the transformation process of

the open economy. However, the model is focused on medium run. In the medium

time period the time is too short for all things to be reallocated, because of the

sluggishness of the market. More precisely, we approach the equilibrium but we

cannot reestablish it in full. To counteract the rigidity of the market, and establish

equilibrium, the entrepreneur will become important as an economic actor. The key

concept of the economic transformation process is the domestic profit rate, or as we

here will call it, rate of return, because it is related to investment. Economic

transformation will be specified as endogenous, and it will become an integral

part of a steady-state equilibrium mechanism.

Chapter 7, a continuation of Chap. 5, uses the ideas of endogenous obsolescence

in Chap. 6 adapted to the CGE mini model. In this chapter, the feature of endoge-

nous obsolescence is included in the equation representing depreciation expendi-

ture. In that sense, the endogenous transformation process is introduced in the CGE

mini model. In short, the focus of this chapter is to provide examples of structural

transformation in an open economy. Thus, the model specification here, as in Chap. 5,

is the total investment equation determined by total saving. The allocation to the

8More recently, CGE has been used to estimate the economic effects of measures to reduce

greenhouse gas emissions. See Stern (2006).9 The CGEmini model is included in the GAMSmodel library which is distributed with the GAMS

system. The CGE mini model is a minor version of an equilibrium model that originally comes

from Chenery, Lewis, de Melo, and Robinson in their work to designing an equilibrium develop-

ment model of Korea. The model is originally designed for study of three development strategies.

The first option was the strategy of export expansion, the second option was the strategy of import

substitution, and the third option was a strategy between the two extreme cases. This model

illustrates the basic use of CGE models. See further Chenery et al. (1986), pp. 311–347.

Introduction xv

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different industry sectors is influenced by the sector-specific profit rate and now

also in terms of endogenous obsolescence.

As a result of the experiments with our model developed in Chap. 3 some sectors

lost some or all of their production to import competition, but other sectors could

expand their export markets. This is known as horizontal specialisation. In this final

chapter, Chap. 8, we focus on vertical specialisation, which has variously been

called fragmentation, off-shoring, and slicing up the value-added chain. The verti-

cal specialisation affects tasks within the production chain regardless of sector.

Since we are discussing production chains, and here structural matters, we focus on

intermediate commodities. Based on input–output data for the two years, 2000 and

2005, we investigate the change of the intermediate import shares. The result is that

the share of intermediate imports has increased in some important sectors. The

conclusion is that the globalisation process has affected the production structure in

the Swedish economy.

References

Barysch K Grant C, Leonard M (2005) Embracing the dragon: can the EU and China be friends?

CESifo Forum 6(3)

De Grauwe P (2007) Economics of monetary union, 7th edn. Oxford University Press

Eurostat: Euro-indicators news release 26/2008. Eurostat Press Office (2008) Statistical office of

the European communities, Unit F2, Labour market statistics

Nickell S (1997) Unemployment and labor market rigidities: Europe versus North America. J Econ

Perspect Summer, 55–74.

Ricardo D (1871) The principles of political economy and taxation. Everyman’s Library, London

Salter WEG (1960) Productivity and technical change. Cambridge University Press, Cambridge

Stern N (2006) The economics of climate change – the stern review, Cambridge. See also

http://www.hm-treasury.gov.uk/sternreview_index.htm

xvi Introduction

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Chapter 1

The Input–Output Model: A Study

of the Interindustry Structure

By the input–output technique the structure of interdependence can be analysed.

Existing applied general equilibrium models have often retained the description of

the economic productions system in terms of mutually interrelated, simultaneous

flows of commodities, technically described in a Leontief input–output model. The

purpose of this chapter is to present the input–output model, and the technique used

for calculation with the help of a numerical example. However, it is important to

remember that input–output analysis is a question of the balancing of supply

(output) and demand in terms of technical input–output relationships, representing

interindustry dependence, rather than a description of a Walrasian type of market

equilibrium.

1.1 Background

Input–output is the study of an economy in terms of the relationship between all

inputs and outputs in the economy. The output of commodities in an economy is

used either in the production of commodities (including itself) or it goes into final

consumption. Thus, the economy can be described as an integrated system of flows

or transfers from each activity of production, consumption or distribution to each

other activity. Each sector absorbs the output from other sectors (intermediate

demand) and it produces commodities or services that in turn are used up by

other sectors, either for further processing or final consumption.1 All these flows

or transfers are set out in a rectangular table – an input–output matrix (transaction

matrix). The way in which the outputs of any industry spread through the rest of the

economy can be seen from the elements making up the rows. Similarly, the origins

of its inputs could be seen directly from the elements of the appropriate column.

Given that structure, the implication of a specific change in one part of the economy

1 For a detailed analysis, see Thijs ten Raa (2005).

R. Noren, Equilibrium Models in an Applied Framework,Lecture Notes in Economics and Mathematical Systems 667,

DOI 10.1007/978-3-642-34994-2_1, # Springer-Verlag Berlin Heidelberg 2013

1

could be traced through to all elements in the system. Wassily Leontief

(1906–1999) put forward the display of this information in the form of a matrix.

Inputs typically are enumerated in the column of an industry. And its outputs are

enumerated in its corresponding row. This format, therefore, shows how dependent

each industry is on all others in the economy both as customer of their outputs and

as supplier of their inputs. Each column of the input–output matrix reports the

monetary value of an industry’s inputs and each row represents the value of an

industry’s outputs.2 It was this work, and later refinements of it, that earned

Leontief the prize in economic sciences 1973 in memory of Alfred Nobel. Leon

Walras’s work on general equilibrium theory is both a forerunner and generaliza-

tion of Leontief’s seminal concept. Leontief’s contribution was that he was able to

simplify Walras’s piece so that it could be implemented empirically.

Leontief knew, of course, of previous efforts to understand and depict the

interdependence of economic activities. Such efforts go back as far as 1758, when

the Tableau Economique by Francois Quesnay was published. Francois Quesnay

(1694–1774), court physician to Madame de Pompadour and later to Louise XV,

developed an earlier version of the commodity flow, inspired by his knowledge of

the circulation of blood, called Tableau Economique,which was published in 1758.3

Quesnay becomes an intellectual leader of the Physiocrats or les Economistes.The Physiocrats were a group of economists who believed that the wealth of nations

was derived from the value of land agriculture. The most significant contribution of

the physiocrats was their emphasis on productive work as the source of national

wealth. This is in contrast to mercantilism, which focused on the ruler’s wealth,

accumulation of gold or the balance of trade. The foundation of the Physiocrats’

economic theories was first described in Francois Ques-nay’s Tableau Economique,a circular flow diagram of the economy that show who produced what and who spent

what, in an attempt to understand and explain the causes to the nation’s wealth.

The model Quesnay created consisted of three economic classes (sectors of the

society) and the flow of payments between them. The “Proprietary” class consisted

of only landowners. The “Productive” class consisted of all agricultural laborers.

The “Sterile” class is made up of artisans and merchants. A chief weakness from the

viewpoint of modern economics is that they only consider the agricultural sector

producing any surplus value, the rest only reproducing what are consumed.

2 The foundation for a Swedish applied input–output model, was undertaken by Hoglund and

Werin (1964).3 Quesnay privately printed on a press in the palace of Versailles three versions (editions) of a short

manuscript. For the definitive text of all three versions, see the work of Kuczynski and Meek

(1972). See also Vaggi (1987).

2 1 The Input–Output Model: A Study of the Interindustry Structure

1.2 The Basic Input–Output Structure

Returning to Leontief’s contribution the structure of an economy (Leontief 1951)

including intermediate commodity can be represented. Assume an economy

represented by three sectors, sector 1, 2 and 3. ΣID denote the sum of intermediate

demand (inputs in the production system), and Y denote final demand, i.e., the non-

intermediate demand. e.g., private consumption, investment demand, government

demand and exports. The Total Demand (TD) is the sum of ΣID and Y. Examples of

final demand are private consumption, investment demand, government demand,

and exports. The input–output table (compromising all zij variables in a transaction

matrix) is represented in Table 1.1 below.

At equilibrium, total output (Z) is equal to total demand (TD) in respective

sector, i.e., the sum of column is the same as the sum of the corresponding row

respective sector. However, the input–output system is not a form of the general

equilibrium system outlined in general equilibrium theory; it is only a linear

empirical approximation of that system. For national accounting purposes, the

model is expressed in value terms, i.e., in monetary units. Starting with the

intermediate commodity xij we can write the following relation: zij ¼ aij Zij. We

define the intermediate requirements, or the input coefficients aij, as the number of

used units of commodity i necessary to produce one unit of output from sector j. Theinput coefficients aij are assumed to be fixed. The order of the subscripts in aij iseasy to remember. The first subscript refers to the input, and the second to the

output. Positive valued coefficients aij indicate that the commodity involved is

produced, negative valued coefficients that the commodity is used up by the

production process, and zero valued coefficients indicate that the commodity is

not involved in the production process. The input coefficients correspond to

Walras’s technological coefficients, the only difference being that in the original

Walrasian system only primary inputs were considered.

To simplify the presentation of the model it is assumed that each production

process leads to the production of only one commodity (no joint production), and

that each commodity can be produced by one fixed-coefficients process only. Thus,

the model is defined in such a way that the production process (industry) is

Table 1.1 The input–output transactions system

To sector (output), i.e., revenues

From sector (input), i.e., costs 1 2 3 ΣID Y Total demand

1 z11 z12 z13 ID1 Y1 TD1

2 z21 z22 z23 ID2 Y2 TD2

3 z31 z32 z33 ID3 Y3 TD3

Labour l1 l2 l3 L

Capital 1 k11 0 0 K11

Capital 2 0 k22 0 K22

Capital 3 0 0 k33 K33

Import M1 M2 M3 M

Total output Z1 Z2 Z3

1.2 The Basic Input–Output Structure 3

synonymouswith the commodity. In other words, we have one to one correspondence,

implying the number of sectors is equal to the number of commodities. The assump-

tion that the input coefficients aij are fixed leads to L-shaped isoquants, and signify thatthere is no substitution between inputs in the production of a given commodity. The

input coefficients are non-negative and constant, implying the relative factor prices is

unchanged. Consequently, with an input–output model the choice-of-techniques

question does not arise. There is only one technique of production available in each

industry for producing each of the commodities in the system.

The input–output system would behave as if it knew only one set of input–output

ratios for each commodity. It does not mean that changes in technological informa-

tion will not result in changes in observed input ratios. It does mean, however, that

with given technology there is one preferred set of input ratios which will continue

to be preferred no matter what the desired level of final demand happens to be.

Further, it does not mean that changes in relative prices will not induce change in

proportions. In the input–output system the relative prices can not change. Relative

prices of commodities will depend only on their direct and indirect labour content.

At each given point in time, there exists a given technology which makes it

possible to use different production methods. Each such production method

represents a process, which converts certain commodities into others at given ratios

of inputs to outputs, and is capable of being operated at any nonnegative activity

level.4 This is described above. In this context, two fundamental assumptions are

frequently adopted. The first assumption is called additivity, and the second is calledproportionality. The two assumptions are concerned with ways in which additional

processes can be obtained from those in the basis. The additivity assumption implies

that the processes can be utilised jointly for the production of several commodities,

one for each process, and that the resulting commodity bundle is equal to the sum of

the net produced amounts in the utilisation of the separate processes. This means that

the production methods used to produce a given commodity are independent of

whether other commodities are produced at the same time or not. Hence, the

additivity assumption means that there is free entry, i.e. no institutional or other

barrier to entry, and rules out external economics and diseconomies.

The proportionality (divisibility) assumption implies that each process can be realised

on a continuous proportional expansion. Thus, the input of each separate commodity in

the production of a given commodity is proportional to the produced amount Zj.Generally, the proportionality assumption stipulates what is known as constant returns

to scale in production. The set of all nonnegative multiples Zj states the produced (gross)amount, and at the same time the level at which the process is utilised.5

It can be shown (Hawkins and Simon condition 1949) that the system is self-

contained, which means that commodities produced by the input–output system

4 Following Koopmans (1951) we may use the term basic activity for any activity aij (differentfrom zero). There is a one-to-one correspondence between basic activities and sectors in the

stipulated economy.5 According to Chenery and Clark (1959) the proportionality assumption is less valid the greater

the degree of aggregation, and the additivity assumption is more valid the larger the aggregates.


should require less than one unit of itself, directly and indirectly, as inputs for

producing one unit of output. Or to put it otherwise, if one unit contains, directly

and indirectly, more than a unit of the given commodity, self-contained production

is not viable. The interpretation is always that the subgroups of commodities should

be “self-sustaining” directly and indirectly.

From the conditions given above, let us extend the defined processes of producedcommodities to include primary commodities and capital stocks (capacities) by

sector. Similar input coefficients as for produced commodities are defined for primary

commodities, denoted bhj and capacities, denoted ckj. Thus, aij, bhj and ckj refer to theinput of a produced commodity i, a primary commodity h, and a capital commodity

k respectively in the production of a unit of the commodity in sector j.Input-coefficients correspond to costs in the production process. The following

expression (column vector) is obtained for the utilisation of an arbitrary process:

f�a1j; :: ; 1� ajj; :: ;�anj; b1j; :: ; bmj; c1j; :: ; cnj g0 Zj (1.1)

By this specification, any possible state of production can be represented by a

nonnegative linear combination of separate processeswith nonnegativemultiplesZj ofaij, bhj and ckjj. The term activity will be used as a synonym for production activity.

Technically, any activitywithin the production system can be expressed by the vectors

(1.1) which state the n processes together with the values of Zj for the actually

produced amount (output). Thus, an activity is composed of a non-negative linear

combination of the n separate processes. The input–output model may be described

Zi ¼X

j; Yi þ zi2 þ ::þ zin (1.2)

Using the input–output coefficients (aij) this may be described

Zi ¼X

j; aijZj þ Yi (1.3)

The theory is that the technical coefficients are constant and invariant with

respect to changes in the total output and the final demand. The matrix is the sum

of the identity matrix I (with I:s in its principal diagonal and with 0:s everywhere

else) and the matrix – A. Thus it can be written as

½I� A�Z ¼ Y (1.4)

The expression [I � A]�1 below denote the inverted matrix, i.e., the matrix for

direct and indirect demand in the production system (compare with the Keynesian

multiplier). We can derive the total production needed in the economy to satisfy the

final demand (Table 1.2).

Z ¼ ½I� A��1 Y (1.5)

1.2 The Basic Input–Output Structure 5

The demand for factors of production, here, labour (L) and capital (C)

½B�Z ¼ L and ½C�Z ¼ C (1.6)

Hence, we can answer the following questions: If final demand is increased with

100, howmuchwill total output increase in the economy to satisfy that increase in final

demand? In addition, by howmuch will the demand for factors of production increase

in different sectors of the economy to satisfy that increase in total output? By the

input–output technique we can calculate the individual output necessary for the final

demand to be satisfied. Thus, if the final demand for one commodity increaseswith one

unit, the total output will be more than that unit because total output of each commod-

ity must be enough to satisfy both the final demand and the intermediate demand.

1.3 A Numerical Example

A two sector numerical input–output model – A calculation example.

The transactions matrix:

To (output)!1 2 Final demand Total demandFrom (input) #

1 20 45 35 100

2 40 15 95 150

Labour 40 90 0 130

Total supply 100 150 130

From the transaction matrix above we get the technical coefficients, i.e.,

coefficients over the direct use of commodities per produced unit.

Matrix A:

0:2 0:30:4 0:1

and the direct use of labour per produced unit.

Matrix B 0:4 0:6

Table 1.2 Input–output in

matrix notationMatrix A 1� a11 � a12 � a13 � Z1 ¼ Y1

� a21 1� a22 � a23 Z2 Y2� a31 � a32 1� a33 Z3 Y3

Matrix B b1 b2 b3 � Z1 ¼ LZ2Z3

Matrix C c11 0 0 � Z1 ¼ c110 c22 0 Z2 c220 0 c33 Z3 c33


The identity matrix (I), i.e., a square matrix with 1:s in its principal diagonal an

0:s anywhere else, minus matrix A, gives us the Leontief matrix [I � A].

0:8 �0:3�0:4 0:9

Assume we have an increase in final demand by: ΔY1 ¼ 60, ΔY2 ¼ 120. How

much must we increase production in total, i.e., direct and indirect from different

sectors in the economy (Z)? The solution is to be found with the help of the inverted

Leontief matrix, thus ΔZ ¼ [I � A]�1 � ΔY.From the Leontief matrix we calculate we determinant (D):

D ¼ 0:8ð0:9Þ � �0:3ð�0:4Þ ¼ 0:6

Recalculate [I � A] as the cofactor matrix [I � A]* 6

0:9 0:40:3 0:8

and transpose the cofactor matrix to get the adjoint of [I � A].

0:9 0:30:4 0:8

Divide the elements of the adjoint of [I � A] by the calculated determinant

(0.6). Hence we get [I � A]�1

1:50 0:500:67 1:33

By multiplying the increase in final demand (Y) with [I � A]�1.

Thus, following the rules of matrix multiplication we get:

1:50ð60Þ þ 0:50ð120Þ ¼ 150

0:67ð60Þ þ 1:33ð120Þ ¼ 200

Total increase in production (Z) in sector 1 is 150, and in sector 2 the increase is

200.

6Matrix inversion is demonstrated in Chiang and Wainwright (2005) on pages 100–102. With

more than two sectors these calculations will be complicated. A computer program for matrix

inversion is recommended.

1.3 A Numerical Example 7

1.4 Concluding Remarks

Most commodities can be supplied not only by domestic production, but also by

importation.7 In input–output tables standard approach is to specify imports as a

primary input (as labour) that is not produced in the economy, i.e., imports are

specified as complementary to domestic production. However, most of the imports

are commodities which can be produced within the economy but which are, as an

alternative to domestic production, also imported, i.e., imports are classified as

competitive. In other words, the imported commodity is viewed as a substitute for

the domestically produced commodity. The input–output model above does not

have any endogenous mechanism of choice among alternative feasible alternatives.

However, in an activity (programming) model, we can obtain the optimum combi-

nation of physical input being defined as that combination which yields the maxi-

mum value of the output obtainable from the inputs. Activity models introduce

flexibility by allowing inequality constraints and introducing the explicit

maximisation of a given preference (objective function) into the model. This

extends considerably the restricted domain of choice in the input–output model.

The programming approach introduces a great deal of flexibility into the basic

linear input–output structure. That technique is presented in the next chapter.

References

Chenery H, Clark PG (1959) Interindustry economics. Wiley, New York

Chiang AC, Wainwright K (2005) Fundamental methods of mathematical economics, 4th edn.

McGraw-Hill/Irwin, Boston

Hawkins D, Simon HA (1949) Note: some conditions of macroeconomic stability. Econometrica

17:245–248, 3–7, July–Oct

Hoglund B, Werin L (1964) The production system of the Swedish economy: an input–output

study, vol IV, Stockholm economic studies, new series. Almqvist & Wiksell, Stockholm

Koopmans TC (1951) Analysis of production as an efficient combination of activities.

In: Koopmans TC (ed) Activity analysis of production and allocation. Wiley, New York

Leontief W (1951) The structure of American economy 1919–1039, Second edition enlargedth

edn. IASP, New York

Quesnay F (1758) Quesnay’s Tableau Economique, edited with new material, translations and

notes by Kuczynski M, Meek RL (1972), Macmillan, London

ten Raa T (2005) The economics of input–output analysis. Cambridge University Press,

Cambridge

Vaggi G (1987) The economics of Francois Quesnay. Duke University Press, Durham

7 Exports are included in the final demand.


Chapter 2

The Outlook of the Sovereign Planner:

The Linear Activity Model

The purpose of this chapter is to formulate a linear numerical general equilibrium

model. The model is essentially a Leontief type of input–output model, extended with

resource constraints. In this chapter the equilibrium model is developed and analysed

under conditions of competitive market behaviour. To provide the reader with an

understanding of the nature of this model and its link to economic theory, the concept

of welfare optimum (Pareto efficiency) and its logical relation to competitive equi-

librium is used as a connecting thread between the concept of economic equilibrium

and the mathematical programming formulation. The following sections will high-

light the major features of the model. At the same time, the assumptions necessary to

make the model operational are made explicit.

2.1 Commodities and Activities

In this study we shall be considering an economy where there exists a finite number

of commodities (commodity groups)1 subject to production, consumption, or both.

The commodity concept also includes services. A commodity is characterised by

the property that two equal quantities of it are completely equivalent for each

consumer and each producer. The commodities are here divided into two groups,

according to whether they are produced within the production system or not.

Commodities in the former group are called produced commodities, in the latter

group, primary commodities.2 Thus, total supply within the economic system

specified in this study is a result of the domestic production system.

1Generally, a commodity is defined by its physical characteristics, its location, and the date of its

delivery. Commodities differing in any of these characteristics will be regarded as different.

However, in this model a commodity is synonymous with the industry supplying the commodity

(sector classification principle).2 Thus, there is only use of primary commodities, not production of them.



9

2.2 Producers

The n producers (industries) execute the production programs represented by the

n nonnegative multiples Zj of aij. The extent to which the activity is utilised must be

feasible, i.e. to say the produced amount Zj must be an element of the production

set Yj.For any producer j there exists a given quantity of capital commodities, previously

produced commodities, and in the short run specific for each produced commodity,

and hence, each producer. In other words, capacities are assumed immobile. For the

producer each activity implies a given transformation of primary commodities into

produced commodities, and to make this transformation possible, a given quantity of

capacities available. By this specification, the capacities are considered as primary

commodities. Hence, the primary commodities can in the short run be partioned in

two kinds of commodities. On one hand, capacities, which in the current point of time

are fixed to the existent establishments and on the other hand resources (labour),

which the different producers (industries) are competing for in the market.

Closely related to the assumptions given above is the assumption of irreversibility

of production, i.e. the production process cannot reversed, thus, excluding negative

activity levels from the solution. Further, free disposal is assumed, i.e. it is possible

for all producers together to dispose of all commodities. Finally the assumption of

free disposal together with the assumption of irreversibility implies the impossibility

of free production, i.e., it requires inputs to produce outputs.3

2.3 Consumers

The s consumers are the only owners and final users of commodities. Each consumer,

denoted i owns the supplied quantity rih of the primary commodity, denoted h, and ashare, denoted θij, of the industry j. By this specification a special economy is then

considered, namely the private ownership economy where consumers own the

resources and control the producers. The rents may be assumed to be distributed

following a certain rule, such as a fixed proportion. It should be noted that no matter

how the rents are distributed, all the rents must be paid to consumers.

The set of consumption which enables consumer i to survive is his attainable setXi, defined for all combinations of demand of desired commodities xij, and suppliesof his initial endowment of primary commodities (labour service) rih, which he can

sell to obtain income. Thus, each consumer is assumed to have an endowment of

leisure, a portion which can be sold as labour service, and the leisure remaining is a

component (nonnegative) in his attainable set.

The consumer’s preferences among different vectors xij and rih are represented

by a utility function Si(xij,� rih) defined for all nonnegative quantities of desired

3 See further Debreu G. (1959), p. 42.

10 2 The Outlook of the Sovereign Planner: The Linear Activity Model

commodities xij and quantities of primary commodities rih, represented as a non-

positive quantity.4 Under the conditions of a private ownership economy, where

primary commodities and capital commodities are owned by individual consumers,

the i:th consumer’s income Ri will be the sum of the value of the supplied quantities

of primary commodities and the shares θij, of the rents (returns of capital as a factorof production) of the producers.

2.4 Feasible Activities

For each process actually carried out within the economic system outlined above,

the variable Zjwill take specific value. This seems agreeable to common sense. Any

feasible state of supply, i.e. the ability of the economy to achieve an allocation

within the limits of its resources, may be stated more formally. Thus, the commod-

ity balance constraint (Eq. 2.1 below) states that each feasible allocation must

contain at least one production activity.

Final supply is made up of the total supply of a commodity minus the amount of

the commodity used within the production system (intermediate demand), where aijdenote the intermediate requirements of commodity i per unit of output of sectorj. On the other hand, use outside of the production system is called final demand,

here denoted Dj, represents domestic final demand, i.e. the sum of private consump-

tion, investment and government expenditures.

Zj �Pj; aij Zj �Pi

Dij (2.1)

Zj � 0; Dj � 0

Equation 2.2, the primary commodity constraint, further restricts the feasible set.

The primary commodity constraint represents here labour, supplied by the

households. This specification distinguishes different skill categories of labour,

where bhj denote the input coefficient of each primary commodity h. in each sector

j. Despite different individuals will be of different productivities, the labour input ineach sector is assumed to be an aggregation of labour of different skill categories.

Hence, there is only one aggregate, and homogenous, primary commodity supplied by

the households. This implies that labour is assumed perfectly mobile across sectors.

Σj; bhj Zj � Σi; rih (2.2)

rih � 0

4 In mathematical language, the utility function S, is continuous and increasing, twice continuouslydifferentiable, strictly quasi-concave and its first derivatives are not all simultaneously equal to

zero.

2.4 Feasible Activities 11

Empirically, labour is measured in unit wage costs, which refer to all wage

payments including collective payroll charges. This implies that factor payments

data is used as observations on physical quantities of factors for use in the

determination of parameters for the model. The total supply of labour resourcesis given exogenously, calculated on the basis of total labour force (minus employed

in the government sector) and we measure it in terms of wages (and salaries). Thus,

the labour balance requirement is stated in value terms and not in physical terms. In

all experiments, the labour resource constraint will be binding, i.e. our model

solutions requiring full employment of labour. However, it is necessary to note

that computed market equilibrium (model solution) may, in principle, permit

unemployment of labour.

Equation 2.3 represents the capital stock by sector. At each point of time it is

assumed that the supply of these commodities is given and specific for each

production unit. With these characteristics we must have a restriction for each

capital commodity i and each sector j.5 This is also the reason for classifying these

commodities as primary commodities in the short run.

cij Zj � Kij (2.3)

Kij � 0

The real capital stock is a composite commodity and the commodity composi-

tion of capital differs across sectors. Consequently, the real capital stock is impos-

sible to measure with any real precision. In this model the capital stock in each

sector is aggregated into a single commodity and no difference is made between the

two definitions, the real and the utilised. Recapitulating, the total supply of

commodities in the economic system is partly a result of the activity within the

domestic production system. Since each process implies use of primary

commodities, and production and use of produced commodities, the possibility to

carry on these processes are therefore dependent on the given quantities of primary

commodities, the produced amount of produced commodities.

2.5 The Programming Formulation

The point of departure for the programming model presented below is an economic

system where an excess demand for any commodity implies an increase of the

corresponding commodity price without any upper limit, and an excess supply of

any commodity that the corresponding commodity prices decreases, given the

restriction that the price will not take any negative value. Thus, while we would

5 This forms a matrix with capacity input coefficients in its principal diagonal and zero elements

everywhere else. Hence, i ¼ j for all cij.


never accept a situation with positive excess demand in some market as equilib-

rium, an excess supply in a market where the price is zero is quite consistent with

our notion of equilibrium. An economic system with these characteristics is com-

patible with a market economy. A state of equilibrium in this market economy is a

situation where no individual. Given the price system and the actions of the other

individuals, has any incentive to choose a different allocation of commodities.

Stated more formal, the equilibrium conditions state that there will be no excess

demand for any commodity and market pricing of each commodity. Thus, the

equilibrium conditions state that each commodity has only one price throughout

the economy, and specifies that when the market equilibrium price for the com-

modity is positive, there is no excess supply or demand. Since the consumers in

spite of the positive commodity prices demand all supplied quantities of Zj, andsupplies the sum of rih up to the quantity demanded by the producers, commodities

with a positive price are regarded as desired commodities.6

The objective of our allocation problem is to find the set of supply activities that

result in a bundle of desired commodities, in the sense that given the specified

resources (resource constraints) it is impossible to increase the net amount of any

desired commodity without decreasing the net amount of some other desired

commodity. Such a bundle is called an efficient final commodity point, and the

collection of all such efficient points traces the efficient supply frontier where each

point is a possible efficient (Pareto efficient) state of allocation. In this framework

the well known concept of Pareto optimality, i.e. a state in which no one’s

satisfaction can be raised without lowering someone else’s, is translated to effi-

ciency, and a term like ‘allocation efficiency’ is a more accurately descriptive of the

concept.7 A state of Pareto efficiency thus defined expresses a concept of allocative

efficiency in converting resources into satisfactions. By the use of the concept of

allocation efficiency, we can formulate the equilibrium model specified above

within a mathematical programming format. Given the objective function and the

constraint set the problem takes the following form, i.e. maximise:

Wðxi; rhÞ � Σi; Siðxij;�rihÞ (2.4)

Subject to

Zj � Σj; aij Zj � Σi Dij (2.5)



Zj � 0; Dij � 0; rih � 0; Kij � 0

6A commodity is desirable if any increase in its consumption, ceteris paribus, increases utility.7 Koopmans T.C. (1957), p. 84.

2.5 The Programming Formulation 13

This is a typical programming problem and we use the Kuhn-Tucker theorem8 to

derive the optimality conditions. If the assumptions regarding the objective func-

tion and the constraint set are satisfied, then a necessary and sufficient condition that

xoj ; roh

� �is the optimum solution to (xj, rh), is that there exists poj � 0; wo

h � 0;

voij � 0 such that the Lagrangean:

Lfxij; rih; Zj; pj; wh; vijg ¼ Σi; Si ðxij;�rilÞþþ pj ðZj � Σj; aijZj � Σi; DijÞ þ whðΣi; rih � Σj; bhj ZjÞþ Σi; Σj; vijðKij � cij ZjÞ

forms a saddle point at xoij; roih; Zoj ; poj ; wo

h; voij

n o.

We identify the Lagrangean multipliers poj ; woh , and voij associated with the

commodity constraints, as efficiency prices and rents. These efficiency prices or

shadow prices of the mathematical program incorporate the effect of the constraints

upon the activity level in the model, so that resources are allocated most efficiently.

Supply choices open to this model are to supply each commodity by domestic

production.

For any given objective function the i:th shadow price measures the opportunity

cost of the last unit of the i:th resource or commodity employed in a binding

constraint. The fact that the shadow prices are computed and measured in terms

of the objective function (all efficiency concepts in our model is measured in terms

of the objective function) implies that the objective function is crucial in determin-

ing and interpreting the shadow price system.9 If the constraint is not binding, i.e.

carries the < or > sign at the optimum, the shadow price will be zero implying that

the resource or commodity is free. In this context, it is worth mentioning that any

resource omitted from the specification of the model is considered as free and

having an opportunity cost of zero. Given this behaviour, it is natural to interpret the

Lagrangean multipliers as equilibrium prices. Thus

@Lo

@xij¼ S0ij � poj ¼ 0 (2.8)

@Lo

@rih¼ �S0ih þ wo

h ¼ 0 (2.9)

8Kuhn H. W. and A. W. Tucker (1950). The Kuhn-Tucker theorem for con-strained optimisation

tells us that the necessary conditions for the solution of the primal are equivalent to finding the

solution of the dual. It does not in itself provide us with a practical solution method for the

problem.9 The shadow prices of the model cannot be considered as “ideal”, because this interpretation

would be valid only if the specification of the objective function quantitatively embodied all goals

of the economy.


@Lo

@Zj¼ poj � Σj; p

oj aij � Σj; w

ohbhj � Σi; Σj; v

oijcij � 0

�00 �<0 ) Zoj ¼ 0

(2.10)

@Lo

@pj¼ Zo

j � Σj; aijZoj � Σi; Dij � 0

�00 � > 0 ) poj ¼ 0

(2.11)

@Lo

@wh¼ Σi; r

oih � Σj; bhj Z

oj � 0

�00 � > 0 ) woh ¼ 0

(2.12)

@Lo

@vij¼ Kij � cij Z

oj � 0

�00 � > 0 ) vokj ¼ 0

(2.13)

Thus, the conditions (2.8), (2.9), (2.10), (2.11), (2.12), and (2.13) spell out the

characteristics of the market pricing and rent system at the optimum that is

consistent with an efficient supply and allocation program.

By the assumption that the utility function is differentiable, the equalities above,

equality (2.8) and (2.9), establish certain classical relations between prices and

marginal rates of substitution relating to consumer equilibrium xoij and roih . These

equalities imply that the marginal rate of substitution of any pair of commodities is

equal to the ratio between any corresponding pair of prices.

Condition (2.10) states that, at the optimum, total profits must be zero in all

production activities actually used and no activity may show a positive profit, i.e.

production costs will exactly equal the shadow pricespoj for all commodities that are

actually produced. The produced commodity is exhausted (Euler’s theorem is met)

by paying to each of the contributing factor its full marginal product. If the strict

inequality holds, then the production costs exceed the shadow price poj and the

commodity will not be produced.

Condition (2.11) states that if the shadow prices poj are zero at the optimum, then

there exists excess supply of final commodities, and if the shadow prices are

positive, there exists no excess supply of any final commodity.

Condition (2.12) states that if the optimum shadow factor pricewoh is positive, the

primary commodity rhmust be used to the maximum availability, and if the shadow

price is zero, then a part of the commodity is left unused.

Condition (2.13) states that rent voij, the shadow price of each sector’s capacity

constraint, on processing plants may at the optimum exceed zero only if the

capacities in each case are fully utilized. Since we are concerned with a short run

model where capital is sectorally fixed, the rent concept can be viewed only within


the context of scarcity, which implies that each sector has a sector-specific scarce

factor with its own shadow price. Therefore, as noted, rents may be greater than

zero only if the capacity is used to the limit. The rents represent the marginal return

(measured in terms of the objective function) of capital employed in a particular

sector and is therefore the marginal product (rate of return) of capital in this sector.

The rents have significance for decision making because they will provide an

estimate to the profitability of investments directed toward capacity expansion.

The optimality conditions, conditions (2.10), (2.11), (2.12), and (2.13), are thus

consistent with the requirements of a price and allocation equilibrium, and the

allocation which maximizes the objective function subject to the constraints, is a

welfare optimum. In the following section it will be shown that the optimality

conditions not only are consistent with the requirements of a price and allocation

equilibrium, but also are consistent with the conditions for a competitive equilibrium.

In order to establish conditions compatible with the characteristics of a competi-

tive equilibrium, equilibrium must prevail, not only on the market, but also for each

producer and each consumer. For each producer in the sense that they cannot

increase their profits by a change in the structure of production, and for each

consumer in the sense that they cannot increase their utility by choosing a new

combination of commodities specified in the utility function. Thus, a market

equilibrium satisfying the system constraints consistent with the assumptions of

competitive equilibrium must be characterised by the existence of a set of prices10

such that profit maximising producers and utility maximising consumers, subject to

their constraints, will generate production and consumption decisions such that the

choices together constitute a balanced allocation of commodities, i.e. excess

demands are non-positive.

The producer equilibrium stipulates that each producer (industry) is assumed to

maximise its profits Πh at given prices poj ; woh subject to the technological and

institutional constraints. The producer’s profit is the difference between the total

revenue from the sale of its commodity i and the expenditure upon all inputs.

Thus, the programming solution guarantees zero profits, equality of supply and

demand for every commodity with non-zero prices, and equality of price and

marginal costs for every producer in every commodity he actually produces.

Consequently, it is clear that a decentralised decision-making process would lead

to the same aggregate production pattern identical to the one which is provided by

the solution of the programming, provided that each producer faces the same set of

prices and strives to maximise profits.

Y

h

¼ poj Zj � Σj; poj aijZj � Σh; Σj; w

ohbhjZj (2.14)

10 These prices carry to each producer and each consumer a summary of information about the

supply possibilities, resource availabilities and preferences of all other decision makers.


Subject to:


Zj � 0; Kij � 0

Stated mathematically, each producer chooses Zj among the points of Yj so as tomaximize:

Max LfZj; vijg ¼ poj Zj � Σj; poj aijZhj � Σh; Σj; w

ohbhj Zjþ

þ Σi; Σj; vij ðKij � cij ZjÞ ð2:16Þ

A necessary and sufficient condition that Zoj ; voij

n ois a nonnegative saddle

point, is:

@Lo

@Zj¼ poj � Σj; p

oj aij � Σh; w

ohbhj � Σi; Σj; vij cij � 0

�00 � < 0 ) Zj ¼ 0

(2.17)

@Lo

@vij¼ Kij � cij Zj � 0

�00 � > 0 ) vij ¼ 0

(2.18)

Condition (2.17) states that if production takes place at a positive level at the

optimum, then the shadow price of the commodity must be equal to the cost of

producing the commodity, where costs have two components, the explicit market

costs of inputs and economic rents, which accrue to the use of the fixed capacities.

Given our assumption of constant returns to scale, the unit cost equals the selling

price, meaning that total profits must be zero on all production activities used and

no activity may show a positive profit. Condition (2.18) state, that the rents are

positive only when the capacity of the available capital stock is exhausted. These

conditions are exactly the same as condition (2.10) and (2.13). This implies that the

equilibrium situation outlined in this model forms for each of the individual

producers a competitive profit maximizing equilibrium. Thus, the programming

solution guarantees zero profits, equality of supply and demand for every commod-

ity with non-zero prices, and equality of price and marginal costs for every producer

in every commodity he actually produces. Consequently, it is clear that a

decentralized decision-making process would lead to the same aggregate produc-

tion pattern identical to the one which is provided by the solution of the program-

ming model, provided that each producer faces the same set of prices and strives to

maximize profits.


In a parallel way, consumer equilibrium is equivalent to the problem that each

consumer maximises his utility Si(xij,� rih) subject to his income constraint. Given

this specification, the consumer derives utility from the consumed quantities of the

desired commodities and the quantities of the primary factors he retains. When the

consumer has an initial endowment of primary commodities, rather than a fixed

income, he may be willing to supply his endowment in the competitive market, and

then choose a bundle of desired commodities to maximise his preferences in the

budget set, defined by the income he receives from his sale of labour plus his profit

earnings. Since a producer optimum is attained, the poj ; woh respective v

oij are known

constants, and consequently the individual’s income is fixed at Ri, where Ri is

the maximum income attainable to him evaluated at the equilibrium point. Thus, the

i:th consumer’s income Ri will be the sum of the values woh rih of the supplied

quantities of rih and the shares θij of the rents voij of the producers.11 Mathematically:

Σj; poj xij � Σh; w

ohrih þ Σi; Σj; θijv

oij � Ri (2.19)

Given that each consumer maximizes his utility Si(xij,� rih) subject to his income

Ri, we form the Lagrangean:

Lfxij;�ri; λig ¼ λi Σh; wohrih þ Σi; Σj; θijv

oij � Σj; p

oj xij

� �(2.20)

xij � 0; ri � 0; λi>0

A necessary and sufficient condition that xoik; roil; λi

� �is a non-negative saddle

point, is:

@Lo

@xi¼ S0i � λip

oi ¼ 0 (2.21)

@Lo

@ri¼ �S0i þ λiw

ol ¼ 0 (2.22)

@Lo

@λi¼ Σh; w

ohrih þ Σi; Σj; θijv

oij � Σj; p

oj xij ¼ 0 (2.23)

11 Following Jaffe (1980),: “When Walras defined his entrepreneur as a fourth per-son, entirely

distinct from the landowner, the worker and the capitalist, whose role it is to lease land from the

landowner, hire personal faculties from the labourer, and borrow capital from the capitalist, in

order to combine the three productive services in agriculture, industry and trade.” Thus, then he

(Walras) said in a state of equilibrium, les entrepreneurs ne font ni benefices ni pertes’(entrepreneurs make neither profit nor loss), he did not mean that there are no returns to capital

in state of equilibrium, but only that there is nothing left over for the entrepreneur, qua entre-preneur, when selling price equal all cost of production including the cost of capital-services for

payment is made to capitalists. “See further Jaffe W. and Morishima M. (1980).


In the equations above, S0i denotes the partial derivatives of Si with respect to xijand rih. The shadow price λi is the marginal utility of money, or the marginal utility

of income. By the assumption that the utility function is differentiable, the

equalities above establish certain classical relations between prices and marginal

rates of substitution relating to consumer equilibrium xoij and roih . These equalities

imply that the marginal rate of substitution of any pair of commodities is equal to

the ratio between any corresponding pair of prices. The condition (condition 2.23),

which specifies that each individual spends all of his income to purchase xj seems to

be trivial. However, the consumer efficiency condition does not stipulate that Ri

must be equal to the sum of pjxij, i.e. the expenditures of each household exhaust its

income, but from a general competitive equilibrium point of view income and

expenditures must balance.12

Thus, market equilibrium would be a more precise concept here. If such market

equilibrium is consistent with profit maximisation and utility maximisation on the

part of each producer and each consumer, then market equilibrium and competitive

equilibrium are consistent. Clearly, a competitive equilibrium is a special case of a

market equilibrium and the programming problem whose solution if it exists is a

competitive equilibrium for the economy stipulated by this model.


In the equilibrium model presented and discussed so far, competitive behaviour has

been specified for all participants, and competitive equilibrium has been taken as

the norm. Capital commodities are assumed to be given and sector-specific. By

relaxing this restriction the model could be made applicable in a dynamic context.

The relationship between optimum theory and competitive equilibrium has been

made explicit in this model. The chapter follows a classical approach, first the

search for the optimum, and then competitive equilibrium.

However, we treat the aggregate demand and factor supply functions as if they

could be generated by a single representative individual. In other words, the central

planner is assumed to be the only maximising actor. Theoretically, that conflicts

with the market equilibrium price system, where the demand and supply decisions

are made separately and independently by various economic actors. Moreover, the

demand for commodities and supply of factors are assumed to remain constant no

matter what happens to prices. In other words, the shadow prices result as a by-

product of the solution as equilibrium prices. Thus, these prices cannot be

interpreted as market-clearing prices of general equilibrium theory because

12Assuming that each consumer is on his budget constraint, the system as a whole must satisfy

Walras’s Law, i.e. the value of market demands must equal the value of market endowments at all

prices.

2.6 Concluding Remarks 19

endogenous prices and general equilibrium interaction to simulate competitive

market behaviour cannot be achieved using this specification.

A technique which removes any of the shortcomings mentioned above will

greatly improve the applicability of the model. For this purpose the quadratic

programming model, a straightforward extension of the linear programming

model, have been developed. That model is presented in the next chapter.

References

Debreu G (1959) Theory of value, Monograph 17. Cowles Foundation. Yale University Press,

New Haven/London

Jaffe W, Morishima M (1980) On interpreting Walras. J Econ Lit XVIII:528–558

Koopmans TC (1957) Three essays on the state of economic science. McGraw-Hill, New York

Kuhn HW, Tucker AW (1950) Non-linear programming. In: Neyman J (ed) Proceedings of the

second Berkeley symposium on mathematical statistics and probability. University of

California Press, Berkeley, pp 481–492


Chapter 3

The Planner and the Market:

The Takayama Judge Activity Model

The linear programming formulation of the Leontief input–output model, established

as the linear activity analysis model, represents an advancement in the construction of

applied general equilibrium models, because it introduces a great deal of flexibility

into the basic linear input–output structure. The lack of price-induced substitution

was overcome by the development of the linear activity model. By allowing inequal-

ity constraints and the introduction of an endogenous mechanism of choice among

alternative feasible solutions, the effects of sector capacity constraints and primary

input availabilities may be investigated in the model.

However, the linear programming formulation retains the assumptions of hori-

zontal supply functions (up to the point where capacity is reached) and vertical final

demand functions for each sector as well as fixed proportion production functions.

Hence, the demand for commodities and supply of factors are assumed to remain

constant no matter what happens to prices. In the linear programming framework it is

natural to interpret the shadow prices that result as a by-product of the solution as

equilibrium prices. However, these prices cannot be interpreted as market-clearing

prices of general equilibrium theory because endogenous prices and general equilib-

rium interaction to simulate competitive market behaviour cannot be achieved using

the linear programming specification. Thus, by using a linear programming formula-

tion, without representing a realistic price system in which endogenous price and

quantity variables are allowed to interact, the interplay of market forces cannot be

described properly. These are simplifying assumptions which severely restrict the

usefulness of the linear programming formulation of the input–output model.

In linear programming problems, the solution is guaranteed to occur at one (or

more) of the vertices, of the feasible set. This implies that the optimal solutions are

always to be found at one of the extreme points of the feasible set, and the solution

will constitute a basic feasible solution of the linear programming problem. Conse-

quently, all we need is a method of determining the set of all extreme points, from



21

which an optimum solution can be selected.1 However, this constitutes a significant

drawback of the applicability of the model because the linear programming specifi-

cation restricts the field of choice to the set of extreme points. Unlike the points of

tangency in differential calculus, the extreme points are insensitive to small

changes in the parameters of the model. That reduces the attractiveness of the

model for comparative static experiments. In order to include some elements of

flexibility within the system and make the linear programming model more realis-

tic, it is desirable to allow for the inclusion of several resource constraints and to

work on a highly disaggregate level. On the other hand, this will substantially

increase the amount of data required to implement the model. A technique which

removes any of the short-comings mentioned above will greatly improve the

applicability of the model.

For this purpose a straightforward extension of the linear programming model,

incorporating demand by sector and factor supply functions, will be developed. From

a complete set of demand and factor supply functions with only the demand and factor

prices as endogenous variables, it is then possible to compute the set of prices and

quantities that determines an economic equilibrium. The incorporation of demand and

factor supply functions provides a more realistic description of the aggregate market

conditions faced by individual decision makers. The Harrington (1973) formulation

of the Takayama and Judge (1964a, 1964b, and 1971) quadratic programmingmodels

of spatial price equilibrium operate in this way and will be followed to provide a

linear activity model for modelling economic equilibrium. This approach represents a

structure, where the technological data and estimates required to implement the

problem are to a great extent compatible with traditional linear programming models.

3.1 The Quadratic Programming Problem

In the quadratic programming formulation of the linear activity model both the

prices and quantities are determined endogenously within the model. In an

optimisation approach, the model is formulated in terms of the maximisation of

the sum of consumers’ and producers’ surplus.2 Based on empirically generated

demand and supply relations, this formulation of the objective function is used to

replace the utility and welfare functions of conventional economic theory.

Given downward sloping final demand and upward sloping factor supply curves,

relative price changes occur between sectors. Constraints on the model’s solution in

the form of fixed proportion production functions, current capacities and primary

resource availability are retained. Given this specification, the existence of a two

way feed-back in which quantity can influence price and price can influence

quantity for each sector, is developed.

1 The simplex method of linear programming represents such a method.2 See Noren (1987). The numerical tables are also presented in Noren (1991).

22 3 The Planner and the Market: The Takayama Judge Activity Model

The feasible set for quadratic programming problems is completely similar to the

feasible set for linear programming problems. On the other hand, the optimum value

of the objective function might occur anywhere in the feasible set. An optimum

solution may be on the boundary on the constraint region, but not necessarily at a

vertex or an extreme point, as we would expect in linear programming. Hence, the

quadratic programming model must permit consideration of non-basic solutions.3

Consequently, the field of choice extends over the entire feasible set and not merely

the set of its extreme points. In contrast to the linear programming model, we do not

have to work with a highly disaggregated model to increase the number of the

extreme points, and hence, extend the field of choice in the economic model. In the

quadratic programming formulation of the linear activity model, a framework has

been developed, that firstly, attempts to capture the role of prices and the workings of

a competitive market system, and secondly, the solution is not necessarily an extreme

point. The latter property implies that the solution is not so insensitive to small

changes in the parameters of the model. In fact, two of the major shortcomings of the

linear programming model have been overcome.

The theoretical basis of the model that will be presented in this chapter was

outlined in 1952 when Samuelson pointed out that an objective function whose

maximisation guarantees fulfilment of the conditions of a competitive market exists.

Samuelson defined this function as the “net social payoff” to avoid any association

with conventional economic concepts. Samuelson was the first to mention the possi-

bility of maximising the sum of consumers’ and producers’ surpluses to compute a

competitive equilibrium through an optimising model by showing how the problem of

partial equilibrium within spatially separated markets, as formulated by Enke (1951),

could be solved through mathematical programming. In the 1964 papers, Takayama

and Judge using linear price dependent demand and supply functions to define an

empirically oriented “quasi-welfare function”, and hence, extended the Samuelson

formulation so that the spatial structure of prices, production, allocation and con-

sumption for all commodities could be determined endogenously within the model

with quadratic programming. This work was followed by articles by Plessner and

Heady (1965), Yaron et al. (1965), and Plessner (1967), which contributed to the

formulation of the quadratic programmingmodel. In the development of the quadratic

input–output model, Plessner’s (1965) formulation of the Walras-Cassel model as

a quadratic programming problem has been of particular methodological interest.

Harrington (1973) followed the contribution of Plessner by showing how an

input–output model can be solved as a quadratic programming model, hence the

quadratic input–output model. The resulting quadratic input–output model is a theore-

tical improvement over the Leontief input–output model by the direct inclusion of

the pricing mechanism endogenously in the model. Thus, the methodological contri-

bution is the incorporation of the pricing mechanism in the programming model.

3 The main disadvantage of most quadratic programming algorithms is the large number of

calculations required for convergence to a solution. This implies that the quadratic programming

formulation is considerably more difficult to solve numerically than the linear programming

model.

3.1 The Quadratic Programming Problem 23

The model is a linearised version of the Walras-Cassel general equilibrium model

(linearised factor supply and commodity demand functions) which utilises the basic

Leontief input–output structure as a production relationship. Given the linearised

factor supply and commodity demand functions, both the prices and quantities are

determined endogenously. In technical terms, the shadowprices are incorporated in the

objective function. The solution of the quadratic programming problem can be

characterised as a simulation of market behaviour under the assumption of

competition.

The quadratic programming model presented in this chapter is applied for the

evaluation of the pattern of domestic production and trade of the Swedish economy.

The evaluation of the pattern of comparative advantages of the Swedish economy is

carried out as an analysis of the choice between import and domestic production in

a temporary equilibrium framework with exogenously given world market prices,

exports and domestic production capacities.

3.2 Specification of the Model

In developing the model, Hotelling’s (1932) total benefit function, based on empir-

ically generated demand and supply relations, is used to replace the utility and

welfare functions of conventional economic theory. We assume aWalrasian system

of private expenditures and factor supply functions, where the demand and supply

quantities are given as linear functions of the commodity price pj and factor price wh

respectively. Given this specification, we treat the aggregate demand and factor

supply functions as if they could be generated by a single representative individual.

To incorporate price-dependent demand and supply functions and derive an

economic equilibrium, mathematical models can be formulated with an objective

of maximising the sum of consumers’ plus producers’ surplus. Consumers’ plus

producers’ surplus or net social benefit is measured as the area between the

compensated demand and factor supply curves (after adjustment to remove income

effects) to the left of their intersection. The most obvious reason for the use of this

objective function is that its behavioural implications are consistent with theoretical

economic behaviour of the participants by sector. An important, although obvious

point, is that sector commodity supply curves and factor demand curves are not

required as they are already accounted for in the system by the fixed factor

proportion production functions calculated from the input–output table.

When this objective function is maximised, subject to the fixed proportion pro-

duction functions, a perfectly competitive equilibrium solution results.4 Constraints

reflecting the production capacities of the production sectors may alter the result, but

in a manner which continues to maximise producers’ and consumers’ surplus. Thus,

4 Takayama and Judge (1964a) present an existence proof based specifically on a mathematical

programming model of a space-less economy. This proof establishes the existence of a perfectly

competitive equilibrium in a mathematical programming framework of the general equilibrium of

an economy.


the market is viewed as a mechanism for maximising the sum of producers’ and

consumers’ surplus. In technical terms, the shadow prices are incorporated in the

objective function. Hence, the solution of the quadratic programming problem can be

characterised as a simulation of market behaviour under the assumption of competi-

tion. Within the competitive framework, it is assumed that each domestic production

sector and the individual groups of consumers are composed of many competitive

micro units, none of which can individually influence quantity or commodity price.5

The concept of consumer’s surplus is defined as the difference between the

maximum amount the consumer would be willing to pay for the commodity and

what he actually does pay for it.6 In equilibrium, the consumption of the i:thconsumer is at the level at which the willingness to pay for the last consumed

unit is equal to its price.

The factor supply curve is upward sloping and measures the marginal cost of the

factor specific to the sector. Diagrammatically, the producer’s surplus is measured

as the area below the price and above the factor supply curve.7 This area has to be

identified with what Marshall (1925) called quasi-rent. Marshallian quasi-rent is

defined as the excess of the price over the marginal cost of the factor (labour) which

accrues to the producer or the factor owner as a profit in the short-run. Within the

short period, during which capital retains its sector specific form and the other

factor is fixed in price, the area above the supply curve as a measure of quasi-rent is

clearly relevant. Quasi-rents generally arise either because it takes time for new

firms to enter or because certain factor prices may be fixed over the short-run.

Generally, the term producer’s surplus is somewhat misleading, because it does not

identify which particular factor, and hence, factor owner to whom the rents are to be

imputed.8 Anyhow, economic rent can be defined to provide a measure of the

welfare change arising from a movement of factor prices, commodity prices

being constant; in exactly the same way that consumer’s surplus provides a measure

of the welfare change arising from a movement in commodity prices, factor prices

being constant.

In order to manage this problem computationally, we assume that linear

functions are acceptable approximations for the private consumption and factor

5 In this context the artificial nature of the objective function must be emphasised. As Samuelson

(1952) noted “This magnitude (the objective function) is artificial in the sense that no competitor in

the market will be aware of or concerned with it. It is artificial in the sense, that after an invisible

hand has led us to its maximisation, we need not necessarily attach any social welfare significance

to the result” (p. 288).6More rigorously, the difference between the money value of the total utility of the consumer’s

purchase and the money he actually pays for it.7 Strictly speaking, the producer’s surplus is the difference between total revenue from his sales,

minus the area under his marginal cost curve.8 Under perfect competition, the producers’ surplus is captured by the factor owner (owners of

specific capital equipment) in form of rent. In this model all the rents must be paid to the

households. Thus, it is possible to have a producers’ surplus and yet zero profit in competitive

equilibrium.

3.2 Specification of the Model 25

supply functions. This specification results in a quadratic net-benefit or, in the

terminology of Takayama and Judge, quasi-welfare function, and market equilib-

rium may therefore be computed by the techniques of quadratic programming to

obtain the optimum prices and quantities.

The final demand and factor supply functions are specified by the Cassel-Wald

(1951) specification, i.e. demand and factor supply functions are functions of

demand respective factor supply prices alone. As demonstrated by Harrington

(1973) the demand and factor supply functions specify, together with the

specifications of the industry supply system, a consistent system without loss of

generality of the Dorfman et al. (1958) specification of the Walras-Cassel model of

a perfectly competitive economy.

To understand the nature of the programming formulation,9 let the consumption

(private consumption) of the final commodity xj be a linear function of price such that:

xj ¼ γj � pj Σi; νij (3.1)

where we assume γj > 0 and νij > 0 for all j > 0. xj is the quantity of demand of the

desired commodity j, pj is the price of the sector’s product, γj is the intercept term,

the νij represents the slope coefficient. Note that the demand function is independent

of the sector activity, i.e. the income variable is dropped from the demand func-

tion.10 Alter-natively, the inverse of the demand-quantity function11 above is the

demand-price function:

pj ¼ αj � Σi; ωij xij (3.2)

Where we, as for Eq. 3.1, assume αj > 0 and ωij > 0 for all j > 0. αj is the

intercept term, ωji represents the slope coefficient and xij the i:th consumer’s

demand of the desired commodity. The matrix of slope coefficients is assumed to

be symmetric and positive definite for all j. The demand functions are continuous,

differentiable and monotonically decreasing functions of the consumed quantity xj,i.e. ∂(Dj((xj))/∂xj < 0 for all j > 0. The adjustment of prices according to the

9A general survey of techniques for formulation and solving multimarket general equilibrium

models in the mathematical programming framework have been spelled out in detail by Takayama

and Judge (1971).10 This formulation does not incorporate the income generated by the sector as a simultaneous

shifter of the model’s commodity demand function. If the sector under consideration is small

relative to the entire economy, this should not be a serious problem. However, if a major sector or

set of sectors is of interest the income generated within that sector (or sectors) may have a major

impact on aggregated consumer demand.11 In making the model operational, inverted demand and supply functions are applied. The

inversion simplifies the mathematical exposition of the model and the interpretation of the

solutions rather than the direct demand and supply functions. Dorfman, Samuelson and Solow

claim that this inversion is not admissible (Dorfman et al. 1958, p. 352). However, their argument

does not apply to the linearised Walras-Cassel model.


market means that the pj’s may be regarded as functions of the xj’s, in spite of

individual consumers considering the pj’s fixed.The area under these demand curves and above the price represent consumers

surplus for each desired commodity. Integrating the set of the demand curves to

determine the area under the curves, a market-oriented net benefit function, denoted

by W, for the economy (comprising all desired commodities) may be specified as a

strictly concave quadratic function:

Wðx�Þ �ðx�

0

Σj

αj �X

i

ωijxij

!dxj (3.3)

Where x* is a vector. Given the specification above, ωij � ωj. Hence:

Σi; ωjixij ¼ ωjΣi; xij ¼ ωjxj (3.4)

This results in:

Wðx�Þ �ðx�

0

Σjαj � ωjxj� �

dxj (3.5)

Dropping the superscript, we obtain:

WðxÞ � Σj; αjxj�1=2Σj; ωjx2j (3.6)

More compactly, the function (3.6) may be written as:

WðxÞ � α0x�1=2x0Ωx (3.7)

where the matrix of slope coefficients is a diagonal, with zeros as off-diagonal

elements.

Similarly, we assume that the supply of factor quantities rih (primary commodities)

depends on the market prices of its productive services. Hence, let the inverse factor

supply function of commodity h (rih the supplied quantity of the primary commodity

h owned by the i:th consumer) be given by:

wh ¼ βh þ Σi; ηihrih (3.8)

Where we usually assume βh > 0 and ηih > 0 for all h > 0. wh is the price of the

primary commodity h. rh is the supplied amount of the primary commodity h. βh isthe intercept term and ηih represents the slope coefficient. The matrix of slope

coefficients is assumed to be symmetric and positive definite for all h. The supplyfunctions are continuous, differentiable and monotonically increasing functions of

the supplied quantity rh, that is ∂(Sh((rh))/∂rh > 0 for all h > 0.


The area under the factor supply curves (comprising all factor supply curves) is

total cost and may mathematically be written as:

Wðr�Þ �ðr�

0

Σh

βh þX

i

ηihrih

!drh (3.9)

According to the specifications above, we have here a model which will simul-

taneously determine the market demand price on final commodities (consumed

quantities of xj) together with the input market equilibrium prices on its primary

commodities (factor supplies of rh).The sum of producers’ and consumers’ surplus is then found by computing the

difference between the area under the final demand curves and the area under the

factor supply curves.

Wðx; rÞ �ðx�

0

Σjðαj � ωjxjÞdxj �

ðr�

0

Σhðβh þ ηhrhÞdrh (3.10)

Thus, total net benefit (comprising all desired commodities and all factor supply

curves) for the stipulated economy is the line integral of individual demand and factor

supply relations of which consumer’s and producer’s surplus is a part. The model can

actually be looked on as combining Koopmans (1957) linear production model with

Walras’s conception of the market, in a quadratic programming formulation.

The matrix of substitution terms in the demand and factor supply functions must

be symmetric. These conditions are the so called integrability conditions. They playan important role in the formulation of the model. The integration process is known

to be feasible when certain symmetry conditions are satisfied by the functions being

integrated, provided that these functions are sufficiently smooth. Hence, the sym-

metry conditions are often simply called the integrability conditions. Given the

symmetry conditions, a utility and cost function exists from which a consistent

demand respective supply function can be derived.12

If the substitution termmatrices do not conform to the assumption of symmetry the

integrability conditions are not satisfied, then we are unable to construct the net

benefit function given above. From an application standpoint, this presents

difficulties. However, the implications of this requirement vary depending upon

whether we are concerned with supply or demand. The classical assumptions of the

theory of production yield the symmetry conditions of the supply functions (Zusman

1969). Takayama and Judge (1971) have pointed out that if the integrability

conditions do not hold, then the system is still solvable and interpretable in terms of

net social monetary gain which is defined as total social revenue minus total social

12 For details, see Varian (1984), pp. 135–139.


production cost. Only the connection to utility maximisation and cost minimisation is

lost by violation of the integrability conditions, not the solvability of the system.13

The symmetric condition is a necessary and sufficient condition for what is known

as path-independence. This implies that the cross-price effects (compensated) are

equal over all commodity pairs. In the present context, this means simply that in

whatever way the order of price changes is calculated the adopted measure of

consumer’s and producer’s surplus for the combination of these price changes is

uniquely determined. The symmetry of the substitution termmatrices (Slutsky terms)

is exactly the condition under which the integral W(x,r) is solely dependent on the

terminal price vectors, and thus, regardless of the order in which the price changes are

taken, i.e. independent of the path. However, given a demand function including the

income variable, the path-independence condition requires that the income

elasticity’s are identical across all commodities of interest. Given the property that

the weighted sum of the income elasticity’s, where the weights are the shares of

income spent on each commodity, sums to one, all income elasticity’s are equal, and

thus, equal to one.14 Unitary income elasticity’s are the demand functions derived

from homothetic indifference maps. This implies that all Engel curves are straight

lines through the origin, i.e. at all income levels, a constant proportion of total

expenditures is allocated to each commodity.

3.2.1 The Introduction of Foreign Trade

Most commodities can be supplied not only by domestic production, but also by

importation. A standard approach is to specify imports as an alternative source of

supply of commodities classified by the input–output sectors (Technically as an

alternative column in the input–output table). A different approach is to specify

imports as a primary input that is not produced in the economy (Technically as a

row in the input–output table).

In the first approach, imports are specified as competitive, here denoted Mj,commodities which can be produced within the country but which are, as an

alternative to domestic production, also imported. The imported commodity is

here viewed as a perfect substitute for the domestically produced commodity.

Consequently, those imported commodities which the agents are free to select for

domestic production are classified as competitive imports. In this context, any

particular commodity classified as competitive imports is assumed to be tradable

in the international market, and has identical characteristics, whether it is produced

at home or abroad. Formally, competitive imports are treated as if they were

13 Takayama and Judge (1971), pp. 121–126 and pp. 233–257.14 The path-independence condition is also fully satisfied if the income elasticity’s of demand of all

commodities are zero (McCarl and Spreen 1980). In this model the income variable is dropped

from the demand function. Thus, the path-independence condition is satisfied.


delivered to the corresponding domestic industries and then distributed by these

industries together with the domestically produced amounts. Thus, the inputs aijZjstate the sums of produced and imported amounts, and not merely the produced

amounts.15

In the second approach imports are specified as non-competitive, here

denoted mqjZj, and instead of perfect substitutes for domestic production, imports

are treated as a complementary input, completely different from domestically pro-

duced commodities. This type of imports consists of commodities which cannot be

produced within the country. Non-competitive imports including predominantly

those commodities which are technically infeasible, and commodities whose produc-

tion is economically unviable because of the present market situation compared with

their minimum scale of production. In our notation, mij denotes the input coefficient

of non-competitive imports and Zj the extent of which the process j is utilised.When a commodity is imported there is an outlay of foreign currency per unit of

imported amountMj respectivemijZj. If PW denotes the world market price in foreign

currency, �PWjMj and �PWjmijZj ex-press the outlay of foreign currency. On the

other hand, when a commodity is exported, denoted Ej, there is a receipt, expressedby PWjEj, of foreign currency earned per unit of exported amount Ej. Consequently,foreign currency is here an intermediate commodity, where the import process

requires foreign currency as input, and foreign currency is the output of the export

process. Thus, in this context there are also given resources, but of foreign currency

only. These resources are made up of net export earnings plus net foreign capital

inflow, denoted F. In this model the amount of net foreign capital inflow is assumed

exogenous. Given the exchange rate, denoted ER, it follows that foreign trade can bedescribed as to be carried out by means of processes with fixed relations. Compatible

with the assumption made for domestic production, it will be assumed that an import

process involves importation of one single commodity. This assumption re-places, as

for domestic production, an optimisation requirement.16 Consequently, we also

assume that an export process leads to the export of one commodity only.

The effects of transportation costs and tariffs are taken into consideration by

including transport costs and tariffs into import prices (tariff augmented world

market prices). Hence, the currency spent on importing a unit of a commodity is

generally somewhat larger than the amount earned by exporting it.17 If it were

smaller, this would mean that the price in the exporting country would exceed the

price in the importing country, which is not compatible with interregional general

equilibrium. In this model world market prices of traded commodities are assumed

to be given. The assumption of given world market prices (the small country

15 The exposition in this section is based on and similar to that of Werin (1965).16 Optimisation implies that the import process, given the smallest currency outlay, as well as the

production process, given the best technique available, is chosen.17 Statistically, imports are calculated in c.i.f. prices and exports in f.o.b. prices. Given this

specification, the currency outlay for imports will not be proportional to the existing world market

prices. This implies that the foreign exchange constraint will not correctly reflect the conditions

prevailing on the world market.


assumption) implies that the country is confronted with infinitely elastic demand for

its exports and supply of its imports, so what the level as well as the pattern of

imports and exports may be endogenously determined only subject to the foreign

exchange restriction.

Considering the assumptions made, the production system is re-presented by an

input–output model extended to include foreign trade as an alternative to domestic

production. Each commodity can now in principle be supplied by two different

activities. One of them is the production activity, the other the import activity,

which is the result of the outlay of foreign currency. This means substitution

possibilities between inputs for the supply of various commodities. A linear activity

model which takes foreign trade into account is, in certain respects, quite similar to

a neoclassical model.18

The foreign exchange constraint (Eq. 3.11) restricts the amount of foreign

currency that can be spent on imports. The supply of foreign currency is generated

through exports and net capital inflows. PWj denote the world market price of each

commodity classified by the input–output sectors. In this model, imports will betreated both as an alternative (and identical) source of supply of commodities

classified by the input–output sectors and as another input (composite) that is not

produced in the economy, analogous to capital and labour. Technically, competitive

imports are placed outside the inter-industry part of the input–output table, specified

by sector of origin, and non-competitive imports are kept within the inter-industry

part of the input–output table, specified by sector of destination.

Σj; Σi; PWjmijZj þ Σj; PWjMj � Σj; PWjEj þ F (3.11)

3.3 The Programming Formulation

Given the net benefit function, and the constraint set as specified above the problem

takes the following form, i.e. maximise:

Wðx; rÞ � Σj; αjxj � 1=2Σj; ωjx2j � Σh; βhrh � 1=2 Σh; ηhrh

2 (3.12)

Subject to

Zj þ Σj; mijZj þMj � Ej � Σj; aijZj � ΣiDij (3.13)


18However, if the model does not include any further restrictions on exports and imports, the

assumption of constant returns of scale in production together with endogenous choice in trade

may lead to an unrealistic specialisation in either trade or domestic production.



Σj; Σi; PWjmijZj þ Σj; PWjMj � Σj; PWjEj þ F (3.16)

Zj � 0; Mj � 0; Ej � 0; Dij � 0; rih � 0; Kij � 0

Making use of the Kuhn-Tucker conditions, the necessary conditions which must

hold for the optimum xoij; roih; Zoj ; Mo

j ; poj ; woh; voij; ERo to be a non-negative saddle

point of the Lagrangean, are:

@Lo

@xij¼ αj � ωjx

oij � poj � 0

�00 � < 0 ) xoij ¼ 0 ð3:17Þ

@Lo

@rih¼ �βh � ηhr

oh þ wo

h � 0

�00 �< 0 ) roih ¼ 0 ð3:18Þ

The constraints of the domestic activities will be the same as in the linear

version. See the discussion in Chap. 2, Sect. 2.5. However, the inclusion of foreign

trade implies two other constraints in the quadratic model. The new constraints are

discussed below as constraint (3.23) and (3.24).

For a given vector of pre-equilibrium prices pj and wh, these prices are revised

until the shadow prices poj and woh associated with the commodity balance Eqs. 3.13

and 3.14. If so, the solution is an equilibrium solution. Thus, the dual variables from

Eqs. 3.13 and 3.14 equals the maximum price the consumers are willing to pay for

the consumption of the commodities available to them, and the minimum price at

which they are willing to supply labour service from their initial endowment of

leisure. If not, the demand and supply prices are revised and start a new function

evaluation. In this way shadow prices have a feedback effect on the demand and

supply prices specified in the objective function. As stipulated above, this is what

leads to the similarity between the market mechanism and the optimisation formu-

lation of the model. A planning authority can use the shadow prices generated by

the plan to decentralise decisions because they are signals of relative scarcity of the

constraint to which they are attached. However, when imposing a number of

additional ad-hoc constraints to make the solution more realistic, the constraints

result in distortions in the shadow price system. If such constraints can be justified

as additional system constraints that define a reasonable notion of economic

equilibrium, there is no theoretical problem to interpret the solution as reflecting

the operation of a market system (Taylor 1975).

Starting with the shadow demand price, denotedpoj ,when the consumption of the j:

th commodity is positive, must exactly be equal to the demand price pj, the maximum

price the consumers are willing to pay for the consumption of the quantity of the


http://dx.doi.org/10.1007/978-3-642-34994-2_2

commodity xj, which in turn are generated by the optimum demand quantity xoj .

However, if xoj ¼ 0, the shadow demand price is greater than or equal to the demand

price. Thus:

if xoj > 0; then αj � ωjxoj ¼ poj ð� 0Þ; (3.19)

if xoj ¼ 0; then αj � ωjxoj � poj ð� 0Þ; (3.20)

for all j.The factor supply equilibrium stipulates, that when the optimum supply quantity

of the h primary commodity is positive, the shadow supply pricewoh must exactly be

equal to the supply price (factor cost) wh, the minimum price at which the resource

owners (consumers) are willing to supply rh, where roh are generated by the optimal

supply quantities roh. However, if roh ¼ 0, the shadow supply price is less or equal to

the supply price. Thus:

if roh > 0; then βh þ ηhroh ¼ wo

hð� 0Þ; (3.21)

if roh ¼ 0; then βh þ ηhroh � wo

hð� 0Þ; (3.22)

for all h.The individual country becomes a price taker in the small open economy model,

because the world market prices of traded commodities are assumed to be determined

in the international market. The domestic economy will at the optimum adjust to the

relative world market price ratio. In a free trade economy,19 the direction of trade will

be determined by the requirement of equality between the domestic and the world

market price ratio. It is the difference between these ratios that leads to trade. Thus,

efficiency requires equality among world market prices, domestic prices, and produc-

tion costs. Since the world market prices are assumed to be given, these prices

determine the domestic shadow prices of tradables.

@Lo

@Mj¼ poj � ERoPWj � 0

�00 �< 0 ) Moj ¼ 0 ð3:23Þ

Next condition (3.23), relates to the alternative way of supplying a commodity,

namely by importation. Condition (3.23) state, that when the optimum import

19 Using the small-country assumption and also assuming that domestically produced and imported

commodities are perfect substitutes this specification leads to extreme specialisation in either trade or

domestic production whenever there are no established domestic capacity constraints. The sector-

specific capacity constraints in this model are used to limit this problem. This implies that the

domestic shadow price system is no longer a simple reflection of world market prices.


activity Moj is positive, the shadow price poj of the imported commodity must be

exactly equal to the value (cost) of the outlay of foreign currency. If the shadow

price poj is lower than the imputed cost of importing the commodity no importation

of the commodity will take place. Production will expand until domestic production

costs rise to the world market price level, converted into a domestic price by the

shadow exchange rate ERo. Consequently, as long as domestic production costs are

lower than established world market prices, it will be profitable to expand domestic

production for exports. On the other hand, if the domestic price is greater than the

world market price, the commodity will not be produced. If the country can always

import at a cost of poj it is never optimal to produce at a marginal domestic cost

higher than poj . This leads to excess domestic capacity which is reflected by a

shadow price of zero for installed capacity. Since, our model only contains

tradables; the shadow exchange rate is simply defined as a conversion factor from

foreign exchange units to domestic commodity units, and has no significance in

terms of relative domestic prices.20

Finally, condition (3.24) below state, that if the optimum price of foreign exchange

is positive, the foreign exchange equilibrium requirement for the economy is exactly

met. Note, that for any positive activity the shadow exchange rate ERo can never be

zero because it is always possible to use foreign exchange to purchase commodities

from abroad.21 If the shadow price of foreign currency is zero at the optimum no

activity (production and importation) take place in the domestic economy. Given this

specification, there is the assumption of a flexible exchange rate system, in which

exchange rate adjusts continuously so as to maintain the foreign exchange constraint

in equilibrium.22 However, specifying tariffs on currency outlay for imports implies

that the domestic shadow prices would reflect the existing tariff structure, and the

tariff-ridden domestic market prices will not be proportional to the existing world

market prices. Hence, the foreign exchange constraint will not correctly reflect the

conditions prevailing on the world market.

@Lo

@ER¼ Σj;PWjE

oj þ F� Σi; Σj;PWjmijZ

oj � Σj;PWjM

oj � 0

�00 �> 0 ) ERo ¼ 0 ð3:24Þ

In the closed economy the basic technological and demand variables determine the

domestic shadow price system.23 However, the situation is quite different in a free

20With non-tradables, the shadow price of foreign exchange will reflect the relative scarcity of

tradables with respect to non-tradables.21 For a discussion of this mechanism, see Dervis et al. (1982), pp. 75–77.22 Assuming given world market prices, an increase in domestic prices implies a depreciation of

home currency. Conversely, a decrease in domestic prices implies an appreciation of home

currency. See further, Sodersten (1980), pp. 315–328.23 The discussion that follows is based on Dervis et al. (1982).


trade economy where the domestic market is small in relation to the world market.

Given the assumption of perfect substitutability between imported and domestically

produced commodities, the small-country assumption implies that the individual

country becomes a price taker facing exogenous world market prices. The theory of

international trade suggests that, as far as some commodities are actually imported or

exported, the domestic shadow prices among them tend to converge to their relative

world market prices.24 Consequently, world market prices determine the domestic

shadow prices of tradables, and a given commodity has (at equilibrium) the same

price whether it is imported or produced domestically. Hence, whereas supply and

demand determine domestic shadow prices in a closed economy, they will adjust to

world market prices in the small open economy.

3.4 A Temporary Equilibrium Specification

The static model as presented above has no formal link between capital formation

and production capacity. Capital commodities are assumed exogenous without any

correspondence to the effect that is created by the supply of investment from sectors

producing capital commodities (investment in final demand). However, a tempo-

rary equilibrium specification endogenises investment and considerably extends the

requirement of consistency in the model. The period output of the capital stock

requirement is inserted as a predetermined variable for the next period optimiza-

tion.25 Once capital stock requirement by sector of destination is established, its

sectoral allocation into a demand for investment commodities by sector of origin

must be specified.

Operationally, the solution for each period is used to create the next period’s

model parameters. Thus, the model is of the temporary equilibrium type. It will

solve the market for equilibrium prices and quantities for one period and then add

the solution obtained to the predetermined variables that are needed to obtain the

market equilibrium solution for the next period. The model does not take into

account future markets despite the fact it explicitly considers time. There is no

inter-temporal optimization26 and the agents have no expectations about future

prices. This concept of equilibrium as static and temporary implies that we are more

interested in the outcomes of the adjustment that yields a new temporary static

equilibrium position than in the dynamics of the adjustment process itself.27

24 Differences may exist due to transportation costs and tariff rates.25 Given the specification of the model, also private consumption is inserted as a pre-determined

variable for the next period optimization.26 In intertemporal models, agents have rational expectations and future markets are considered

when optimizing. Endogenous variables follow an optimal path over time and there are no

incentives to deviate from this path at any point of time.27 Hence, we can overlook the issue of adjustment.

3.4 A Temporary Equilibrium Specification 35

Investment is made up of two parts, replacement investment and net investment.

Replacement investment is that portion of the total which exactly maintains the

capital stocks while net investment is that portion which depends on the level of

demand. In this specification, only net (private) investment in buildings and

machinery is considered. Logically, we disregard depreciation. Another component

of capital formation is inventories. However, the model treats inventories as an

exogenously given component of final demand, and thus, does not incorporate

inventories in the investment concept.

The change in capital stock is by definition the amount of investment. As long as

domestic demand is unchanged, the capital stock is adequate and no investment is

needed. Increases in domestic demand, however, call for additional capital and net

investment is positive. Formally, we assume investment (given the assumption of

full capacity) to be linearly dependent on the current period’s request for newcapacity. This implies that investment adjusts immediately to changes in capacity

requirement within a single period.28 Nevertheless, there is certainly reason to

suspect that in the real world firms do not respond immediately. Hence, it is

assumed that each period is long enough for relative prices to adjust to clear

markets. In quantitative terms, the request for capital commodities by sector of

destination ΔKj is translated into a demand for investment commodities by sector of

origin Ik (producing sectors of capital commodities). Thus we have

IiðtÞ ¼ ΣjτkjΔKjðtÞ (3.25)

Where τkj denotes the matrix of sectoral investment allocation shares, i.e. the

proportion of capital stock in sector j originating in sector k. Note that Στij ¼ 1 for

all j (summation is taken over i). The matrix of sectoral investment shares is

compiled by the Ministry of Finance for the 1984 Medium Term Survey Model

of the Swedish economy.29

It is important to note that the model, in this version, only considers positive net

investments. In other words, given a decrease in the capital stock requirement by

sectors of destination (ΔK < 0) the net investments by sectors of origin are zero.

For this alternative, only sectoral capital stocks are adjusted (scrapping) for the next

period optimization. Moreover, fixed coefficients are used to allocate investment

among sectors. Thus, profitability across sectors is assumed fixed over time. This

implies that we have no allocation process explicitly modelled, in which investment

gradually adjust to equalize profitability across sectors. Hence, the workings of

financial markets in the investment allocation process are ignored. Technically, the

capital stock in each sector is a well defined aggregate of various commodities with

28 This is the famous accelerator principle. In its simplest form, the accelerator rest upon the

assumption that the firm or industry at each level of distribution seeks to maintain its optimal

capital stock at some constant ratio to sales.29 SOU 1984:7, LU 84 (The 1984 Medium Term Survey of the Swedish Economy), Appendix 17,

Table 2:18. Only 9 sectors produce investment commodities for domestic capacity expansion.


a fixed compositional structure (by sector of origin). Finally, there are assumed to

be fixed incremental capital-output ratio by sectors.30

3.5 Empirical Findings: Applications

As stipulated above, the model works stepwise from period to period, and solves the

market for prices and quantities. The solution for each period (four periods in total)

is used to create the next period’s model parameters. Hence, a sequence of

equilibria can be achieved. The period output of capital stock requirement, invest-

ment demand and private consumption are inserted as predetermined variables for

the next period optimization.31

The point of departure for the experiments below (here named applications)

is the version of the model which describes the techno-logical conditions,

labour costs, capacities and estimated demand relations representing the Swedish

economic situation in the year 1980 (benchmark equilibrium data set).32 This year

is selected since it con-forms with data availability, and capacity utilization during

the whole of 1980 on the average can be characterized as normal full capacity.

Thus, the 1980 data provide a comparative benchmark for the experiments in this

chapter. In all solutions, the same maximand is used, i.e. maximize the consumers´

surplus (Eq. 3.3), subject to the constraints (Eqs. 3.13, 3.14, 3.15, and 3.16). Given

the assumptions above, a foreign payments imbalance cannot arise. Moreover, we

assume that the labour constraint (Eq. 3.14) is binding, i.e. labour resources are used

to the maximum availability. In all solutions the total supply of labour resources is

given exogenously and assumed perfectly mobile and free to flow among all sectors

of the economy. Hence, labour moves across sectors until the value of its marginal

product is the same everywhere. This assumption, the value of that marginal

product of labour are equalized in all uses in equilibrium, permits labour payments

data by industry to be used as observations on physical quantities of labour in the

determination of parameters for the model.

In general terms, adjustment to structural equilibrium is a process where profit-

ability in the different sectors will adjust to a “normal” level of profitability for the

economy as a whole. For sectors where profitability is high relative to this normal

level, the adjustment to equilibrium implies an increase in domestic production

relative to other sectors. On the other hand, a sector where profitability is low

relative to the normal level, an adjustment to equilibrium implies a decrease in

30 The temporary equilibrium approach used in this study does not imply that the underlying

economic system is viewed as discrete. Instead, the discrete moments are simply approximations

(artificial to some extent) of the essentially continuous system being modelled.31 Adjustment costs for the installation of capital are not considered.32 The model of the Swedish economy comprises 24 sectors. These are defined in the Appendix, in

accordance with both the Standard Swedish Classification of Economic Activity (SNI) and the

code for the ADP system for the Swedish National Accounts (SNR).

3.5 Empirical Findings: Applications 37

domestic production relative to other sectors. Thus, a development which implies

that a country adjusts to its comparative advantages33 is characterized as an

adjustment towards equalizing the relative profitability between sectors. The results

of this adjustment are reflected in the direction of domestic production.

In technical terms, the domestic shadow prices adjust to the exogenous world

market prices in this model. Thus, the concept of a normal level of profitability for

the different sectors is determined by the relative world market prices. If the

domestic shadow price is greater than the world market price, the domestic produc-

tion of the commodity relative to other sectors will fall. If it is not possible to reduce

domestic production costs to the level of world prices, the commodity will be

imported altogether. On the other hand, if the domestic shadow price is lower

than the world market price, domestic production relative to other sectors will

expand at the expense of imports until domestic costs rise to the level of world

market prices.34 If this equality is not satisfied in the case when the adjustment to

equilibrium implies a zero import level, it would be profitable to expand domestic

production for exports.

Generally, due to the assumed linearity of the underlying technology, the

solution in the model imposes that fewer commodities will be produced domesti-

cally, but in increased quantities in the least-cost sectors. On the other hand, the

specialisation will lead to an increasing amount of import in the high-cost sectors.

In all experiments, it is the difference between the world market prices (here

assumed to be given)35 and the pre-trade domestic commodity transformation

rates that leads the model to take part in trade.

To obtain a reasonable pattern of specialisation, exports are assumed exogenous.

As exogenous values of exports we have maintained the 1980 figures. By this

assumption extreme specialisation is prevented. Unfortunately, these constraints

reduce the experimental attractiveness of the model.

Given the model specification, the equilibrium data of the former period provide

a comparative benchmark for each experiment (four experiments in total).36 Appli-

cation 1 is considered as the first period. It is important to emphasize that the results

have been obtained under strong simplifying assumptions. The results of the

experiments are presented in the Appendix 2 (Tables 3.3, 3.4, 3.5, and 3.6).

As a starting point for the experiments we assume an increase in the sectorally

fixed capital stocks by 10 %. This implies that domestic resources may be shifted to

33Given two sectors 1 and 2, the economy has a comparative advantage in sector 2 if the pre-trade

ratio of sector 2 costs to sector 1 costs is lower than the world price ratio.34 Following Norman (1983) a domestic sector is competitive if (and only if) its marginal cost is

lower or equal to its foreign competitor, measured in the same currency. To be compatible with the

concept of comparative advantage, and hence meaningful, marginal cost is here defined as long run

marginal cost. This implies that the concept of marginal cost includes payment to factors that are

fixed in the short run, e.g. capital.35 The world market prices are specified as unity prices.36 The first experiment (application 1) provides the benchmark data for the second experiment

(application 2) and application 2 provides the benchmark data for the third experiment (application 3).


the lowest-cost sectors (given the capacity restriction) and thus increase the effi-

ciency in resource allocation. Logically, the model chooses to import in some

sectors (Sector definitions in Appendix 2, Table 3.2) rather than utilize the existing

capital stock. As expected, we obtain an increase in engineering (15) and a total

contraction of the shipyards (16). Moreover, the result obtained shows a decline of

domestic production in the basic metal industries (14). As specified above,

the sectoral demand for capacity expansion, evaluated in the former period (appli-

cation 1), is translated into investment by producing sectors in the current period

(application 2). In this connection, the increase in some sectors of the index

representing sectoral demand prices should be noted. The demand prices

(Tables 3.3, 3.4, 3.5, and 3.6, column 13) of the private consumption variables

are expressed in terms of an initially established index, assigned as 1,000. The

explanation for this increase in demand prices is that investment required for

capacity expansion (given as input from application 1) have increased for most

sectors producing capital commodities. Consequently, in some sectors a decrease

(crowding out) of other demand components (here, private consumption only) is

necessary to make capacity expansion possible. At the beginning (application 1 and

application 2) the request for capacity expansion is considerable. However, a

continuing fall in mobility, due to the limited supply of labour resources (measured

in terms of wages), increasing capital stocks in the investment sectors, and the

linear specification of the model, will in the long run reduce the demand for

capacity. The diminishing welfare effect, due to reduced potential in resource

allocation, is the main factor behind this development. Thus, in the next two

experiments (application 3 and 4) it is quite obvious that the demand for net

investment by sectors will fall. These calculations are presented in Table 3.1.

Capacity expansion and the process of structural transformation is restricted to

the existing structure of production. The technological structure is kept the same.

Not unexpected, the results presented in Table 3.1 indicate that the resource

transformation process alone is not sufficient to sustain a high rate of growth in

industrial real capital formation. Successively increasing investments in new tech-

nology, introduction of new commodities, and in its extension, the formation of

new activities (operations), are strongly needed to maintain the capacity for indus-

trial renewal.

From an evolutionary theoretical point of view (Schumpeter is among the classics

in this field) the model, and theory,37 outlined here is in this respect inadequate to

capture the process of structural renewal, and hence, the specification of the

mechanisms that creates incentives for the entrepreneur to enforce new investments

to maintain the capacity for growth. In assessing these results it must be emphasized

that investment is restricted to capacity expansion, i.e. net investment. Moreover, all

investments are in established industries and hence, according to the specification of

the model, directed to the production of a given set of commodities. In the real world,

37 The perfect competition theory defines the equilibrium state and not the process of adjustment.

(Kirzner 1973, p. 130).

3.5 Empirical Findings: Applications 39

however, investments made to increase the total capacity as well as the replacement

and scrapping of old production units change the production characteristics.

Investments in new capacity embodying best-practice techniques will decrease the

sector’s input coefficient at full capacity. Thus, new capacity has in general

input–output proportions different from those of existing production units due to

changed relative prices and technical progress, which may be embodied or

disembodied (learning by doing). Furthermore, investments introduce input–output

combinations, and in the long run, production of commodities which cannot be found

within the initial production possibility set.

Returning to application 4, the equilibrium model does no longer choose to

establish agriculture and fishing (1) and the mining and quarrying industry (3) in the

Swedish economy. On the other hand, engineering (15), wood, pulp and paper industry

(8) and chemical industry (11) belongs to sectors38 highly exposed to foreign compe-

tition, where expansion of domestic production is requested. Besides manufacturing,

private services (23) indicate an increasing share of domestic production.

In all experiments labour is assumed to be an aggregation of different skill

categories. In other words, labour is specified as homogenous in the model. Hence,

we can not value labour services (labour productivity) by skill group. Nevertheless,

the chemical industry and engineering are particularly intensive in terms of

technicians and skilled labour. In this respect, it seems that the joint utilisation of

human and physical capital provides an important input in the Swedish industry.39

In a model that does not include any restrictions on trade, a commodity is either

imported or exported, but never both.40 The explanation of this is that the commodity

imported and the commodity exported is assumed identical in the model. The

Table 3.1 Net private

investment by producing

sectors million kr – 1,975

prices

Sector Application Request in

1 2 3 4 5

1 281 326 358 0 0

2 346 684 0 0 0

7 161 296 203 100 87

8 807 500 334 155 175

15 21,840 34,862 26,841 11,405 6,253

16 1,299 2,251 2,476 0 0

17 28 20 22 0 0

19 26,118 15,978 12,562 3,697 1,904

23 650 3,214 2,490 967 324

38 The engineering industry is usually analyzed in terms of five sub-branches, i.e. metal goods

industry, machine industry, electrical industry, transport equipment (excl. ship-yards), and mea-

suring and controlling equipment industry. The machine industry is the largest sub-branch

(measured in number of employees and value added respectively). The sub-branches for metal

goods, electrical equipment and transport equipment are all roughly of the same size.39 See also Flam (1981), pp. 97–101.40 It is important to note that the level of aggregation will affect the value of the measures of intra-

industry trade. The higher the level of aggregation, the greater will be the share of intra-industry


tendency for specialisation would be even more explicit, if we were to leave sectoral

capital stocks as endogenous variables.41 Needless to say, extreme specialisation in

production and trade conflicts with empirical evidence, which on the contrary, shows

relatively little specialisation on the sectoral level. However, as pointed out byWerin

(1965), the observed combination of domestic production and trade may be in

complete accordance with the theoretical model. First, the country under study

consists of many regions, which implies that a commodity may be imported to one

region and exported from another, but never be both imported to and exported from

one single region. Second, the same argument is applicable to the fact that the model

is specified to cover a period of some length. Hence, a commodity may be both

produced and traded at different points of time during the period of specification.

Finally, the commodities of the model are aggregates of different commodity

categories. For each of these commodities the theoretical requirement may be

fulfilled.

3.6 Comparative Advantages?

Whereas the Swedish economy, as expounded by the equilibrium experiments

above, tend to illustrate a comparative advantage in industries with large

requirements of human capital42 several empirical studies examine the net trade

patterns and the specialisation of production of Sweden with the EU (in the

beginning EEC) and other OECD countries, indicate a weaker market position in

human capital intensive industries (Ems 1988). Moreover, the R&D intensity did

not seem to influence the international competitiveness of the Swedish industry at

all. The pattern of change in the competitiveness of the Swedish industry versus the

EEC in 1970–1984 (Lundberg 1988) seem to reveal a comparative advantage in

industries requiring large inputs of physical capital and domestic natural resources.

Human capital intensity does not seem to have influenced net export ratios during

the period.

The discussion above has already stressed that a model that does not include any

restrictions on trade, a commodity is either imported or exported but never both.

However, during the post-war period there has been a marked increase in interna-

tional specialisation within the differentiated product groups and a substantial

trade (Grubel and Lloyd 1975). Although the share of intra-trade is reduced by disaggregation,

substantial two-way trade remains (Blattner 1977) on the most detailed aggregation level.41 A common approach to avoid unrealistic specialisation in multi-country trade models is to use

the Armington (1969) formulation, which treats similar commodities produced in different

countries as different commodities (commodity differentiation by country of origin). Bergman

(1986) makes use of the Armington formulation and applies a numerical solution technique in

order to solve the model.42 Nearly all available evidence indicates that Sweden has a comparative advantage in human

capital intensive production. A survey of these studies is given in Flam (1981), pp. 97–101.

3.6 Comparative Advantages? 41

growth in the share of intra-industry trade, i.e., imports and exports in the same

statistical commodity group.43 Thus, the increase in trade and specialisation is

dominated by reallocation on resources within rather than between industries.

The increase in intra-industry trade between Sweden and the EEC has been

particularly strong. Theoretical elements explaining the determinants of intra-

industry trade are based on the roles of product differentiation and economies of

scale. One point of departure in seeking to explain the growth of intra-industry trade

(Petersson 1984) has been the Lancaster (1980) theory which places central impor-

tance on product differentiation and scale economies specific to the product

(production runs). The adoption of a global production strategy and specialisation

within a limited range of commodities and product variants enables a country’s

producers to achieve long production runs. Similar opportunities for the producers

of other countries gave rise to a flow of import and an improvement in consumers’

choice. Hence, the existence of product differentiation (which is especially found in

consumer products) implies monopolistic competition which, from the consumer’s

viewpoint may correspond to a demand for variety in commodities.

Economies of scale with product differentiation normally prevails where

corporations make horizontal investments, i.e. to produce abroad the same lines

of commodities as they produce in the home market. Swedish firms which have

manufacturing affiliates abroad (multinational corporations) account for some

50 % of manufacturing employment in Sweden and almost 60 % of Swedish

exports (Swedenborg 1988). Moreover, they are dominating in engineering and

are highly internationalized. In 1986 less than 25 % of their total sales were sold in

the home market. Of the 75 % sold in foreign markets over half was produced

abroad. Empirical observation (Erixon 1988) suggest that the reduced market

share for Swedish exports may to a great extent be explained by the tendency for

Swedish multinational corporations to supply through local production in the

largest markets rather than through exports from Sweden. Thus, the size of the

market affects not only the volume of sales in a country but also leads to a higher

propensity to supply the market through local production (Krugman 1980).

Comparing the discussion above with the pattern of changes that emerges from

the experiments with the equilibrium model is interesting. In the equilibrium

model the necessary reallocation of sectoral resources is reached solely by an

adjustment in the structure of inter-industry trade. However, within industries

where the equilibrium experiments call for a substantial growth in domestic

production the economic gains is mainly intra-industry in nature. These

gains are in the form of economies of scale utilized to a great extent by

foreign production, rather than arising from reallocation of resources according

to comparative advantages. Thus, we have to be careful in interpreting the

obtained results in a too mechanical fashion.

43 The expansion of intra-industry trade in Europe which was particularly marked in the 1960s

appears to have largely halted in recent years. A somewhat similar situation is apparent for the US

(Hine 1988).



To conclude this chapter, it seems reasonable to compare the mathematical pro-

gramming (linear and quadratic) models above with models developed within the

tradition of computable general equilibrium (CGE) modelling. In such a compari-

son the programming models seem to be based on overly restrictive assumptions.

For example, while most standard CGE-models incorporate technology

descriptions that allow for factor substitution, there are fixed coefficients in the

linear programming model. Generally, due to the assumed linearity of the underly-

ing technology, the solution in the model imposes that fewer commodities will be

produced domestically, but in increased quantities in the least-cost sectors. On the

other hand, the specialisation will lead to an increasing amount of import in the

high-cost sectors. To obtain a reasonable pattern of specialisation, exports must be

specified to vary within certain limits or be assumed exogenous. By this assumption

extreme specialisation is prevented, but it is still a serious deviation from reality,

especially when foreign trade is a large part.

Another serious restrictive assumption is the treatment of maximising behaviour

by agents in mathematical programming models. In this chapter as well as in the

previous the central planner is assumed to be the only maximising actor. Theoreti-

cally, that conflicts with the market equilibrium price system, where the demand

and supply decisions are made separately and independently by various economic

actors. While most CGE-models incorporate complete systems of final demand

functions, usually derived from explicit utility functions, the demand representation

in the mathematical programming models are based on linear demand functions

with no explicit relation to utility maximisation under a budget constraint. Hence,

no ad hoc assumptions in order to avoid unrealistic solutions will be needed.

Not unexpected, these constraints reduce the experimental attractiveness of the

programming models in our study of a market economy.

Appendix 1: The Reformulation of the Walras-Cassel Model

To provide the methodology for the reformulation of the Walras-Cassel general

equilibrium model as a quadratic programming problem, and hence, the basic

structure of the quadratic input–output model, Harrington (1973) linearises the

Walras-Cassel model and specifies the Walrasian factor supply and commodity

demand functions into inverse form.44 The inversion simplifies the mathematical

exposition of the model while retaining the generality of the Walrasian factor supply

and commodity demand functions. Dorfman, Samuelson and Solow (1958) claim that

44 The Walras-Cassel model is specified in Dorfman, R., Samuelson, P. A. and Solow, R. M.,

(1958), pp. 346–389. The Walrasian model of the market system was first sketched by the

nineteenth-century French economist Leon Walras (1874–7).

Appendix 1: The Reformulation of the Walras-Cassel Model 43

this inversion is not admissible because there is no mathematical reason for assuming

the existence of inverse demand or supply relationships in a model were prices

depend on quantities only.45 However, their argument, as demonstrated by

Harrington, is well-founded in the general case but does not apply to the linearised

Walras-Cassel model. The quadratic input–output model is a linearised version of the

Walras-Cassel general equilibrium model which utilizes the inter-relatedness of

production established in the input–output structure. In this context, it is shown by

Harrington that the conventional input–output model is a limiting case of the

linearised Walras-Cassel model. In the linear form of the Walras-Cassel model the

assumptions of homogeneity of degree zero of factor supply and commodity demand

functions can be relaxed because the homogeneity constraint is satisfied elsewhere in

the model formulation. Furthermore, the Cassel-Wald specification of commodity

demand quantities as a function of product prices alone, and factor supply quantities

as a function of factor prices alone (Wald 1951), specify a consistent linear system

without loss of generality of the Walras-Cassel model.

In order to understand the underlying structure of the model that constitutes the

framework of this study a mathematical exposition of Harrington’s (1973) contri-

bution is given in this section.46 Let A denote a matrix of fixed coefficient produc-

tion processes, homogenous of degree one, partioned into a primary factor

transformation m � n matrix, Ar, and an intermediate commodity transformation

n � n matrix Aq. Let G(w, p) denote a linear factor market supply function defined

over all factor prices w (m1 1) and commodity prices p (n � 1), and let F(w, p)denote a linear commodity market demand function defined over all factor prices

w and commodity prices p.47 Thus, the assumptions above linearise the Walras-

Cassel model. Note, that the factor supply and commodity demand functions are not

assumed to be homogenous of degree zero in w and p.48 Under the assumption of

linearity of the factor supply and commodity demand functions the G and Fmatrices (Gr (m � m), Gq (m � n), Fr (n � m), Fq (n � n)) may be partitioned as:

Grwþ Gqp ¼ r and Frwþ Fqp ¼ q (3.26)

where q specifies a vector of final demand quantities, and r a vector of factor supplyquantities. Transforming factors into commodities require the following condition

on primary factor transformations:

45 Dorfman et al. (1958), p. 352 (footnote).46 The exposition in this section is based on Harrington’s own presentation of the subject.47 The factor supply functions are specified in the factor markets, the commodity demand functions

are specified in the commodity markets, and the transformation matrices are specified in the

production sectors.48 It is impossible to meet both the specification of linearity and homogeneity of degree zero in the

same function. Since F and G are matrices of constants they are by definition homogeneous of

degree one.


Arz ¼ r (3.27)

Intermediate commodity transformations require:

½I� Aq�z ¼ q (3.28)

where z represents a vector of gross output per sector. [I � Aq] referred to as the

Leontief matrix, is based on the conditions of conventional input–output analysis,

hence, its inverse exists. Consequently:

½I� Aq��1q ¼ z (3.29)

Given the specification above, the condition of efficient pricing implies that the

final commodity price must equal the sum of factor costs and the cost of intermedi-

ate commodities required in the production of a unit of the final commodity. Thus:

A0rwþ A0

qp ¼ p (3.30)

The first term is the price component of rewards to primary factors and the

second term is the price component of rewards to intermediate commodities at their

market prices.49

Solving Eq. 3.30 for p gives:

A0rw ¼ p� A0

qp (3.31)

A0rw ¼ I� A0

q

� �p (3.32)

I� A0q

� ��1A0

rw ¼ p (3.33)

Substituting from Eqs. 3.29 and 3.33 into Eq. 3.26 gives:

Grwþ Gq I� A0q

� ��1A0

rw ¼ Ar½I� Aq��1q (3.34)

Frwþ Fq I� A0q

� ��1A0

r w ¼ q (3.35)

Pre-multiplying Eq. 3.35 by Ar ½I� Aq��1, direct and indirect factor

requirements, gives:

49 This equation is equivalent to the price formulation of input–output analysis. The price system

appears as the dual of the quantity system, and vice versa, and the two can be studied indepen-

dently. Following these principles, we obtain the transpose of Aq and Ar,, which is denoted by A0q

and A0r.

Appendix 1: The Reformulation of the Walras-Cassel Model 45

Ar ½I� Aq��1Frwþ Ar½I� Aq��1Fq½I� A0q��1

A0r w ¼

Ar½I� Aq��1q ð3:36Þ

It follows that:

Gq ¼ Ar½I� Aq��1 Fq (3.37)

Gr ¼ Ar½I� Aq��1 Fr (3.38)

Equations 3.37 and 3.38 specify the effects of commodity demand functions on

factor supplies (direct and indirect factor requirements) necessary for the efficient

production, (3.27) and (3.28), and the efficient pricing condition (3.30) to hold.

Equation 3.37 specifies these conditions on the commodity price matrix assuming

that Fq is specified, and Eq. 3.38 specifies these conditions on the factor price

matrix assuming that Fr is specified. Given the assumptionm ¼ n and the rank of Ar

is equal to n the generalized inverse50 of Ar exists. Thus, applying the generalized

inverse of {Ar [I � Aq]�1} to Eq. 3.38 gives:

Fr ¼ ½I� Aq�½A0r Ar��1A0

rGr (3.39)

Equation 3.39 specifies the generation of the income constraint on demand.

Similarly, Eq. 3.38 specifies the generation of the income constraint on the factor

supply functions. Hence, the commodity demand functions and the factor supply

functions may be specified by the Cassel-Wald specification:

FðpÞ ¼ q and GðwÞ ¼ r (3.40)

which together with Ar and Aq specify a consistent linear system without loss of the

generality of Dorfman, Samuelson and Solow specification of the Walrasian equi-

librium system. As a consequence, commodity prices can be expressed as function

of factor prices alone, using the non-substitution theorem of Samuelson (1951).

The Fr and Gq matrices of the linearised Walras-Cassel model are completely

specified by the Fq, Gr, Ar and Aq matrices together with the conditions of efficient

production, Eqs. 3.27 and 3.28, and the efficient pricing condition (3.30). Thus, the

information contained in Gq and Fr in the Walrasian specification is redundant.

Both functions (F and G) together with the specifications given above specify a

system homogeneous of degree zero in w and p. This implies, that the F and Gfunctions need no longer be specified with homogeneity of degree zero. The

equations in (3.40) can be converted to inverse form:

50 For details, see Penrose, R., (1955). A summary is given in Maddala, G. S., (1977).


w ¼ G�1ðrÞ and p ¼ F�1ðqÞ (3.41)

where G�1 and F�1 are the inverses of G and F, respectively. Hence, the objectionby Dorfman, Samuelson and Solow that this inversion is not admissible in general

does not hold for the linearised Walras-Cassel model.

Appendix 2: Tables 3.2, 3.3, 3.4, 3.5, and 3.6

Table 3.2 Sectors and their definitions in the model

Sector Definition Column Definition

1 Agriculture, fishing 1 Domestic production (Z)

2 Forestry 2 Non-competitive imports (m)

3 Mining and quarrying 3 Competitive imports (M)

4 Sheltered food industry 4 Exports (E), 1980 values

5 Exposed food industry 5 Change in domestic production

6 Beverage and tobacco

industry

6 Change in competitive imports

7 Textile and clothing

industry

7 Change in exports

8 Wood, pulp and paper

industry

8 Capacity utilization in percent of the sectorally

established capital stocks

9 Printing industry 9 Percentage share of domestic production

10 Rubber products

industry

10 Percentage share of competitive imports

11 Chemical industry 11 Net trade ratio (E � M)/(E þ M), 1 only

exports, �1 only imports, 0 balance

12 Petroleum and coal

industry

12 Private consumption (x)

13 Non-metallic mineral

products

13 Equilibrium prices (p) of the quadratic

variables (x) – indexed at 1,000

14 Basic metal industries

15 Engineering, excl.

shipyards

16 Shipyards

17 Other manufacturing

18 Electricity, gas, heating

and water

19 Construction

20 Merchandise trade

21 Transport and

communications

22 Housing

23 Private services

24 Foreign tourist services

Appendix 2: Tables 3.2, 3.3, 3.4, 3.5, and 3.6 47

Table of 1980 statistics – million Skr – 1975 prices

Column

1 2 3 4 5678 9 10 11 12 13Sector

1 14,202 1,863 1,007 1,174 000100 2.69 1.13 0.08 6,617 1,000

2 8,388 284 272 129 000100 1.55 0.30 �0.36 230 1,000

3 4,381 6,371 1,712 2,457 000100 0.81 1.92 0.18 43 1,000

4 23,915 38 1,484 773 000100 4.41 1.66 �0.32 16,549 1,000

5 12,769 645 2,664 758 000100 2.36 2.99 �0.56 9,333 1,000

6 12,149 383 256 93 000100 2.24 0.29 �0.47 11,285 1,000

7 14,439 154 7,636 2,599 000100 2.66 8.54 �0.49 17,549 1,000

8 44,252 51 2,625 19,680 000100 8.17 2.94 0.76 4,374 1,000

9 11,544 0 610 413 000100 2.13 0.68 �0.19 2,772 1,000

10 1,941 19 1,097 599 000100 0.36 1.23 �0.29 991 1,000

11 16,796 995 8,681 6,096 000100 3.10 9.73 �0.18 4,479 1,000

12 19,188 26 6,159 2,300 000100 3.54 6.90 �0.46 6,125 1,000

13 5,878 0 1,447 1,022 000100 1.08 1.62 �0.17 396 1,000

14 18,875 96 5,342 8,123 000100 3.48 5.99 0.21 – –

15 84,100 0 32,90238,045 000100 15.52 36.88 0.07 13,122 1,000

16 5,138 0 722 1,660 000100 0.95 0.81 0.39 1,363 1,000

17 2,908 0 1,045 506 000100 0.54 1.17 �0.35 2,125 1,000

18 11,571 0 110 108 000100 2.14 0.12 �0.01 4,386 1,000

19 49,971 0 0 0 000100 9.22 0 0.00 – –

20 50,818 0 1,230 1,561 000100 9.38 1.38 0.12 – –

21 35,208 0 3,487 7,685 000100 6.50 3.91 0.38 7,047 1,000

22 33,683 0 0 0 000100 6.22 0 0.00 31,459 1,000

23 59,752 0 2,860 3,258 000100 11.03 3.21 0.07 19,719 1,000

24 0 0 5,861 2,960 000– 0 6.57 �0.37 3,171 1,000

Total 541,86610,92589,209101,728000 163,134


Table

3.3

Application1:Tem

porary

equilibrium

–period1

Column

12

34

56

78

910

11

12

13

Sector

115,590

2,082

816

1,174

1,388

�191

0100

2.69

0.91

0.18

7,168

750

29,227

312

266

129

839

�60

100

1.59

0.20

0.35

238

750

34,819

7,008

1,271

2,457

438

�441

0100

0.83

1.42

0.32

68

750

426,306

42

2,642

773

2,391

1,158

0100

4.55

2.94

�0.55

19,453

750

514,044

709

2,549

758

1,275

�115

0100

2.43

2.84

�0.54

10,005

750

613,364

421

093

1,215

�256

0100

2.31

01.00

12,150

735

715,884

169

11,219

2,599

1,445

3,583

0100

2.75

12.50

�0.62

22,504

750

848,675

56

256

19,680

4,423

�2,369

0100

8.41

0.29

0.97

5,027

750

912,699

0465

413

1,155

�145

0100

2.19

0.52

�0.06

3,219

750

10

2,135

21

1,117

599

194

20

0100

0.37

1.24

�0.30

1,101

750

11

18,476

1,094

8,659

6,095

1,680

�22

0100

3.19

9.65

�0.17

5,222

750

12

21,113

29

5,789

2,300

1,925

�370

0100

3.65

6.45

�0.43

6,677

750

13

6,466

01,082

1,022

588

�365

0100

1.12

1.21

�0.03

456

750

14

16,422

84

7,426

8,123

�2,453

2,084

079

2.84

8.28

0.04

––

15

92,508

027,832

38,045

8,408

�5,070

0100

15.99

31.02

0.16

14,683

750

16

00

5,917

1,660

�5,138

5,195

00

06.59

�0.56

1,637

750

17

3,200

0967

506

292

�78

0100

0.55

1.08

�0.31

2,287

750

18

12,399

00

108

828

�110

097

2.14

01.00

4,744

226

19

50,637

00

0666

00

92

8.75

00.00

––

20

55,899

061

1,561

5,081

�1,169

0100

9.66

0.07

0.92

––

21

38,728

02,716

7,685

3,520

�771

0100

6.69

3.03

0.48

7,944

750

22

34,298

00

0615

00

93

5.92

00.00

32,074

181

23

65,729

01,687

3,258

5,977

�1,173

0100

11.36

1.88

0.32

21,460

750

24

00

6,991

2,690

01,130

0–

07.79

�0.44

4,301

750

Total

578,617

12,027

89,728

101,728

36,751

519

0182,418


Table

3.4

Application2:Tem

porary

equilibrium

–period2

Column

12

34

56

78

910

11

12

13

Sector

117,149

2,290

01,174

1,559

�816

0100

2.90

01.00

7,135

1,015

29,975

338

0129

748

�266

098

1.69

01.00

260

436

35,162

7,507

02,457

343

�1,271

097

0.87

01.00

64

1,042

428,937

46

199

773

2,631

�2,443

0100

4.89

0.22

0.59

18,933

1,045

515,448

780

1,557

758

1,404

�992

0100

2.61

1.75

�0.35

9,884

1,045

614,700

463

093

1,336

00

100

2.48

01.00

13,383

624

717,474

186

8,947

2,599

1,590

�2,272

0100

2.95

10.07

�0.55

21,616

1,045

849,430

57

019,680

755

�256

092

8.35

01.00

5,925

655

913,969

00

413

1,270

�465

0100

2.36

01.00

3,591

792

10

2,349

23

983

599

214

�134

0100

0.40

1.11

�0.24

1,081

1,045

11

20,323

1,204

7,383

6,095

1,847

�1,276

0100

3.43

8.31

�0.10

5,089

1,045

12

23,227

31

3,175

2,300

2,114

�2,614

0100

3.93

3.57

�0.16

6,578

1,045

13

6,933

00

1,022

467

�1,082

097

1.17

01.00

527

703

14

202

120,093

8,123

�16,220

12,667

01

0.03

22.62

�0.42

––

15

101,760

032,424

38,045

9,252

4,592

0100

17.20

36.50

0.08

14,403

1,045

16

00

6,855

1,660

0938

0-

07.72

�0.61

1,588

1,045

17

3,519

0427

506

319

�540

0100

0.59

0.48

0.08

2,258

1,045

18

12,429

00

108

30

00

91

2.10

01.00

5,057

324

19

41,088

00

0�9

,549

00

74

6.94

00.00

––

20

57,836

00

1,561

1,937

�61

094

9.77

01.00

––

21

42,602

00

7,685

3,874

�2,716

0100

7.20

01.00

8,023

978

22

34,870

00

0572

00

92

5.89

00.00

32,646

238

23

72,302

00

3,258

6,573

�1,687

0100

12.22

01.00

22,248

887

24

00

6,789

2,690

0�2

02

0–

07.64

�0.43

4,099

1,045

Total

591,683

12,926

88,832

101,728

13,066

�896

0184,388


Table

3.5

Application3:Tem

porary

equilibrium

–period3

Column

12

34

56

78

910

11

12

13

Sector

17,912

1,057

11,689

1,174

�9,237

11,689

042

1.30

12.28

�0.82

7,569

803

29,638

326

0129

�337

00

88

1.58

01.00

283

328

31,464

2,129

9,622

2,457

�3,698

9,622

026

0.24

10.11

�0.59

84

803

431,831

51

259

773

2,894

60

0100

5.21

0.27

0.50

21,220

803

516,992

858

0758

1,544

�1,557

0100

2.78

01.00

10,774

668

616,168

510

093

1,468

00

100

2.65

01.00

14,789

570

719,218

205

11,101

2,599

1,744

2,154

0100

3.15

11.67

�0.62

25,541

803

851,131

59

019,680

1,701

00

94

8.38

01.00

7,165

524

915,236

00

413

1,267

00

99

2.50

01.00

4,407

544

10

2,584

25

916

599

235

�67

0100

0.42

0.96

�0.21

1,168

803

11

22,359

1,324

6,211

6,095

2,033

�1,172

0100

3.66

6.53

�0.01

5,674

803

12

25,549

35

1,372

2,300

2,322

�1,803

0100

4.19

1.44

0.25

7,012

803

13

6,808

00

1,022

�125

00

87

1.12

01.00

636

547

14

00

21,104

8,123

�202

1,011

00

022.18

�0.44

––

15

111,940

017,665

38,045

10,180

�14,759

0100

18.34

18.56

0.37

15,631

803

16

00

7,296

1,660

0441

0-

07.67

�0.63

1,804

803

17

3,872

0250

506

353

�177

0100

0.63

0.26

0.34

2,385

803

18

12,842

00

108

413

00

94

2.10

01.00

5,404

250

19

37,409

00

0�3

,679

00

61

6.13

00.00

––

20

60,381

00

1,561

2,545

00

89

9.89

01.00

––

21

44,496

00

7,685

1,894

00

95

7.29

01.00

9,930

468

22

35,493

00

0623

00

86

5.81

00.00

33,269

170

23

77,067

00

3,258

4,765

00

97

12.63

01.00

26,187

434

24

00

7,679

2,690

0890

0–

08.07

�0.48

4,989

803

Total

610,387

6,578

95,164

101,728

18,704

6,332

0205,921


Table

3.6

Application4:Tem

porary

equilibrium

–period4

Column

12

34

56

78

910

11

12

13

Sector

121

321,893

1,174

�7,891

10,204

00.24

022.32

�0.90

8,446

602

29,943

337

0129

305

00

94

1.59

01.00

308

240

30

013,973

2,457

�1,464

4,351

00

014.25

�0.70

124

602

435,014

56

2,372

773

3,183

2,113

0100

5.60

2.42

�0.51

25,839

602

517,587

888

0758

595

00

94

2.81

01.00

12,200

469

617,787

561

093

1,619

00

100

2.84

01.00

16,348

524

721,140

225

17,057

2,599

1,922

5,956

0100

3.38

17.39

�0.74

33,451

602

852,694

61

019,680

1,563

00

94

8.43

01.00

8,748

393

916,752

00

413

1,516

00

100

2.68

01.00

5,457

413

10

2,842

28

908

599

258

�80

100

0.45

0.93

�0.21

1,343

602

11

24,591

1,457

5,474

6,095

2,235

�737

0100

3.93

5.58

0.05

6,856

602

12

28,102

38

02,300

2,553

�1,372

0100

4.49

01.00

8,114

500

13

6,318

00

1,022

�490

00

84

1.01

01.00

778

408

14

00

21,506

8,123

0402

0–

021.93

�0.45

––

15

118,694

00

38,045

6,754

�17,665

096

18.98

01.00

19,311

409

16

00

5,266

1,660

0�2

,030

0–

05.37

�0.52

2,239

602

17

4,258

0145

506

386

�105

0100

0.68

0.15

0.55

2,642

602

18

13,368

00

108

526

00

95

2.14

01.00

5,789

168

19

28,456

00

0�8

,953

00

69

4.55

00.00

––

20

62,939

00

1,561

2,558

00

95

10.07

01.00

––

21

47,320

00

7,685

2,824

00

97

7.57

01.00

12,285

343

22

36,152

00

0659

00

93

5.78

00.00

33,928

122

23

81,343

00

3,258

4,276

00

96

13.01

01.00

30,911

321

24

00

9,476

2,690

01,797

0–

09.66

�0.56

6,786

602

Total

625,322

3,653

98,070

101,728

14,935

2,906

0241,903


References

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Staff Pap 16:159–178

Bergman L (1986) ELIAS: a model of multisectoral economic growth in a small open economy.

IIASA, Laxenburg

Blattner N (1977) Intraindustrieller Aussenhandel; Empirische Beobachtungen im Falle der

Schweiz und Teoretische Interpretationen. Weltwirdschaftliches Archiv 113(1):88–103

Dervis K, de Melo J, Robinson S (1982) General equilibrium models for development policy.

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McGraw-Hill, New York, pp 346–389

Ems E (1988) Exportindustrins framtid, SIND 1988:2. Stockholm

Enke S (1951) Equilibrium among spatially separated markets: solutions by electric analogue.

Econometrica 19:40–47

Erixon L (1988) Loner och konkurrenskraft – lonekostnadernas betydelse for Sveriges

marknadsandelar. I Ems (ed) Exportindustrins Framtid, SIND 1988:2

Flam H (1981) Growth, allocation and trade in Sweden, vol 12, Institute for International

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J Polit Econ 40:557–616

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Krugman P (1980) Scale economies, product differentiation and the pattern of trade. Am Econ Rev

70(5):950–959

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10:151–175

Lundberg L (1988) The Nordic countries and economic integration in Europe: trade barriers and

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Chapter 4

A Market with Autonomous Economic Decision

Makers: Features of the CGE Model

Alternative to the standard linear programming model in the previous chapter,

where the central planner is the maximising actor, economic models have been

developed that attempt to capture the endogenous role of prices and the workings of

the market system, where the essence of the general equilibrium problem is the

reconciliation of maximising decisions made separately and independently by

various actors. The objective of this literature is to convert the Walrasian general

equilibrium structure, from an abstract representation of an ideal economy (Arrow

and Debreu model 1954) into numerical estimates of actual economies.

In the construction of applied general equilibrium models two different

approaches must be emphasised.1 On one hand, the computable general equilibrium(CGE) models introduced by Adelman and Robinson (1978), extending the

approach of Johansen (1960),2 which, given a set of excess demand equations,

simulate the behaviour of producers and consumers to study the competitive

adjustment mechanism of a system of interdependent markets. One the other

hand, the activity analysis general equilibrium (AGE) models introduced by

Ginsburgh and Waelbroeck (1975) and Manne (1977), which are characterised by

inequality constraints and specified as a mathematical programming problem to

examine the optimisation solutions of which are a competitive equilibrium. The

linear programming model, based on the traditional Koopmans activity model, was

presented in the previous chapter. Now, we will present the basic features of the

CGE-model.

1 See Bergman (1990) for a survey of the development of the computable general equilibrium

model. See also Borges (1986).2 The first successful implementation of an applied general equilibrium model is due to the

pathbreaking study by Johansen (1960) of the Norwegian economy. Johansen retained the fixed-

coefficients assumption in modeling intermediate demand, but employed Cobb-Douglas produc-

tion functions in modeling the substitution between capital and labour services and technical

change.



55

4.1 The Basic Structure

Rather than being a single maximisation problem, the CGE model involves the

interaction and mutual consistency of a number of maximisation problems sepa-

rately pursued by a variety of economic actors. The problem involves the reconcili-

ation of distinct objectives and not only the maximisation of a single indicator of

social preference.3 As we know from Chap. 2, the duality theorem ensures that the

objective function of the dual will equal, at optimum, the objective function of the

primal. Thus, an overall budget constraint is satisfied. Nothing guarantees, how-

ever, that the budget constraints of the individual actors in the economy are

satisfied. The essence of the general equilibrium problem is the reconciliation of

maximising decisions made separately and independently by various actors in an

economic system. In that sense, this problem is absent from the standard linear

programming model, where the central planner is the only maximising actor. That

is to say, the problem arises when one attempts to go from the shadow prices of

linear programming model to the market-clearing prices of general equilibrium

theory.4 Theoretically, market equilibrium prices are prices at which the demand

and supply decisions of many independent economic actors maximising their

profits and utilities given initial endowments are reconciled.

In the CGE model we incorporate the fundamental general equilibrium links

representing the decentralised interaction of various actors in a market economy.

Thus, prices in the CGE model must adjust until the decisions by the producers are

consistent with the decisions made by the various actors representing final demand.

This implies that the model includes a general feedback mechanism that would

require an adjustment in prices, i.e., and the workings of market-clearing processes.

In addition, the CGE model can accommodate different types of distortions, such as

taxes and tariffs or monopolistically fixed factor prices. However, most CGE

models conform only loosely to the theoretical general equilibrium paradigm.

The CGE model seems to address issues we recognise from macro-econometric

models. But what are then the differences between the traditional macro-

econometric models and the CGE models? In short, the macro-econometric models

have a very high content of statistics, but almost no content based on economic

theory. In other words, one tries to find a pattern in the data, i.e., subsequently

explained by economic phenomena. The macro-econometric models are located

somewhere in between, drawing both on classical statistical methods as well as

some economic theory. The macro-econometric models usually address macro

issues such as the role of inflation or Keynesian unemployment. In this respect,

the empirical content is crucial in the macro-econometric model but the connection

to economic theory (optimisation behaviour) is small.

3 A presentation of the theoretical structures underlying the CGE models and their relationship to

economic theory, see: Dervis et al. (1982).4 Taylor (1975).

56 4 A Market with Autonomous Economic Decision Makers: Features of the CGE Model

http://dx.doi.org/10.1007/978-3-642-34994-2_2

With CGE modelling, however, one starts with a theoretical model, i.e.,

maximisation behaviour of the individual actors in the economy, and then finds

data that fits the model. The used data are estimated independently and which are

reported in the literature and are then calibrated to represent a situation close to

general equilibrium. The CGE model cannot address macro issues such as the role

of inflation or Keynesian unemployment but market-clearing prices, and thus,

questions of economic efficiency, is important. Consequently, the content of eco-

nomic theory is crucial but the weakness is the lack of empirical validation of the

model.

The empirical implementation of general equilibrium models starts with Leif

Johansens (1960) path-breaking MSGmodel of the Norwegian economy. However,

it was in the early 1970s that a major breakthrough made possible the development

of detailed and complex general equilibrium models, which could be solved

computationally. The breakthrough was the introduction of an algorithm for the

solution of the general equilibrium problem, i.e., for the computation of equilibrium

prices – which was developed by Herbert Scarf (1967). The most striking aspect of

this algorithm was its general nature. In fact, it was guaranteed to converge, i.e., find

the equilibrium vector of prices, under most general conditions. Since the algorithm

is based on the proof of existence of equilibrium prices, and actually follows the

steps used in that proof, it is guaranteed to work without any constraints on the

specification of the model, apart from the general requirement that excess demand

functions be continuous and that Walras’s law be observed.5

There is no precise definition of a CGE model. The group of related numerical

multisectoral economic models usually referred to as CGE models has a set of

common features. One of these is that both quantities and prices are endogenously

determined within the models. In this respect CGE models differ to a great extent

from input–output and programming models. Another feature is that CGE models

in general can be numerically solved for market clearing prices for all product and

factor markets. CGE models are generally focused on the real side of the economy,

although financial instruments and financial markets are included in some models.

The CGE approach descends directly from the work of Arrow and Debreu

(1954) and uses the Walrasian general equilibrium framework calibrated by real-

world data to ensure consistency with observed empirical facts. CGE models can

also be seen as a logical culmination of a trend in the literature on planning models

to add more and more substitutability and nonlinearity to the basic input–output

model.

Nevertheless, existing CGE models have often retained the assumptions of fixed

coefficients for intermediate technology and the compositions for capital

commodities. In contrast, the production technology for primary factors is

described by a neoclassical production function that allows smooth substitution

among several factor inputs. The degree of substitution is governed by the elasticity

of substitution specified. Intermediate inputs are required according to fixed

5 For a general discussion, see Shoven and Whalley (1992), pp. 37–68.

4.1 The Basic Structure 57

input–output coefficients; aggregated labour and capital are combined to create

value added according to a specified production (Cobb-Douglas or CES) function.

Aggregate labour is an aggregation of labour of different types, and the aggregate

capital used in each sector is a linear aggregation of capital commodities from

different sectors. Sectors are assumed to maximise profits, and labour demand

functions come from the first order conditions equating the wage with the marginal

revenue product of labour of each category.

For each sector, the production function describes the technology available.

Given the level of demand by sector, producers minimise costs by using optimal

quantities of primary factors and intermediate commodities as a function of their

relative prices. Once the optimal combination of inputs is determined, sectoral

output prices are calculated assuming competitive supply conditions in all markets.

Since each sector supplies inputs to other sectors, output prices and the optimal

combination of input are determined simultaneously for all sectors. The assumption

of perfect competition in commodity markets amounts to assuming that firms take

commodity price as given. Under these circumstances one can treat each sector as

one large price-taking firm.

Domestic supply of each sector is given by a constant-returns Cobb-Douglas or

CES production function with labour of different skill categories and sector-specific

capital stocks, which is assumed fixed within each period, subject to depreciation.

This implies that current investment will add to capacity only in future periods.

Hence the production function (ex post) will exhibit decreasing returns to scale in

labour, the only variable. Unit production costs will be a function of the level of

output, and a given sector can always maintain international competitiveness by a

suitable change in the scale of operation. Thus, complete specialisation is avoided.

4.2 The Construction of a Simple CGE Model

In this section we will discuss the construction of a simple computable general

equilibrium model (CGE model).6 Our example is a model of constant to returns to

scale production functions. We use the Cobb-Douglas production function with

constant returns to scale to illustrate the fact that with a linear homogenous

production function it is possible to derive factor demand functions and unit cost

equations. First we set up a formal model for an economy with constant returns to

scale in production, and then extends the analysis by showing how inter-industry

flows (input–output flows) and a foreign sector can be included in the model.

The nature of supply and demand functions is dictated by economic theory. The

consumer is assumed to maximise utility subject to a budget constraint which states

that the household’s total expenditure on commodities (consumption, denoted X)must be equal to the consumer’s income R.

6 The model is based on Dinwiddy and Teal (1988).


Maximise U ¼ UðX1; Xi; . . .XnÞ (4.1)

Subject to p1X1 þ piXi; . . . pnXn ¼ R (4.2)

From the solution to the consumer’s constrained optimisation problem come the

demand relations

X1 ¼ X1ðp1X1 þ piXi; . . . pnXn;RÞ (4.3)

showing that consumption depends upon commodity prices and income.

The Cobb-Douglas production function is assumed to be linear and homogenous,

increasing all the factor inputs by a given proportion will lead to an equi-

proportionate increase in output (Zj), i.e., there are constant returns of scale.

Zj ¼ Kαj L

1�αj (4.4)

Using the v and w to represent respectively the prices of capital and labour the

total cost (TC) of the representative firm is given by

TCj ¼ vKj þ wLj (4.5)

From Eq. 4.4 we can solve for Kj in terms of Zj and Lj:

Kj ¼ ZJ

LJ1�α

� �1α

(4.6)

Substituting Eq. 4.6 in Eq. 4.5, and minimising this function with respect to Lj,gives the necessary condition:

@TCJ

@LJ¼ �v

1� α

α

� �ZJLJ

� �1α þ w ¼ 0 (4.7)

Solving for Lj, to find the conditional demand for labour:

Lj ¼ 1� α

α

v

w

� �α

Zj (4.8)

Similarly, we can solve for Lj, from Eq. 4.4 in Eq. 4.5, and minimising this

function with respect to Kj, gives the necessary condition:

Lj ¼ ZJKJ

α

� � 1

1� α(4.9)

4.2 The Construction of a Simple CGE Model 59

Substituting Eq. 4.9 in Eq. 4.5 gives a functioning that is minimised with respect

to Kj and thus gives the necessary condition:

@TCJ

@KJ¼ v� w

α

1� α

� � ZJ

KJ

� � 1

1� α ¼ 0 (4.10)

Enables us to derive the conditional demand for capital:

Kj ¼ α

1� α

w

v

� �1�αZj (4.11)

The two Eqs. 4.8 and 4.11 represent the two conditional demands for the factors

of production labour and capital when the firm’s production function is given by the

constant returns of scale version of the Cobb-Douglas function.

These two equations (unit cost equations) can be written in terms of factor

demand per unit of output (value added) by dividing both sides of the equation by

Zj. Denoting the per unit factor demands for capital and labour by the lower case

letters kj and lj, we have

kj ¼ KJ

ZJ

� �¼ α

1� α

w

v

� �1�α(4.12)

lj ¼ LJZJ

� �¼ 1� α

α

v

w

� �α

(4.13)

showing that the per unit factor demands are functions of the two factor prices rand w. By using these two equations the expression defining the firm’s profit can be

written in terms of kj and lj, i.e., the unit profit equation

Πj ¼ pjZj � vkjZj � wljZj (4.14)

This makes it clear that the perfectly competitive profit-maximising firm with

constant returns to scale will make zero profits. Only with zero profits can a firm

with a constant return to scale technology be in equilibrium, and this equilibrium is

compatible with any one of the set of possible output levels. The unit cost (price)

equation can also be written in terms of k and l.

Pj ¼ vkj þ wlj (4.15)

Note, that there is no supply function with constant returns to scale. This implies

that we must use the unit cost function above.

In the open economy model it is assumed, for simplicity, that commodity 1 is

exported (E) and commodity 2 is imported (M). Thus

E ¼ Z1 � X1 (4.16)

M ¼ X2 � Z2 (4.17)


With this in mind, we have now to incorporate inter-industry flows

(input–output) in the model. We assume two firms and two commodities, 1 and 2.

Total output (Z) of the two firms is given by:

Z1 ¼ a11Z1 þ a12Z2 þ X1 þ E1 (4.18)

Z2 ¼ a21Z1 þ a22Z2 þ X2 �M2 (4.19)

We can now more closely see the relationship between total output (Z) and

value added. The assumption of fixed coefficients for intermediate inputs implies

that there is no substitution possible between these inputs. The production function

now compromising the intermediate inputs zij together with the value-added

components, i.e., Kj and Lj. This can be written:

Zj ¼ zij;K:αj L

:1�αj i ¼ 1; 2 (4.20)

In order to preserve full-employment of our model, we shall assume that

substitution between the primary factors K and L is possible, and that it still

represents a linear homogeneous function. This will again mean that price the per

unit of output will be equated with the unit cost of production. In the input–output

model, cost per unit will include not only capital and labour costs, but also the cost

per unit of inter-industry inputs. Thus, the unit prices for the two firms are:

p1 ¼ a11p1 þ a21p2 þ vk1 þ wl1 (4.21)

p2 ¼ a12p1 þ a22p2 þ vk2 þ wl2 (4.22)

In this simple model we are assuming that the total quantity of capital and labour

are fixed. The market clearing equations therefore take the form:

K1 þ K2 ¼ K� (4.23)

L1 þ L2 ¼ L� (4.24)

The household’s income R has to be defined. The household not only supplies

the factor service (labour), but is also the sole shareholder in the economy. The

income of the household is therefore defined by the following equation:

R ¼ vðK1 þ K2Þ þ wðL1 þ L2Þ (4.25)

The economy engaged in world trade is presented with given world market

prices, p1W and p2

W, which will not be affected by the country’s level of exports (E)and imports (M). Thus, the open economy includes two set of prices, endogenous

domestic production costs and exogenous world market prices. The open economy

4.2 The Construction of a Simple CGE Model 61

also includes the exchange rate (ER). Hence, the world market prices are converted

to domestic prices by:

p1 ¼ ER p1W (4.26)

p2 ¼ ER p2W (4.27)

The world market prices, p1W and p2

W , are treated as exogenous variables in a

small open economy. For commodities in trade, the domestic production costs

are, in equilibrium, equal to the exogenous world market prices. ER is, however,

an endogenous variable.

Assuming here that capital flows are excluded from the model, the balance of

payments equation may be described as:

p1WE� p2

WM ¼ 0 (4.28)

The general equilibrium system is now complete. It consists of 20 equations in

the following 20 endogenous variables: X1, X2, Z1, Z2, K1, K2, L1, L2, k1, k2, l1, l2, p1,p2, w, v, R, E, M. and ER. In addition there are eight exogenous variables: a11, a12,

a21, a22, p1W , p2

W , K*, and L*.The model:

Commodity markets

Household demand X1 ¼ X1(p1, p2, R) (1)

X2 ¼ X2(p1, p2, R) (2)

Unit price equations p1 ¼ a11p1 þ a21p2 þ vk1 þ wl1 (3)

p2 ¼ a12p1 þ a22p2 þ vk2 þ wl2 (4)

Market clearing: (Commodity markets) X1 ¼ a11Z1 þ a12Z2 � E (5)

X2 ¼ a21Z1 þ a22Z2 þ M (6)

Factor markets

Demand k1 ¼ k1(w,v) (7)

K1 ¼ k1Z1 (8)

k2 ¼ k2(w,v) (9)

K2 ¼ k2Z2 (10)

l1 ¼ l1(w,v) (11)

L1 ¼ l1Z1 (12)

l2 ¼ l2(w,v) (13)

L2 ¼ l2Z2 (14)

Market clearing: (Factor markets) K1 þ K2 ¼ K* (15)

L1 þ L2 ¼ L* (16)

Household’s income

R ¼ v(K1 þ K2) þ w(L1 þ L2) (17)

Foreign sector

Price equations p1 ¼ ER p1W (18)

p2 ¼ ER p2W (19)

Balance of payments p1W E � p2

W M ¼ 0 (20)


We often assume that exports and domestically sold commodities, as above, are

perfect substitutes. This specification of export supply, however, over-states both

the links between exports and domestic prices and the responsiveness of exports to

demand shifts on world markets. With the possibility to specify foreign trade, not

only as perfect substitutes as in the linear model, but as a close substitute to

domestic production, and a substitution that can vary according to specification,

the CGE model offers a greater capacity to reflect empirical evidence. As a result,

export prices for any commodity may differ from world market prices as well as

from prices paid on the domestic market, and a country may export and import

commodities in a given sector. In this way the model captures the phenomena of

intra-industry trade. This represents a significant departure from the “small country

assumption” of traditional trade theory in which countries can export any amount

of a given commodity at a given price and nothing at a higher price. Since the

possibility to specify substitution (in production, foreign trade and demand) is very

essential in the CGEmodelling approach, the technique is presented more closely in

the next section. We choose the just discussed, and most frequent, example –

foreign trade.

4.3 Foreign Trade: The CES and CET Specification

In the closed economy the basic technological and demand variables determine the

domestic shadow price system. However, the situation is quite different in a free

trade economy where the domestic market is small in relation to the world market.

Given the assumption of perfect substitutability between imported and domestically

produced commodities, the small-country assumption implies that the individual

country becomes a price taker facing exogenous world market prices. The theory of

international trade suggests that, as far as some commodities are actually imported

or exported, the domestic shadow prices among them tend to converge to their

relative world market prices. Consequently, world market prices determine the

domestic shadow prices of tradables, and a given commodity has (at equilibrium)

the same price whether it is imported or produced domestically. Hence, whereas

supply and demand determine domestic shadow prices in a closed economy, they

will adjust to world market prices in the small open economy.

Needless to say, extreme specialisation in production and trade conflicts with

empirical evidence, which on the contrary, shows a relatively little specialisation on

the sector level. However, the observed combination of domestic production and

trade may be in complete accordance with the theoretical model. First, the country

under study consists of many regions, which implies that a commodity may be

imported to one region and exported from another, but never be both imported to

and exported from one single region. Second, the same argument is applicable

to the fact that the model is specified to cover a period of some length. Hence, a

commodity may be both produced and traded at different points of time during the

4.3 Foreign Trade: The CES and CET Specification 63

period of specification. Finally, the commodities of the model are aggregates of

different commodity categories. For each of these commodities the theoretical

requirement may be fulfilled.

In the standard small-country assumption, often made in international trade

theory, a traded commodity is assumed to be one for which the single country is

a price-taker and the domestically produced commodity is a perfect substitute for

that sold in the world market. The earlier discussion has already stressed that the

small-country assumption leads to the result that the domestic price of a traded

commodity is equal7 to its world price (PWi). Moreover, we also stressed that

assuming perfect substitutability implies that there is no product differentiation

between imports and domestic products and that a commodity will either be

exported or imported but never both (intra-trade is eliminated). This implies that

changes in world market prices, exchange rates and tariff rates, are entirely trans-

lated into changes in domestic prices, and hence, exaggerate the effects of trade

policy over the domestic price system and the domestic economic structure. Fur-

thermore, the small country assumption together with an assumption of constant

returns to scale in production, leads to a tendency toward extreme specialisation in

production that is not always desirable.8 In the discussion above we have repeatedly

stressed that extreme specialisation in production and trade conflicts with empirical

evidence (Flam 1981; Lundberg 1988), which on the contrary shows a considerable

amount of intra-industry trade even within rather disaggregated production sectors.

At a level of high aggregation, each sector represents a bundle of different

commodities. In this model,9 we solve this problem by relaxing the perfect substi-

tutability assumption. Instead, we stipulate that for any traded commodity, imports

Mj (perfectly elastic in supply) and domestically produced commodities xZj are not

perfect but relatively close substitutes. Thus, we relay on the Armington (1969)

assumption that commodities of different origin are qualitatively different

commodities. Formally, we define for each tradable commodity category a com-

posite (aggregate) commodity xj, which is a CES utility function of commodities,

produced abroad (imports, Mj) and commodities produced domestically, xZj . We

have:

xj ¼ ACj δjM�ρjj þ ð1� δjÞxZ�ρj

j

h i�1=ρj(4.29)

where ACj is the CES function shift parameter, δj , the value shares (distribution

parameter) of imports in total domestic expenditure is a constant, and σj , the

7Differences may exist due to transportation costs and tariff rates.8 Samuelson (1952).9 The computable general equilibrium (CGE) model to be described is a variant of the model

developed by Dervis et al. (1982). This section is, in certain parts, based on Condon, Dahl and

Deverajan (1987).


elasticity of substitution between the two sources of supply in all domestic uses, is

given by σj ¼ 1=ð1þ ρjÞ.This formulation implies that consumers (at home as well as abroad) will choose

a mix of Mj and xZj (inputs in the CES utility function “producing” the composite

output xj) depending on their relative prices.10 Minimising the cost of obtaining a

unit of utility (the composite commodity xj):

pjxj ¼ pZj xZj þ pMj Mj (4.30)

Subject to Eq. 4.29 yields:

Mj

xZj¼ pZj

pMj

!σjδj

1� δj

� �σj

(4.31)

where pZj denote the domestic commodity price and pMj denote the domestic currency

price of imports (domestic currency outlay of imports). Thus, the solution is to find a

ratio of inputs (Mj to xZj ) so that the marginal rate of substitution equals the ratio of the

price of the domestically produced commodity to the price of the imported commod-

ity. In standard trade theory the trade substitution elasticity is infinity so that pZj ¼ pMj. If pZj exceeds p

Mj , x

Zj would have to be zero. Equation (4.3) allows for a richer set of

responses,11 but as σj gets larger, the responsiveness of Mj=xZj to changes in pZj =p

Mj

rises. In that case pZj =pMj will stay close to its base value and we approximate the case

wherepZj , at the equilibrium, will stay fixed topMj . On the other hand, ifσj is very low,

large changes in pZj =pMj may take place.12 Thus, as a result of this specification, pZj is

no longer fixed to pMj , it is endogenously determined in the model. The variable pMj ,

however, is linked to the exogenously fixed world market price, pWj by:

pMj ¼ pWj ER (4.32)

where ER is the exchange rate (fixed initially in the model). This implies that we

maintain the assumption of exogenously fixed world market prices of imports.

Turning to export demand standard trade theory assumes that a small country

faces a perfectly elastic demand for its exports. This implies that any balance of

payment problem can be solved by an indefinite expansion of exports at constant

10 Consequently, there can be both import and export of each category of tradable commodities in

equilibrium.11 If the trade substitution elasticity equal unity, the CES utility function reduces to a Cobb-

Douglas utility function.12 In the extreme case where sigma is zero, Mj=x

Zj would be fixed, and imports become perfect

complements of domestic products.


world market prices of the most profitable commodities. This profile of trade may

not be realistic for many countries. While they may not be able to affect the world

market prices with their exports, the countries may register a declining market share

as their domestic costs rise. In addition, increasing selling costs will normally

reduce the net return from exports as the quantity is increased. The most satisfying

way to reflect this situation would be a specification were export demand Ej is a

decreasing function of the domestic export costs (prices) in foreign currency. If we

let pEj denote the domestic currency price of exports (domestic currency receipts of

exports)13 and pWj , as above, the world market price in foreign currency (exoge-

nously fixed), we would have:

pEj ¼ pWj ER (4.33)

Given the assumptions of standard trade theory, the variable pEj is linked to the

exogenously fixed world market price pWj . However, assuming product differentia-

tion leads to less than infinitely elastic demand functions for exports. The individual

country is still regarded as a small country in the world market, hence, pWj is

assumed exogenously fixed. But the foreign currency price of a particular country’s

exports, denoted pWEj , is endogenously determined by its domestic production costs

pZj (average output price), and exchange rate policy ER. We get:

pWEj ¼ pZj

ER(4.34)

Consequently, we consider the following constant elasticity export demand

function:

Ej ¼ Eoj

PWj

pWEj

!nj

(4.35)

where nj is the price elasticity of export demand and Eoj is a constant term reflecting

total world demand for each commodity category and the country’s market share

when, at equilibrium,pWj ¼ pWEj . Logically, the domestic currency price of exports is:

pEj ¼ pWEj ER (4.36)

Given the fact that our country is small, changes in pWEj will not affect pWj , but it

will have effects on our country’s market share for aggregate commodity category j.

13 Foreign currency is here regarded as an intermediate commodity (not desired in itself), where

the import process requires foreign currency as input, and foreign currency is the output of the

export process.


For example, a devaluation of the exchange rate leads to a fall in pWEj and hence,

with constant pWj , an increase in its market shares. Conversely, an increase in

domestic production costs, pZj , leads to an increase in pWEj , and with constant pWj , its

market share will decline. This implies that export prices pEj (or pWEj ) are no longer

fixed to the world market price in foreign currency pWj . The small-country assump-

tion, requiring fixed terms of trade, will no longer hold. Consequently, the small

country assumption is retained only in the sense that world market prices pWj on

international traded commodities is to be regarded as given.

On the supply side exports is usually derived residually by subtracting domestic

demand from total domestic production. Given the standard small-country assump-

tion, domestic production will expand until domestic production costs rise to the

world market price level. As long as domestic production costs are lower than

established world market prices, it will be profitable to expand domestic production

for exports.14 As a result, export supply may exhibit an excessively strong response

to changes in domestic prices. When a domestic price rises, producers are induced to

increase supply and domestic consumers to reduce their demand. The net result is a

dramatic increase in exports. However, in reality, exports may not rise this fast,

because the domestically consumed and exported commodities in the same sector

may be quite different. Thus, the small-country assumption together with the

assumption that the supply of exports is simply the difference between total domestic

production and domestic absorption may in several cases greatly overestimate the

responsiveness of export supply, and again, the problem increases with the degree of

aggregation. Hence, we postulate a constant elasticity of the transformation (CET)

function between domestically consumed xZj and exported Ej commodities:

Zj ¼ ATj γjEjϕj þ ð1þ γjÞxjZ

ϕjh i1=ϕj

(4.37)

Zj is domestic output, ATj is the CET function shift parameter, γj is a constant,

and the elasticity of transformation τj is given by: τj ¼ 1=ð1� ϕjÞ.Maximising the revenue from a given output:

pZj Zj ¼ pZj xZj þ pEj Ej (4.38)

Subject to Eq. 4.37 yields the following allocation of supply between domestic

sales and exports:

Ei

xZi¼ pEi

pZi

� �τi 1� γiγi

� �τi

(4.39)

14On the other hand, if the domestic price is greater than the world market price, the commodity

will not be produced.


This leads to the export price pEj (or pWEj ) diverging from the domestic price pZj .

The supply of exports by sector is a function of the ratio of the price in domestic

currency of exports. This treatment partially segments the export and the domestic

markets. Prices in the two markets are linked together but need not be identical.

Imports and domestic products are assumed to be imperfect substitutes. Imports and

domestic commodities are combined according to a CES trade aggregation func-

tion, with consumers demanding the composite commodity. The trade substitution

elasticity determines the extent to which import shares adjust in response to changes

in relative prices. For both exports and imports, the word price in foreign currency

is assumed to be constant – the small country assumption.


The model is Walrasian in that only relative prices matter. This proposition reflects

the well-known fact that if all prices increase in the same proportion, but relative

prices are unaltered, the relationships in the economy remain unchanged. On order

to solve the model to find the equilibrium prices, we arbitrarily set one price equal

to one, and then solve the system for all other prices. The commodity with price set

equal to unity is known as the numeraire commodity, and the prices of all other

commodities are determined in terms of the numeraire. Provided the general

equilibrium is homogeneous of degree zero it does not matter which commodity

is chosen to be the numeraire. However, in applied models it is convenient to use a

price-normalisation rule that provide a no-inflation benchmark against which all

price changes are relative price changes.15

According to Walras’s law, there cannot be a situation of aggregate excess

demand or supply. In other words, if one market has positive excess demand,

another must have excess supply, to such an extent that in value terms they cancel

out. To see that Walras’s law always hold, it is sufficient that, the total value of

output, and the total value of expenditures balances. This result will always be true

if all economic agents meet their budget constraints. Because each spending unit’s

demand are subject to a budget constraint which says that outlay must equal

income, it is clear that such a budget constraint also hold in the aggregate and

will hold not only at equilibrium, but for all allowable price vectors. The static

model as presented above has no formal link between capital formation and

production capacity. Capital commodities are assumed exogenous without any

correspondence to the effect that is created by the supply of investment from sectors

producing capital commodities (investment in final demand).

15 See Dervis et al. (1982), p. 150.


Appendix: A Summary of Models Presented

The presentation of multisectoral general equilibrium models in this study is now

complete. Here follows a summary of the most essential features:

The Linear Model

The central planner is assumed to be the only maximising actor.

No market (prices and quantity) interaction. In the linear programming model

we interpret the shadow prices that result as a by-product of the solution as

equilibrium prices.

These prices cannot be interpreted as market-clearing prices of general equilib-

rium theory because endogenous prices and general equilibrium interaction to

simulate competitive market behaviour cannot be achieved.

Foreign trade specified as perfect substitutes to domestic production. Only inter-

trade, i.e., full specialisation.

An optimum solution may only be at a vertex or an extreme point.

The Quadratic Model

The quadratic model is an improvement of the welfare function.

The model in Chap. 3 is formulated in terms of the maximisation of the sum of

consumer’s and producer’s surplus. See also page 317–319 in Nicholson. But still

the central planner is assumed to be the only maximising actor.

The existence of a two way feedback in which quantity can influence price and

price can influence quantity for each sector (market interaction), is developed.

Foreign trade specified as perfect substitutes to domestic production. Only inter-

trade, i.e., full specialisation (because the linear constrains are retained).

The optimum value of the objective function might occur anywhere in the

feasible set, but not necessarily at a vertex or an extreme point.

The Computable General Equilibrium (CGE) Model

Alternative to the standard linear (and quadratic) programming model, where the

central planner is the only maximising actor, the CGE model has been developed to

capture the endogenous role of prices and the workings of the market system.

Decisions: The essence of the CGE model is the reconciliation of maximising

decisions made separately and independently by various actors.

Appendix: A Summary of Models Presented 69

http://dx.doi.org/10.1007/978-3-642-34994-2_3

Prices: The model includes a general feedback mechanism that would require an

adjustment in prices, i.e., the workings of market-clearing processes. Theoretically,

market equilibrium prices are prices at which the demand and supply decisions of

many independent economic actors maximising their profits and utilities, given

initial endowments, are reconciled.

Foreign trade: With the possibility to specify foreign trade, not only as perfect

substitutes as in the models above, but as a close substitute to domestic production,

and a substitution that can vary according to specification, the CGE model offers a

more close relation to empirical evidence. In this way the model captures the

phenomena of intra-industry trade.

The reader has to note, that both a neo-classical production function of the value

added component, and inter-industry flows (the input–output flows) in the com-

modity balance equations can be incorporated in the CGE model.

Real World Applications: The GAMS Program

If you are interested in the practical application of real word problems the GAMS

computer program is recommended. GAMS homepage is www.gams.com. Here

you will find the GAMS program library. Here you will also find reference to

literature, tutorials, and course outlines on GAMS.

A short, and here recommended, description on programming in GAMS is AGAMS Tutorial. The handbook A Standard Computable General Equilibrium(CGE) Model in GAMS can be used as a reference book for further studies. Note,

that some references are rather extensive in the number of pages. Hence, study the

reference first on screen, and then print out only the selected parts you need.

The GAMS program itself (student version) can be installed on your computer. It

is possible to download the program (student version) on your own private com-

puter from the GAMS homepage. If you choose to download the GAMS program

from the GAMS homepage, read the instructions carefully.

MPSGE is a mathematical programming system for general equilibrium analy-sis which operates as a subsystem within GAMS. MPSGE simplifies the modelling

process and makes AGE modelling accessible to any economist who is interested in

the application of these models. http://www.gamsworld.org/mpsge/index.htm.

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economy interactions: five approaches. Resources for the Future, Washington, DC

Samuelson PA (1952) Spatial price equilibrium and linear programming. Am Econ Rev

42:283–303

Scarf H (1967) On the computation of equilibrium prices. In: Feliner WJ (ed) Ten economic

studies in the tradition of Irving Fisher. Wiley, New York

Shoven J, Whalley J (1992) Applying general equilibrium. Cambridge University Press,

Cambridge

Taylor L (1975) Theoretical foundations and technical implications. In: Blitzer CR et al (eds)

Economy-wide models and development planning. Oxford University Press, Oxford

References 71

Chapter 5

An Applied Model: The CGE Mini Model

In this chapter a CGE model (the CGE mini model1) is presented. The model is

simple enough to be presented in a few pages and yet complicated enough to

demonstrate the application of the general CGE structure. In short, the focus of

this chapter is to provide examples of structural adjustment in an open economy.

The numerical applications of this chapter will be an examination of the sensitivity

of the model to systematic variation in key variables of the adjustment process.

Here we emphasise the effect of changes (government intervention) in the fixed rate

of real exchange and growth in the capital stock.

5.1 The Basic Structure of the CGE Model

The behaviour of economic agents in this model is designed according to neoclas-

sical microeconomic theory with relative prices playing a major role in the deter-

mination of economic activities. Producers minimise costs subject to a given

production technology, and consumers maximise utility given their total expendi-

ture determined as a constant fraction of their income. Firms (within sectors) are

assumed to maximise profits, and labour demand functions come from the first

order conditions equating the wage with the marginal revenue product of labour of

each category. The model assumes perfect competition in all markets and domestic

and foreign commodities are treated as imperfect substitutes according to

1 The CGE mini-model is included in the GAMS model library which is distributed with the

GAMS system. The CGE mini-model is a minor version of an equilibrium model that originally

comes from Chenery, Lewis, de Melo, and Robinson in their work in designing an equilibrium

development model for Korea. The model is originally designed for the study of three develop-

ment strategies. The first option was the strategy of export expansion, the second option was the

strategy of import substitution, and the third option was a strategy between the two extreme cases.

This model illustrates the basic use of CGE models. See further: Chenery et al. (1986),

pp. 311–347.



73

Armington’s (1969) specification. Exports are determined by an exogenous foreign

demand and the relative export price is measured in foreign currency.2 Prices in the

foreign markets are linked but need not be identical to the domestic market.

However, the world price in foreign currency (dollars) is assumed to be exogenous,

i.e., the small country assumption.3

Thus, the CGE model simulates the working of a market economy. In each

period, it solves for wages and prices that clear the markets for labour and

commodities. The model is Walrasian in that only relative prices matter. The

numeraire against which all relative prices are measured is defined as an index of

domestic prices. The model satisfies Walras’s law, which implies that there cannot

be a situation of aggregate excess supply or demand. However, the model also

comprises non-tradable commodities. Non-tradable commodities are commodities

that are not subject to international trade. Government service as well as housing fit

this category. Intermediate inputs are required according to fixed input–output

coefficients; aggregate labour and capital are combined to create value added

according to a Cobb-Douglas production function. The labour market is segmented

in three distinct categories. Each labour category linked to respective sector. There

is no mobility of labour between sectors within periods. Sectors are assumed to

maximise profits, and labour demand functions come from the first order conditions

equating the wage with the marginal revenue product of labour of each category.

Sectoral capital stocks are fixed within periods, but they change over time given

aggregate growth of the capital stock. Investment is allocated endogenously to

make sectoral rental rates equal. These general characteristics of the CGE model

were stipulated in the preceding chapter. Applications of theoretical models will

often involve a number of compromises in order to make the models more realistic

and more useful in an applied setting.

However, the model does not take into account future markets despite the fact it

explicitly considers time. There is no intertemporal optimisation4 and the agents

have no expectations about future prices. Given this formulation, the model does

not embody the true concept of a dynamic model but rather is akin to comparative

static’s, which analyses periods as a number of discrete moments, using a static

model for each of these moments. Our study is focused on structural adjustment in

pure market variables only. In this model, that implies that improvements in

technology and technological substitution in the process of production, an impor-

tant source of industrial innovation and structural renewal (Freeman 1974), is

omitted as an endogenous variable in the analysis. The explanation is the technical

2 Note, that the export demand function (Eq. 4.35) is not included in the CGE mini model.3 In other words the word price in foreign currency is given. The reader must note, that price

incentive policy such as taxes, subsides, and tariffs are now explicitly incorporated. Domestic

prices can be altered by the government by changes in price incentive policy, and hence, affect the

economic structure.4 In intertemporal models, agents have rational expectations and future markets are considered

when optimising. Endogenous variables follow an optimal path over time and there are no

incentives to deviate from this path at any point of time.

74 5 An Applied Model: The CGE Mini Model

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assumptions that underlie the input–output accounting system. By systematically

generating and incorporating changes in the aggregate technical coefficients, tech-

nological substitution and improvements in technology can be introduced exoge-

nously. Moreover, all investments are in established industries and hence,

according to the specification of the model, directed to the production of a given

set of commodities. In this model a balance between savings and investment is

achieved by setting total investment equal to the sum of domestic and foreign

savings. Thus, total investment is determined by savings in the economy (saving

determined investment). A fixed fraction of the foreign capital inflow is assumed to

enter directly into savings. The reminder being saved by the sectors and a portion of

it being used as private consumption. Domestic savings is made up of government

and private savings. Private savings is in this model specified as a rising function of

GDP. That implies that a rising GDP will increase investment. In the total savings

equation, Eq. 5.33, total depreciation expenditure is included. For example, an

increase in total depreciation expenditure would increase savings, and thus the total

level of investment.

In the real world, investments made to increase the total capacity as well as the

replacement and scrapping of old production units change the production

characteristics. New capacity have in general input–output proportions different

from those of existing production units due to changed relative prices and technical

progress, and in the long run, production of commodities which cannot be found

within the initial production possibility set.

As the reader will recall, the numeraire against which all prices are measured is

defined as an index of domestic prices. Thus, variations in the nominal exchange

rate in the model directly affect the ratio of the price – in domestic currency – of

imports and exports to the price of domestic sales and in that way represent a

change in the real exchange rate. A devaluation increases the domestic price of

imports and exports relative domestic sales, and thus, encourages exports and

import substitution.5 With the price normalisation, the formal presentation of the

core equations of our extended CGE model is complete. The description above

sketches only the particular characteristics of our model. A detailed description of

all mathematical equations is presented in an appendix to this chapter.

5.2 The Numerical Experiments

Given the specification above, we will now be equipped with a numerical general

equilibrium model designed as a tool to determine the optimum resource allocation

and, given the numerical results, the significance of equilibrium. The equilibrium

conditions in the model include a supply–demand balance in three different types of

market: labour, commodity, and foreign exchange. A fourth macroeconomic

5 For a discussion, see Dervis et al. (1982), pp. 192–197.

5.2 The Numerical Experiments 75

equilibrium condition is the balance between saving and investment, i.e., the macro

closure of the model.6

With reference to Dervis et al. (1982)7 the model can easily degenerate into a

magic black box that yields quantitative results but do not really add to our

understanding of the mechanisms governing the model. Considering this comment,

the experiments are designed to outline the basic adjustment mechanisms that will

determine the direction, and hence, the fundamental structure of the solutions.

Following Chenery et al. (1986) the model contains three institutions, namely

production sectors, factors of production, and household types. The production

system comprises three production sectors. The production sectors; agriculture,

industry, and service, represent the whole economy. The production sectors are

associated with a specific labour category, namely agricultural labour, industrial

labour, and service labour.8 Each household category is characterised by a single

type of factor it owns and supplies. Here, there will be two categories of

households; labour household and capitalist household. The labour household

supplying the three different kind of labour and receive the wage rate of value

added, and the capitalist household being the owners of capital and receive the

residual value added.9

Given the assumptions of the model the economy is assumed to be in equilib-

rium, a so called benchmark equilibrium. A benchmark equilibrium data set is a

collection of data in which equilibrium conditions of an assumed underlying model

are satisfied. The benchmark dataset is calibrated to the base year data.10 Calibra-

tion is the process of assignment of numerical values to the model parameters. The

purpose of calibration procedure is to make sure that the solution of the model

reproduces exactly the observed statistics of the base year, and then we only use

base year data as input.11 The method is to calculate values of shift and share

parameters of production functions, Armington functions, and CET functions.12

Since we do not accomplish an empirical comprehensive study, but only use the

6 The choice of which variables are to be exogenous is called the model closure. In all experiments

in this book the exchange rate is fixed and the net flow of foreign borrowing is unfixed. Following

this specification, the trade deficit is free to vary.7 Dervis et al. (1982), p. 183.8 Alternatively, the sectors can be defined in terms of input characteristics; labour-intensive,

capital-intensive, and knowledge-intensive commodities.9 Note, that in equilibrium the expenditures of each household exhaust its income. However, in this

chapter we consider saving. In any case, total income generated in the system always equals total

national product at market prices.10 To compute benchmark equilibrium can also be an alternative if the benchmark year is not

accepted as a representative equilibrium.11 This assumes that the benchmark year is a representative equilibrium.12 The parameters of the functions are calibrated “backwards” from the benchmark dataset

(Petersen 1997). See Shoven and Whalley (1984, 1992). See also Condon et al. (1987).


model as an illustration, we shall use the data supplied with the CGE mini-model.13

As anyone who deals with empirical studies knows, obtaining adequate and reliable

data for the model is the most time-consuming task faced in the study. Therefore the

data collection in this numerical study is reduced to a minimum. The first task is to

present Table 5.1. The table below represents the benchmark equilibrium as it is

presented in the GAMS program library.14 The variables in Table 5.1, together with

the computations in each experiment, will make Tables 5.1, 5.2, 5.3, 5.4, and 5.5

self-contained.

Real exchange rate, general price level, foreign savings, and government con-

sumption are fixed. Capital stock has an upper limit in the short run. Since the CGE

mini model is applied for a particular country, Korea, the computations are in

billion won. Exchange rate is defined as won per dollar. Foreign savings, net

Table 5.1 Benchmark equilibrium

Agriculture Industry Services

Domestic prices 1.000 1.000 1.000

Rate of capital rent 1.000 1.000 1.000

Value added price 0.737 0.291 0.662

Composite commodity supply 711.644 930.351 497.443

Domestic output 657.368 840.050 515.430

Domestic sales 641.704 812.222 492.031

Exports 15.664 27.828 23.399

Imports 69.941 118.129 5.412

Capital stock 657.575 338.708 1548.519

Depreciation by sector 0 0 0

Intermediate uses 256.645 464.166 156.260

Private consumption 452.176 307.856 202.042

Government consumption 2.823 9.881 128.448

Investment by origin – 148.449 10.693

Investment by destination 20.688 46.151 92.302

Domestic price of imports 1.000 1.000 1.000

Domestic price of exports 1.000 1.000 1.000

Average output price 1.000 1.000 1.000

Price of composite commodities 1.000 1.000 1.000

Real exchange rate 1.000, General price level 1.000, Government revenue 194.555, Tariff revenue

28.657, Indirect tax revenue 65.275, Total household savings 66.569, Government savings 53.380,

Total depreciation expenditure 0.000, Total savings 159.142., Total investment 159.142, Foreign

savings 39.174, Net flow of foreign borrowing 58.759, Household tax revenue 100.617, and

Private GDP 1129.261

13As noted, the mini-equilibrium-model is included in the GAMS model library, which is

distributed with the GAMS system. Readers who have access to the GAMS program can thus

take an active part of the model developed here. Readers who also are interested in downloading

the current version of the GAMS distribution will find necessary information in the appendix of

this chapter and Chap. 4.14 See the end of the appendix for this chapter.


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remittances from abroad, and net flow of foreign borrowing is, however, expressed

in billion dollars.

With each equilibrium experiment, follows a presentation of the employment

results. LABOUR1 is agricultural labour, LABOUR2 is industrial labour, and

LABOUR3 is service labour.

Summary matrix with sectoral employment results

LABOUR1 LABOUR2 LABOUR3

Agriculture 2515.900 442.643 –

Industry – 767.776 –

Services – 355.568 948.100

Summary matrix with aggregate employment results


Average wage rate 0.074 0.140 0.152

Labour supply 2515.900 1565.987 948.100

We are now prepared to draw attention to the elaboration of the experiments, and in

this context, evaluate the results of the computations. As is well known, the choice of

Table 5.2 Physical deterioration of the capital stock






Domestic output 643.646 902.741 437.371

Domestic sales 620.343 875.410 423.609

Exports 22.424 27.320 13.311

Imports 44.568 129.840 4.560

Capital stock 657.575 338.708 1032.484

Depreciation by sector 40.964 52.689 160.796












Total depreciation expenditure 254.449, Total savings 343.935, Total investment 343.935, Foreign

savings 39.174, Net flow of foreign borrowing 48.280, Household tax revenue 72.461, and Private

GDP 813.256


endogenous variables are crucial when illustrating the equilibrium mechanism of the

model, and hence implicitly, the specification of numerical experiments.15 Remember,

in all experiments we assume that the exchange rate is fixed and the balance of trade is

endogenous, so that foreign capital inflow adjusts. This redefines the balance of

payments constraint. As a consequence, the value of imports no longer has to be

exactly equal to the value of exports. Further, the foreign capital inflow (net flow of

foreign borrowing) constitutes an addition to the income generated within the econ-

omy, and is also incorporated in the capital income equation.

5.2.1 Capital Stock Subject to Physical Deterioration

As well known to the reader, the capital stock is subject to physical deterioration.

The physical deterioration, depreciation expenditure rates (DEPRj), in this model

are now assumed to be 6 % in agriculture, 15 % in industry, and 15 % in services.

These coefficients have now been added in the equation representing the total

Table 5.3 Devaluation of domestic currency






Domestic output 644.007 899.780 430.067

Domestic sales 605.879 858.884 411.207

Exports 33.190 39.872 18.873

Imports 28.724 111.742 4.103

Capital stock 657.575 338.708 988.527












28.355, Indirect tax revenue 66.867, Total household savings 43.299, Government savings

�4.918, Total depreciation expenditure 249.678, Total savings 355.068, Total investment

335.068, Foreign savings 39.174, Net flow of foreign borrowing �10.169, Household tax revenue

65.460, and Private GDP 734.685

15 The model is solved by the GAMS program. A description of how the system of equations can

be implemented in GAMS, see Condon et al. (1987). See also Lofgren et al. (2002).


depreciation expenditure. That inclusion influences the basic numerical values of

the model. Since we only use this model as an illustration, the assumed values are

without empirical significance. The result from the new computation is presented in

Table 5.2 below.

Table 5.1 provides a comparative benchmark for this experiment. Notice, that

the value of marginal product of capital (rate of capital rent) is the same for all three

sectors. However, the issue of structural transformation naturally emphasises the

importance of including investment as well as disinvestment. Hence, the focus of

the presentation is principally directed to the depreciation expenditure and the

investment by destination. By the introduction of capital depreciation expenditure

rates in the equilibrium model part of the capital stock is not used for domestic

output. In model terms that part is now used for depreciation expenditure. The

direct effect will be a reduction in domestic output in agriculture and services, but

an increase in industry. The capital stock has physically been reduced in the

services sector (Table 5.2). Hence, the strong decrease in domestic output. Effi-

ciency in reallocation has not succeeded to compensate for this loss. The increased

investment in the first period is only the demand for investment. The physical

increase in real capital will be added to the capital stock in the subsequent period.

The assumed state of technology is determined by the production function shift

parameter in the production function. The next period will be presented in Table 5.5.

But we will first focus on the change in the real exchange rate.

Table 5.4 Appreciation of domestic currency






Domestic output 642.468 910.525 446.218

Domestic sales 628.567 892.097 435.946

Exports 13.891 17.037 8.539

Imports 73.868 155.595 5.158

Capital stock 657.575 338.708 1090.138















Private GDP 892.332




Agriculture 2515.900 323.690 –


Services – 363.908 948.100




Labour supply 2515.900 1565.987 948.100

5.2.2 A Change in the Real Exchange Rate

In the second experiment we start with an increase in the real exchange rate, i.e., a

devaluation of domestic currency (here won). We assume arbitrarily devaluation

Table 5.5 Growth in the domestic capital stock






Domestic output 646.272 941.866 444.970

Domestic sales 624.184 912.035 431.173

Exports 23.439 29.844 13.296

Imports 47.195 133.174 4.658

Capital stock 659.675 382.196 1063.822















GDP 829.836


by 20 %. We start from the computed equilibrium data in Table 5.2. Thus, Table 5.2

provides a comparative benchmark for this experiment. Table 5.3 presents the

results obtained.

What will be the consequences? Firstly, we have to consider the activities in

foreign trade. The devaluation affects exports and import prices uniformly. That is

confirmed in Table 5.3. Secondly, the devaluation is expected to expand the

production of exportables. For exports to expand, however, their foreign price

must decline on foreign markets. However, to get a more specific answer, we

must carry out a more detailed empirical study under a longer period of time.

That means that the capital stock must be permitted to adjust.

With fixed import prices in foreign currency, a devaluation leads to a deteriora-

tion in the terms of trade because the increased import prices in domestic currency

implies a fall in imports (short run effect) and an increased domestic import

substitution (long run effect). Thus, adjustment by devaluation affects both exports

and imports in each sector. Regarding the results in Table 5.3 (trade deficit

decrease) the beginning of such a change has started. The composite commodity

supply is decreasing in agriculture, industry and services. Domestic output has

increased in agriculture but decreased in industry and service. As a result of these

effects, GDP have decreased. This implies that devaluation in the short run has, in

most cases, a decreasing initial effect on output. We can only look at initial effect

because capital stocks are restricted to the predetermined values of one singe

period. Moreover, the foreign currency price of a particular country’s exports is

generally endogenously determined by its domestic production costs and exchange

rate policy. However, in this mini CGE model the export demand function,

discussed in Chap. 4 (Eq. 4.35), is not included. To reveal if the current account

follows a J-curve pattern,16 the study must include an elasticity export demand

function and comprise subsequent periods.



Agriculture 2515.900 326.396 –


Services – 366.583 948.100




Labour supply 2515.900 1565.987 948.100

In the next experiment (Table 5.4 below) we have a decrease in real ex-change

rate, i.e., an assumed appreciation of domestic currency by 20 %.

16 The J-curve describes the time lag with which a real currency devaluation improves the current

account.


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Again, we start from the computed benchmark equilibrium data. As expected,

the reverse to the experiment above is the case, i.e., all of the features from the

earlier experiment are preserved but in opposite direction. The experiments in this

section have illustrated an important trade-off in the open economy, namely the

trade-off between competitiveness, i.e., between increased import substitution

versus domestic structural renewal, and hence, potential export expansion. The

change in the real exchange rate has an influence on that balance. First we present

the summary, and then the Table itself.



Agriculture 2515.900 315.015 –


Services – 358.366 948.100




Labour supply 2515.900 1565.987 948.100

5.2.3 Growth in the Domestic Capital Stock

In the next experiment (Table 5.5 below) we go back to the first experiment

(Table 5.2), and ask ourselves what will be the consequences of growth in the

capital stock. Table 5.2 provides a comparative benchmark for this experiment.

Operationally, the solution for the first period is used to create the next period’s

model parameters. It will solve the market for equilibrium prices and quantities for

one period and then add the solution obtained to the pre-determined variables that

are needed to obtain the market equilibrium solution for the next period. The

sequence with links to equilibria does not refer to the calendar time. The outcome

sequence time index is named ‘period’. Thus, the solution for each period,

depending only on current and past variables, is used to create the next period’s

variables in the model. The model is solved as a sequence of static equilibrium, with

no intertemporal optimisation. Thus, the model is comparable with the approach

used and discussed in Chap. 3, the quadratic programming model. Dynamics appear

through changes in domestic and international conditions.17 The static equilibrium

represents an optimum for producers and consumers. The updated exogenous

variables and parameters specify cumulative dynamic process such as factor accu-

mulation and productive growth. The model is thus solved forward in a dynamically

17 For details, see the discussion in Chap. 3.


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recursive fashion.18 However, one important difference occurs, disinvestment

(depreciation expenditures) is specified in the CGE model, but was not in the

quadratic programming model.

For each period the sector capital stocks are adjusted. Given the computed data

of investment by destination minus computed total depreciation expenditure by

sector, added to the current sector capital stocks, will become the next period’s

sector capital stocks. The net sum of these changes in capital will be our definition

of growth.




Capital stock 657.575 338.708 1032.484

New capital stock 659.675 382.196 1063.822

The first period, the starting point of the temporary equilibrium computations, is

represented by the equilibrium solution presented in Table 5.2. The subsequent

period (Period 2) is presented in Table 5.5 below. In the second period the domestic

prices have increased in agriculture and services but have decreased in industry.

The composite commodity supply has increased in agriculture, industry and

services. Domestic output has increased in all three sectors, but it is most apparent

in industry. GDP has increased. The explanation is the growth in capital stocks.

Since the capacity expansion in capital stocks are assumed proportional, the result

has not demonstrated a change in the structure of production.

Depreciation expenditure by sector has decreased in agriculture but has

increased in industry and service. However, investment by destination has

increased in all three sectors. Rate of capital rent has decreased. The explanation

is again the growth in capital stocks. Exports have increased in agriculture and

industry but have decreased in service. Imports have increased in all three sectors.



Agriculture 2515.900 335.020 –


Services – 374.909 948.100




Labour supply 2515.900 1565.987 948.100

18 Recursive-dynamic CGE models are those which can be solved sequentially (one period at a

time): they assume that behaviour depends only on current and past states of the economy.



Although we do not here present an exhaustive set of experiments, the workings of

the model have been clarified, and at the same time, the model has indicated how

future empirical applications might be implemented. Thus, we have been able to

examine the importance of different initial conditions and the economic structure

within a framework that imposes inter-sector consistency. The three numerical

experiments presented in this chapter would need to be justified by an empirical

analysis. However, the numerical input values have only been used as a concept in

our CGE model, in other words, the numerical values have not been derived from

any empirical observation.

This type of model can accommodate different types of distortions, such as taxes

and tariffs or monopolistically fixed factor prices. Consequently, the model used

here incorporates price-incentive variables that represent tools of policy makers.

These tools have not been discussed, and not been used as policy instruments in the

numerical experiments. However, in empirical application where the evaluation of

economic policy is essential, the situation will become somewhat different. The

structure of the model provides here a comprehensive and efficient technique for

accomplishing this type of analysis.

In most CGE models capacity expansion and the process of structural adjustment

are restricted to the existing technical structure of production. Structural adjustment

is the key to understanding the importance of individual and collective motivations,

and thereby provide the framework for the entrepreneur in economic analysis.19

From an evolutionary theoretical point of view20 the equilibrium models are

inadequate to capture the specification of the mechanisms that creates incentives

for the entrepreneur to enforce new activities to maintain the capacity for growth.

However, one thing is to have knowledge of the problem, another is to make the

problem operational. To start with the structure of ownership of the business

sectors, and then specify the incitement behaviour that is assumed to follow that

type of ownership, may be a good point of departure to make entrepreneurship

operational in an economic model. In later years the structure of ownership in the

business sectors has rapidly changed. That change may have many causes, but the

strong increase in structural transformation, recorded in the past two decades, is

probably closely connected to this development.

Disinvestment is an important component in the transformation process, and

even a condition for investment and growth. To under-stand the importance of this

argument a model of the economic transformation process is developed. Economic

transformation will be specified as endogenous, and it will become an integral part

of a steady-state equilibrium mechanism. In the next chapter, Chap. 6, a model of

the fundamental structure of the transformation process of the open economy in an

equilibrium framework is carried out.

19 The perfect competition theory defines the equilibrium state and not the process of adjustment.

(Kirzner 1973).20 Schumpeter 1942 and 1976.


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Appendix 1: The Mathematical Equations of the Model

Prices

Definition of Domestic Import Prices

pMj ¼ pWMj � ER� ð1þ tmj þ prjÞ (5.1)

pWMj is the world market price of imports, ER is the real exchange rate, tmj is the

tariff rate on imports, and prj is the import premium rate. Note, that the world

market price of imports pWMj and the tariff rates are fixed. Depending on the

exchange rate, the domestic import price pMj is flexible or fixed.

Definition of Domestic Export Prices

pEj ¼ pWEj � ð1þ tejÞ � ER (5.2)

pEj is the domestic price of exports, pWEj is the world market price of exports, tej are

the export duty rates, and ER is the real exchange rate. Note, the world market price

of exports pWEj and the duty rates are fixed. Depending on the exchange rate, the

domestic export price pEj is flexible or fixed.

Value of Domestic Sales

Pi � xi ¼ pZj � xZj þ pMj �Mj (5.3)

pi is the price of composite commodities, xi is the composite commodity supply, pZjis the domestic price, xZj are the domestic sales, pMj is the domestic price of imports,

and Mj is imports by sector.

Value of Domestic Output (Market Value)

pZj � Zj ¼ pZj � xZj þ pEj � Ej (5.4)


pZj is the average output price by sector, Zj is the domestic output by sector, xZj are

domestic sales, pEj is the domestic price of exports, and Ej is exports by sector.

Definition of Activity Prices

pZj � 1� ITAXj

� � ¼ PVAj þ Σj; aij � pi (5.5)

pZj is the average output price by sector, ITAXj is the indirect tax rate, PVAj is the

value added price by sector, aij are the input–output coefficients, and pi is the priceof composite commodities.

Definition of Capital Commodity Price

pKj ¼ Σi; pi � cij (5.6)

pKj is the rate of capital rent by sector, pi is the price of composite commodities, and

cij is the capital composition matrix.

Definition of General Price Level

pindex ¼ Σi; pwtsi � pi (5.7)

pindex is the general price level, pwtsi are the CPI weights, and pi is the price of thecomposite commodity.

Output and the Factors of Production

Production Function (Cobb-Douglas)

Zj ¼ ADj ΠlcLj;lc αj;lc Kj1�Σlc; αj;lcð Þ (5.8)

Appendix 1: The Mathematical Equations of the Model 87

Zj is the domestic output by sector, ADj is the production function shift parameter,

αj,lc is the labour share parameter, Lj,lc is the employment by sector and labour

category (lc), and Kj is the capital stock by sector.

First Order Condition for Profit Maximum

PLlc �Wdist � Lj;lc ¼ xZj � PVAj � αj;lc (5.9)

PLlc is the average wage rate by labour category (lc), Wdist are the wage

proportionality factors, Lj,lc denote the employment by sector and labour category,

and PVAj is the value added price by sector.

Labour Market Equilibrium

Σj; Lj;lc � Llc (5.10)

Lj,lc denote the employment by sector and labour category, and Llc is the labour

supply by labour category (lc).

CET Function: Exports (Domestic Output)

Zj ¼ ATj γj Eϕj

j þ ð1� γjÞxZϕj

j

h i1=ϕj

(5.11)

Zj is the domestic output by sector, ATj is the CET function shift parameter,

GAMMA is the CET function share parameter, Ej is exports by sector, ϕj is the

CET function exponent, and xZj are the domestic sales. This function applies to

commodities that are both sold domestically and exported. The equation above

reflects the assumption of imperfect transformability between domestic sales and

exports.

Export Supply

Ej

xZj¼ pEj

pZj� 1� γj

γj

1ϕj�1 (5.12)


pEj is the domestic price of exports, and pZj is the domestic price.

CES Function: Composite Commodity Aggregation Function

xi ¼ AC: j δj M�ρjj þ ð1� δjÞxjZ:�ρj

h i�1=ρj(5.13)

xi is the composite commodity supply, ACj is the Armington function shift param-

eter,δj is the Armington function share parameter,Mj is imports, ρj is the Armington

function exponent, and xZj are the domestic sales. This function applies to

commodities that are both produced and sold domestically and imported, i.e.,

composite commodities. The equation above reflects the assumption of imperfect

substitutability between imports and domestic produced commodities sold

domestically.

Cost Minimisation of Composite Good

Mj

xZj¼ pZj

pMj� δj1� �δj

11þρj

(5.14)

pZj is the domestic prices, and pMj is the domestic price of imports.

Domestic Sales for Non-traded Sectors

A first step toward more realism has been taken by introducing non-tradable

commodities. Non-tradable commodities are commodities that are not subject to

international trade. In general, most service as well as housing and construction fit

this category.

xZj ¼ Zj (5.15)

xZj are the domestic sales, and Zj is the domestic output by sector.


Composite Commodity Aggregation for Non-traded Sectors

xi ¼ xZj (5.16)

xi is the composite commodity supply, and xZj are domestic sales.

Demand

Total Intermediate Uses

xij ¼ Σj; aij � Zj (5.17)

xij are the intermediate uses, aij is the input–output coefficients, and Zj is the

domestic output by sector. The sector balances of intermediate inputs (inter-

industry matrix) form the basis of the input–output table. The input–output matrix

is derived from the inter-industry matrix, by dividing each element in a column by

the row sum of the corresponding row. The Leontief matrix is obtained from the

input–output matrix by subtracting it from an n by n identity matrix. This changes

the sign of all off-diagonal elements and makes all diagonal elements into their

complements to one. Theoretically, the input coefficients are in physical terms.

Empirically, the coefficients are in monetary terms. As long as we assume that

prices are constant, the input coefficients should be the same either in physical or

monetary terms.

The transactions may be valued at either the price received by the producer,

producer’s value, or at the price paid by the consumer, purchaser’s value. Thedifference between these values is that transport margins, net indirect commodity

taxes, i.e., indirect taxes less subsides, and trade margins are added to the basic

producer’s values in the national accounts. Since the demand components are

computed at purchaser’s values, production and imports are converted to these

values too.

Inventory Investment

DSTj ¼ DSTRj � Zj (5.18)

DST j is inventory investment by sector, DSTR j is the ratio of inventory investment

to gross output, and Zj is the domestic output by sector.


Private Consumption Behaviour

Pj � CDj ¼ Σh; CLESj;h � ð1�MPShÞ � YHh � ð1� HTAXhÞ (5.19)

pj are the price of composite commodities, CDj is the final demand for private

consumption, CLESj,h are the private consumption shares, MPSh is the marginal

propensity to save by household type, YHh is the total income by household type,

and HTAXh is the income tax rate by household type

Private GDP

Y ¼ Σh YHh (5.20)

Y is private GDP, YHh is the total income by household type.

Total Income Accruing to Labour

YHh ¼ Σlc; PlcL � Llc þ REMIT � ER (5.21)

YHh is the total income by household type, PlcL is the average wage rate by labour

category, Llc is the labour supply by labour category, REMIT is the net remittances

from abroad, and ER is the real exchange rate.

Total Income Accruing to Capital

YHh ¼Σj; PVAj � Zj � DEPRECIA � Σlc;PlcL � Llc

þ FBOR � ERþ YPR (5.22)

YHh is the total income by household type, PVAj is value added price by sector, Zj is

the domestic output by sector, DEPRECIA is total depreciation expenditure, PlcL is

the average wage rate by labour category, Llc is the labour supply by labour

category, FBOR is the net flow of foreign borrowing, ER is the real exchange

rate, and YPR is total premium income accruing to capitalists.


Saving and Income

Household Savings

HSAV ¼ Σh; MPSh � YHh � ð1� HTAXhÞ (5.23)

HSAV are the total household savings, MPSh is the marginal propensity to save by

household type h, YHh is the total income by household type, and HTAXh is the

income tax rate by household type.

Government Revenue

GR ¼ TARIFF� NETSUBþ INDTAX þ TOTHTAX (5.24)

GR is the government revenue, TARIFF is the tariff revenue, NETSUB is the export

duty revenue, INDTAX is the indirect tax revenue, TOTHTAX is the household tax

revenue.

Government Savings

GR ¼ Σj; pj � GDj þ GOVSAV (5.25)

GR is the government revenue, pj are the price of composite commodities, GDj is

the final demand for government consumption, and GOVSAV are government

savings. It is an essential assumption for a real equilibrium model that the govern-

ment must balance its budget.

Government Consumption Shares

GDj ¼ GLESj � GDTOT (5.26)

GDj is the final demand for government consumption, GLESj is the government

consumption shares, and GDTOT is the total volume of government consumption.


Tariff Revenue

TARIFF ¼ Σj; TMj �Mj � pWMj � ER (5.27)

TARIFF is the tariff revenue, TMj are the tariff rates on imports,Mj are imports,pWMj

are world market price of imports, ER is the real exchange rate.

Indirect Taxes on Domestic Production

INDTAX ¼ Σj; ITAXj � pZj � Zj (5.28)

INDTAX is the indirect tax revenue, ITAXj is the indirect tax rates, pZj is the average

output price by sector, and Zj is the domestic output by sector.

Export Duties

NETSUB ¼ Σj; tej � Ej � pWEj � ER (5.29)

NETSUB is export duty revenue, tej are export duty rates, Ej are exports by sector,

pWEj is the world market price of exports, ER is the real exchange rate.

Total Import Premium Income

YPR ¼ Σj; pWMj �Mj � ER� pr (5.30)

YPR is the total premium income accruing to capitalists, pWMj is the world market

price of imports, Mj are imports, ER is the real exchange rate, and pr is the import

premium.

Total Household Taxes Collected by Government

TOTHTAX ¼ Σh; HTAXh � YHh (5.31)

TOTHTAX is the household tax revenue,HTAXh is the income tax rate by household

type h, YHh is the total income by household type h.


Capital Formation

Depreciation Expenditure

DEPRECIA ¼ Σj; DEPRj � pKj � Kj (5.32)

DEPRECIA is the total depreciation expenditure, DEPRj is the depreciation rate, Kj

is the capital stock by sector, pKj is the rate of domestic capital rent by sector, ER is

the exchange rate. As the capital stock gets older, the quasi-rent in the Marshallian

sense falls and eventually becomes zero. The economic decision is then taken to

scrap the capital object as obsolete.

Total Savings

SAVINGS ¼ HSAV þ GOVSAV þ DEPRECIAþ FSAV � ER (5.33)

SAVINGS are total savings, HSAV are total household savings, GOVSAV are

government savings, DEPRECIA is total depreciation expenditure, FSAV are

foreign savings. Thus, the sum of domestic and foreign savings in domestic

currency.

Domestic Investment by Sector of Destination

In the CGE mini-model domestic investment by sector of destination is given by:

pKj � IDj ¼ KIoj � INVEST � KIoj � Σj; DSTj � pj (5.34)

Thus, pKj is rate of capital rent by sector, IDj is volume of investment by sector of

destination,KIoj are the shares of investment by sector of destination, INVEST is the

total investment,DSTj is inventory investment by sector, pj is the price of composite

goods. The sector share parameters for investment are assumed fixed. Total invest-

ment is determined by savings in the economy (saving determined investment).

The sector capital stocks Kj are fixed within periods. However, they change over

time given aggregate growth of the capital stock and the sector allocation of invest-

ment. Sector share parameters of investment by sector of destinationKIoj are assumed

to be fixed. For information, the numerical values of the sector share parameters of

investment are in these applications arbitrary assumed to be: 0.13 for agriculture, 0.29

for industry, and 0.58 for services. The sum is equal to one. However, the sector

allocation of investment is here assumed to be adjusted over time (endogenously) to

equate rental rates pKj in the industrial sectors by the terminal year.


Investment by Sector of Origin

The request for the volume of investment by sector of destination IDj (the sector

capital accumulation) is translated into a demand for investment commodities by

sector of origin ISi (producing sectors of capital commodities), thus investment by

sector of origin:

ISi ¼ Σj; IMATij � IDj (5.35)

ISi is the final demand for productive investment, IMATIJ is the capital composi-

tion matrix, and IDj is the volume of domestic investment by sector of destination. In

accordance with the production structure, as represented by the input–output model,

the investment by sector of origin ISi is also known as final demand for productive

investment. The summation of the capital composition matrix IMATIJ is, as the

sector share parameters of investment, equal to one. Following this application, the

two sectors producing capital commodities are industry (the dominating sector),

and a small fraction from services.

Balance of Payments

Σj; pWMj �Mj ¼ Σj; pWE

j � Ej þ FSAV þ REMIT þ FBOR (5.36)

pWMj is the world market price of imports, Mj are imports, pWE

j is the world market

price of exports, Ej are exports by sector, FSAV are foreign savings, REMIT are net

remittances from abroad, and FBOR is the net flow of foreign borrowing. In the

experiments in this book the exchange rate is fixed and the net flow of foreign

borrowing is unfixed. Following this specification, the trade deficit is free to vary.

Market Equilibrium

Commodity Market Equilibrium

xi ¼ xij þ CDj þ GDj þ ISi þ DSTj (5.37)

xi are the composite commodity supply, xij are intermediates uses, CDj is the final

demand for private consumption, GDj is the final demand for government con-

sumption, ISi is the final demand for productive investment, and DSTj is the

inventory investment by sector.


Objective Function

OMEGA ¼ Πj CDjCLESj;h (5.38)

OMEGA is the objective function variable, CLESj,h is the private consumption

shares, and CDj is the final demand for private consumption.

For full specification of the numerical input in the original input version of the

model, see the computer program of the CGE mini-model. The CGE mini-model is

a minor version of an equilibrium model that originally comes from Chenery,

Lewis, de Melo, and Robinson in their work on designing an equilibrium develop-

ment model for Korea. The model illustrates the basic use of CGE models. See

further: Chenery et al. (1986). The model is included in the GAMS model library

(korcge.gms). The reader can reach the GAMS homepage at www.gams.com.

Appendix 2: Some Parameters Assignments of the Model

PARAMETER ASSIGNMENTS

INCOME TAX RATE BY LABOUR ¼ 0:08910

INCOME TAX RATE BY CAPITALIST ¼ 0:08910

LABOUR SHARE PARAMETER IN THE PRODUCTION FUNCTION


Agriculture 0.38258 0.06740 0.00000

Industry 0.00000 0.53476 0.00000

Services 0.00000 0.16234 0.42326

INPUT–OUTPUT COEFFICIENTS


Agriculture 0.12591 0.19834 0.01407

Industry 0.10353 0.35524 0.18954

Services 0.02358 0.11608 0.08390

CAPITAL COMPOSITION MATRIX


Agriculture 0.00000 0.00000 0.00000

Industry 0.93076 0.93774 0.93080

Services 0.06924 0.06226 0.06920


http://www.gams.com

WAGE PROPORTIONALITY FACTORS


Agriculture 1.00000 0.52780 0.00000

Industry 0.00000 1.21879 0.00000

Services 0.00000 1.11541 1.00000

PRIVATE CONSUMPTION SHARES

LAB-HH CAP-HH

Agriculture 0.47000 0.47000

Industry 0.31999 0.31999

Services 0.21001 0.21001

References



Chenery H, Lewis J, de Melo J, Robinson S (1986) Alternative routes to development. In: Chenery

H, Syrquin M (eds) Industrialization and growth: a comparative study. Oxford University

Press, New York

Condon T, Dahl H, Devarajan S (1987) Implementing a computable general equilibrium model on

GAMS – the Cameroon model, DRD discussion paper 290. The World Bank, Washington, DC



Freeman C (1974) The economics of industrial innovation. Penguin Books, Harmondsworth,

Middlesex

Kirzner IM (1973) Competition and entrepreneurship. The University of Chicago Press, Chicago

Lofgren H, Harris RL, Robinson S (2002) A standard computable general equilibrium (CGE)

model in GAMS, vol 5, Microcomputers in policy research. International Food Policy

Research Institute, Washington, DC

Petersen TW (1997) An introduction to CGE-modelling and an illustrative application to Eastern

European Integration with the EU. The Institute of Economics at the University of

Copenhagen, Denmark. The working paper is only available on www.dreammodel.dk/

Schumpeter J (1942, 1976) Capitalism, socialism and democracy. Harper & Row, New York

Shoven J, Whalley J (1984) Applied general equilibrium models of taxation and international

trade: an introduction and survey. J Econ Lit XXII:1007–1051

Shoven J, Whalley J (1992) Applying general equilibrium. Cambridge University Press,

Cambridge

References 97

http://www.dreammodel.dk/

Chapter 6

A Suggested Model of Economic Transformation

In this chapter a model of an open economy to illustrate the principles of the

industrial transformation process, i.e., investment and disinvestment, is discussed.

However, the model is focused on medium run. In the medium time period the time

is too short for all things to be reallocated, because of the sluggishness of the

market. More precisely, we approach the equilibrium but we cannot reestablish it in

full. To counteract the rigidity of the market, and establish equilibrium, the entre-

preneur will become important as an economic actor. The key concept of the

economic transformation process is the domestic profit rate, or as we here will

call it, rate of return, because it is related to investment. Economic transformation

will be specified as endogenous, and it will become an integral part of a steady-state

equilibrium mechanism.

6.1 Introduction

In times of insecurity and economic turbulence, economic adjustment problems

take the central place of the economic discussion. The transformation process, i.e.,

by transferring resources from no longer viable to more expansive activities of the

economy, will be in focus. The transformation process is long term in character and

has a long time-lag in its impact on production. Long-term investments in new

industrial plants and knowledge in new areas, gives new directions of growth, and

consequently, a transformation of industrial structure. To maintain a given level of

growth, a frequent structural transformation is necessary. The change of the capital

stock is a dynamic process in a dual sense. Firstly the dismantling of old

investments subject to physical or economic deterioration, and secondly investment

in new and more efficient machines brought into production.1 However, the concept

1 The influence from the Swedish economist Dahmen is evident here. Dahmens contribution to the

economic analysis of industrial dynamics has greatly influenced much research both in Swedish

economic history and in economic policy. For a survey, see Carlsson and Henriksson (1991).



99

of economic transformation in the medium run is the key to understanding the

importance of individual and collective motivations, and thereby provides the

framework for the entrepreneur in the transformation process.2 The long run period

is a period of time required for economic agents to reallocate resources, and

reestablish equilibrium. However, in the medium time period the time is too short

for all things to be reallocated, because of the sluggishness of the market. More

precisely, we approach the equilibrium but we cannot re-establish it in full. To

counteract the rigidity of the market in medium run the entrepreneur will be

important as an economic actor. Entrepreneurial ideas arise (Holcombe 1998)

when an entrepreneur adds ideas developed by earlier entrepreneurs that once

combined produce a new process or output. Entrepreneurs are here understood

and based on the Schumpeterian notion (Schumpeter 1934) of creative destruction.

The entrepreneur is a person who is developing new methods, combination and

processes. The number of patents applications as the ratio of total labor force is a

variable is closely related to growth-oriented entrepreneurship, and closely inspired

by Schumpeter.3 Following Hayek (1945), a decentralized economy that allows

individuals to act on their entrepreneurial insights, and rewards them for doing so,

produces an environment where additional entrepreneurial insights are likely to be

produced. Hence the expected reward, or the profit rate, is very essential motivation

for individual entrepreneurial activity. However, the entrepreneur is very absent in

the literature discussing structural change and economic transformation.

This chapter discusses the adaptability to meet the demand for structural change

in medium term. A simple model is constructed to illustrate the principles of the

industrial transformation process is used. To succeed with the re-construction of

the economy the entrepreneurial activity is important. The transformation process

can be analyzed in separated parts. In all parts the activity of the entrepreneur must

be included.

6.2 Outline of the Transformation Model

The exchange rate, factor prices, and the value of output (value added) are in the

context of the transformation process important variables. They all, to various

degrees, influence the domestic profit rate, or as we here will call it, the rate of

2 The word “entrepreneur” has its origins in the work of Richard Cantillon in his Essai sur laNature du Commerce en General (1755) and Jean-Baptiste Say (1803 or 1834) in his Treatise onPolitical Economy. According to Jean-Baptiste Say, an entrepreneur is “one who undertakes an

enterprise, especially a contractor, acting as intermediatory between capital and labor”. See further

Sheshinski et al. (2007).3 To alternative measures of entrepreneurship, self-employment and the number of patents, are

evaluated by Salgado-Banda (2002) in an extensive study on 22 OECD countries for the period

1980–1995. The results are that entrepreneurship measured by patents is positively linked to

economic growth and that entrepreneurship measured in terms of self-employment is negatively

related to growth.

100 6 A Suggested Model of Economic Transformation

return. Decreased production costs (perhaps through a innovation and/or increased

productivity) increases competitiveness, raises the profit rates, and thus, creates a

risk that necessary cost reductions will not be realized. Hence, the incentives to

dismantling old investments on obsolescence diminish. On the other hand, a fall in

relative productivity can imply, due to decreasing competitiveness and falling profit

rates, a risk of exaggerated cost cuts. Logically, the incentives to dismantling old

investments on obsolescence increase. These two examples are simple, but provide

a strong argument for recognizing the disinvestment process in the economic

analysis. Indeed, this leads to the question of finding the appropriate balance

between competitiveness and an efficient transformation to sustain a desirable

growth path in the economy. However, different individual firms adjust differently,

and a structural transformation between sectors will take place. The outcome of this

transformation is a new structural profile of the economy. In equilibrium terms, as it

will become demonstrated below, the profit rate coordinates investment and disin-

vestment, and thus, the structure of the transformation process.

In this process the entrepreneur’s skills come to a test. Formally, the difference

in rate of return between different activities will become crucial for the producer’s

decision to expand production capacity. The domestic rate of return, denoted rDj , is

here the relative profitability of an investment project, for a firm or an industry.4

The capital is assumed measured in market value in present or alternative use. The

allocation of total investment here denoted Ij, will respond to rate of return

differentials in different countries. The most satisfying way to reflect this situation

computationally is to use a constant elasticity transformation (CES) function

between foreign investments (IFj ) and domestic investments (IDj ). By this specifica-

tion the exposed position of the domestic economy is reflected.

Ij ¼ δj IF ρjj þ ð1� δjÞID ρj

j

h i1=ρj(6.1)

Where Ij is the total investment specified for foreign and domestic investments.

The parameter δj , the distribution parameter, measures the relative investment

shares of the funds allocated in the investment process.

The elasticity of substitution σj is given by σj ¼ 1=ð1� ρjÞ . Within this

framework, the individual country is regarded as small in the world market:

hence, the foreign market rate of return on production rFj , for any industry and

time period, is assumed exogenously fixed and linked to the world market rate of

return. In contrast, the domestic rate of return rDj is endogenously determined in the

domestic economy. Maximizing the revenue of available investment supply (Ij)

rDj Ij ¼ rDj IDj þ rFj I

Fj (6.2)

4 Profitability of investment is here similar to the concept of the rate of return on investment. See

Bodie et al. (2011).

6.2 Outline of the Transformation Model 101

subject to Eq. 6.2 yields the following allocation of supply of funds available for

investment between domestic and foreign investment markets:

IFjIDj

¼ rFjrDj

!σj1� δjδj

� �σj

(6.3)

Thus, the solution is to find a ratio of inputs (IFj to IDj ) so that the marginal rate of

substitution equals the ratio of the domestic rate of return to the rate of return abroad.

Equation 6.3 allows for a rich set of responses. As σj gets larger, the responsivenessof IFj =I

Dj to changes in rFj =r

Dj rises. In that case rFj =r

Dj will stay close to its base value

and we approximate the case where rFj , at the equilibrium, will stay fixed torDj . On the

other hand, ifσj is very low, large changes in rFj =rDj may take place.5 Thus, as a result

of this specification, rDj may, at the equilibrium, differ from rFj . The variable rFj ,

however, is linked to the exogenously fixed world market rate of return, rwj .

Increasing technological achievements, privatizations, and the switch of empha-

sis by firms to geographical diversification, are some of the more important

explanations to the strong expansion in structural change recorded in the past two

decades. Since 1990s the pace of international economic integration has

accelerated. Factors behind the process are dismantling of trade barriers and foreign

direct investments. New technology has reduced the costs for transportation and

communication. Demand for high skilled labor, and the activity of the

entrepreneurs, is here crucial.

Whatever the origins, the expected development of the rate of return is crucial for

investment. The economic activity must result in future profitability if domestic

investments, denoted IDj , have to continue in next period. We can illustrate investment

by the accelerator principle. If the parameter kj denote the domestic capital/output

ratio, and rDj tþ1� rDj t

h idenote the difference between the expected rate of return in

the future period (rDj tþ1, is the expected rate of return) and the rate of return from the

present period (rDj t). The expected rate of return is here assumed to be influenced by

the entrepreneurial activity, measured in number of patents. As a suggestion, we

add a parameter α that represents the entrepreneurs influence on the expected rate of

return. If α is >1, the entrepreneurial effort is successful. If α is <1, it is a failure.

If ¼ 1 it is neither good nor bad. Formally, we can now write (αrDj tþ1). Thus, here

the change in the rate of return, i.e. productivity of investment, with the entrepre-

neurial activity included, is the driving force for investment. Hence, we can write:

IDj t¼ kj αrDj tþ1

� rDj t

� �(6.4)

5 In the extreme case where σj is zero, the relation between foreign and domestic investment would

be fixed and foreign investment activities become perfect complements of domestic investments.


However, the capital stock is subject to economic obsolescence, here denoted

DEPRDj . As the capital stock gets older, the quasi-rent in the Marshallian sense

(Marshall 1920) falls and eventually becomes zero. The economic decision is then

taken to scrap the capital object as obsolescent despite its continuing physical

durability. If we let μj represent the rate of return elasticity of obsolescence

of capital equipment, and KDo

j be reflecting the capital stock when, at equilibrium,

rDj ¼ rD�j (rD�j the initial rate of return). When rDj > rD�j the incentives to dismantling

old investments on obsolescence diminish. When rDj < rD�j the incentives to

dismantling old investments on obsolescence increase. It can very simply be

described as:

DEPRDj ¼ KDo

j 1=rDj

� �μj(6.5)

Thus, the obsolescence of capital is uniquely determined by the rate of return.

What will then happen to growth in the long run? It depends on the individual

firm’s reaction to the change considering the trans-formation potential, the change

in the domestic rate of return, and the general credibility for the policy-makers

management of economic policy. Entrepreneurs must be encouraged to react and

adjust to changing conditions and must develop an effective structural organization

in order to manage dynamic settings. The single entrepreneur’s reaction is reflected

in the rate of return elasticity of obsolescence μj.An important part of disinvestment, especially in the small business firms, is

bankruptcy (White 2001). A forgiving bankruptcy law that offers a “fresh start”

from pre-bankruptcy depts will permit inframarginal entrepreneurs to re-enter the

economy after a business failure. Following empirical research6 bankruptcy

laws have the most statistically and economically significant effect on levels of

self-employment across countries, and matter more than economic determinants

such as real GNP growth and MSCI stock market returns.7 Forgiving personal

bankruptcy laws and ready access to limited liability offer significant policy

instruments for enhancing entrepreneurial activity, and thus, economic growth.

In this model, a more forgiving bankruptcy law is assumed to have an effect on

innovation and it will result in increased number of patents. It would be easier for

the entrepreneur to disinvest and transfer the resources to new investments in new

projects. Thus, the possibility to a “fresh start” in-creases the incentive for

investment.

6 Armour and Cumming (2008) investigate the relationship between bankruptcy laws and entre-

preneurship using data on self-employment over 16 years (1990–2005) and 15 countries in Europe

and North America.7 The MSCI World is a stock market index of 1,500 ‘world’ stocks. It is maintained by MSCI Inc.,

formerly Morgan Stanley Capital International, and is often used as a benchmark for

asset allocation decisions and performance measurement. It uses a capitalization-weighted average

and individual indices are produced for the different countries, by regions, by industry, by

economic sector, as well as a complete world index.

6.2 Outline of the Transformation Model 103

6.3 The Process Towards Steady-State

Following the adjustment according to the model above, the increase in rate of

return implies an increase in investment, and a decrease in disinvestment. Accumu-

lation of real capital increases. On the other hand, a decrease in rate of return

implies a decrease in investment, and an increase in disinvestment. Accumulation

of real capital decreases. In this process the entrepreneurial activity can be

important.

Let us now look more closely towards the adjustment to steady state8 to which the

economy is assumed to converge. First we have a situation then investment exceeds

the disinvestment, i.e., IDj >DEPRDj per worker. In a long run situation, as growth

models refer to, capital per worker increases, and output per worker as well.9

However, in the medium term interpretation the established old industries can be

an obstacle. In medium term all factors are assumed flexible, but old and not

completely efficient capacity can still have influence in the production process.

Factors of production can still be tied to these establishments because of the

sluggishness of the market. Economic transformation is necessary, and the entrepre-

neur will be important as an economic actor.

Then investment exceeds disinvestment in medium term situations at full capac-

ity further investments may be restricted. The investment ratio and the growth in the

economy will fall. The step to retain the investment level is to increase the level of

the disinvestment process (creative destruction). In terms of the model above,

changes in by the effects on the rate of return elasticity of obsolescence (μj) willhave an impact on economic transformation. Then it is easier to re-enter the

economy after a business failure it will also make it easier for entrepreneurs to

take the decision to disinvest old capacity, and thus the investment level can be

retained and also increased. Thus, an increase on the rate of return elasticity of

obsolescence (μj) may in-directly follow.

In the long run too large capital stocks can in certain industries become conduc-

tive to structural problems in the economy. The increase in output by the new

investment is too small to cover the costs of the increased disinvestment. By

disinvestment of unprofitable capacity, and thus, a reduction of the capital stock,

profitability at the margin will increase. Disinvestment of old activities creates

opportunities and makes investment in new activities possible. If the disinvestment

policy of old industries is successful it will reinforce the conditions for investment

in new industries and result in higher productivity and growth in the long run. That

is in the literature known as the golden rule level of capital.10 Consequently,

disinvestment is an important component, not only to retain the investment level,

but to increase investment at medium term, and thus, the growth process.

8 Investment is just enough to cover disinvestment, and capital per worker remains constant.9 This is a well known concept from the Solow model (Solow 1956).10 Defined as the maximum steady-state consumption per worker.


On the other hand, then investment is less than disinvestment per worker,

i.e., IDj >DEPRDj , capital per worker decreases. One tool to counteract this devel-

opment is by technological development make investment in new capacity more

efficient. The process of establishing and encouraging investments can be measured

in different phases, depending on their purpose. Following Karlsson and Lowstedt

(1990) three phases can be distinguished.11 The first phase is influence, i.e., by

measures that promote and create an interest among individuals in starting to invest

in established or new firms. The motives may be the desire for independence or the

need for achievement, another is inner control. The second phase is guidance, i.e.,measures that help and facilitate the establishment process for new and recent

investors, for example by solving problems of financing, education, and consulting

services. The third phase is assistance, i.e., follow-up the carried out investments

to strengthen their change of long-term survival, to growth, and to establish a

competitive position.12

Assuming capital mobility is high, a fall in the domestic expected return on

investment would lead to the outflow of capital from a country we study. If wages

cannot be adjusted to a lower level in the short run, only by reducing employment,

the return on capital will be restored to keep the country attractive for investment.

However, since highly mobile capital implies the equalization of the cost of capital,

the relative expected return on investment will not recover and the outflow of

capital will continue. That would result in lower total investment. Hence, under

perfect capital mobility, an initial adverse disturbance may have permanent effects,

which will result in lower relative growth.13 In a sovereign country the currency is

depreciated by the market, or in a country with fixed exchange rates, devaluated by

economic policy. A devaluation of the domestic currency leads to an increase in rDjand hence, with constant foreign rate of returns (rFj ), will increase the demand for

investment in the domestic country. The incentives to disinvest diminish. As a

consequence, the aggregate capital stock is increasing and the equilibrium will be

re-established in the long run.

When pessimism prevails, investors reduce their expenses, there-by reducing

total sales, and hence, output. In the end, not only a falling investment demand (IDj )

is observed but also a falling competitiveness of the economy. If the economic

transformation becomes sluggish, it can create a structural crisis. The reinforcement

of the conditions for higher productivity and growth, that is necessary, will take

time to achieve. Hence, economic entrepreneurship must also include “the ability to

marshal resources to seize new business opportunities” (OECD 1998). That must

also include the economic policy makers.

11 See also Reynolds and White (1993).12 Here we can draw connections to the field of strategic entrepreneurship. See further von

Friedrichs and Boter (2009).13 See Krugman (1993).

6.3 The Process Towards Steady-State 105

The emphasis here is the investment allocation and the scrapping of capital

equipment on obsolescence, are both endogenous deter-mined by the variations in

the rate of return. In equilibrium terms, constituting the necessary transformation in

order to remain in a steady-state, as

Σj; DEPRDj ¼ Σj;

IDj

1þ ωoj

� � (6.6)

Equipment of recent vintage will have lower labor costs per unit of output

because they embody productivity increase due to technical progress in existing

production units.14 Within this framework, the capital stock in use comprises

equipment of different vintage. Technical progress represents also the

entrepreneurs influence on the investment process. Thus, entrepreneurs influence

is, in this model, defined as technical progress in existing production units. The

parameter ωoj is by this description interpreted as the productivity parameter of the

model. Technically, the necessary transformation pressure is derivable from the rDjequilibrium values.

6.4 Conclusions

Reconstruction, down-sizing, and replacement by new and growing firms and

industries are the consequences of economic transformation. In this context, the

activities by the entrepreneur become relevant. The attention for a successful

growth-oriented entrepreneurship has in-creased in the later years. Entrepreneur-

ship has become an alternative or complement to fiscal policy.

This is the global effect of international integration. This chapter is focused on

economic transformation in the medium run. In the medium time period the time

the time is too short for all things to be reallocated, because of the sluggishness of

the market. To counteract the rigidity of the market the entrepreneur will become

important as an economic actor. This brings us to the point, that it is necessary to

capture the specification of the mechanisms that create incentives for the entrepre-

neur to enforce transformation activities. Also an adequate transformation process

is important for the management of economic policy.

However, one thing is to have knowledge of a problem, another is to make the

problem operational. To start with the structure of ownership of the business

sectors, and then specify the incitement that is assumed to follow the specified

ownership, may be a good point of departure to make entrepreneurship operational

14 The analysis envisaged here, is based on the assumption of substitutability between capital and

labor before the installation of new capital equipments but fixed labor requirements after

installation.


in an economic model. By altering the business norms paths of adjustment different

alter-natives can be analyzed. Entrepreneurship is here in first hand in innovations

and measures in the number of patents. A legislation that offer significant policy

instruments for enhancing entrepreneurial activity in innovation is thus important.

In the light of the discussion in this chapter, disinvestment is also an important

component to creating opportunities for investment, and hence, growth.15 The

literature on investment is numerous, but if disinvestment is noticed, it is as a

rule assumed to follow a constant geometric rate. Hopefully, this chapter represents

a break from that general idea.

References

Armour J, Cumming D (2008) Bankruptcy law and entrepreneurship. Am Law Econ Rev

10:305–350

Bodie Z, Kane A, Marcus AJ (2011) Investments and portfolio management, 9th edn. McGraw-

Hill Higher Education, New York

Carlsson B, Henriksson RGH (red.) (1991) Development blocks and industrial transformation: the

Dahmenian approach to economic development. IUI, Stockholm

Dahmen E (1989) Avveckling – en forutsattning for utveckling (Disinvestment – a condition for

development), Ur festskrift till Klaus Waris (From festschrift in honor of Klaus Waris)

Hayek F (1945) The use of knowledge in society. Am Econ Rev 35:519–530

Holcombe RG (1998) Entrepreneurship and economic growth. Quart J Aust Econ 1(2):45–62

Karlsson A-K, Lowstedt E-L (1990) Nyforetagande i Frankrike (The starting of new companies in

France). SIND 1990:7

Krugman PR (1993) Lessons of Massachusetts for EMU. In: Torres F, Giavazzi F (eds) Adjust-

ment and growth in the European monetary union. Cambridge University Press, Cambridge

Marshall A (1920) The principles of economics. MacMillan, New York

OECD (1998) Fostering entrepreneurship. OECD, Paris

Reynolds P, White S (red.) (1993) Wisconsin’s entrepreneurial climate study, preliminary report.Marquette University

Salgado-Banda H (2002/6) Entrepreneurship and economic growth: an empirical analysis, Dis-

cussion paper in economics. Department of Economics, Birkbeck College, University of

London

Schumpeter J (1934)The theory of economic development. HarvardUniversity Press, Cambridge,MA

Sheshinski E, Strom RJ, Baumol WJ (eds) (2007) Entrepreneurship, innovation, and the growth

mechanism of the free-enterprise economies. Princeton University Press, Princeton/New York

Solow R (1956) A contribution to the theory of economic growth. Quart J Econ 70(1):65–94

von Friedrichs Y, Boter H (2009) Meeting radical change and regional transition: regional

closedowns and the role of entrepreneurship. Manag Global Trans 7(2):99–122

White MJ (2001) Bankruptcy and small business. Regulation 24:18–20

15 See Dahmen (1989).

References 107

Chapter 7

Back to the CGE Mini Model

This chapter, a continuation of Chap. 5, uses the ideas of endogenous obsolescence

from Chap. 6 and adapts them to the CGE mini model. In this chapter the feature of

endogenous obsolescence is included in the equation representing depreciation

expenditure. In that sense, the endogenous transformation process is introduced in

the CGE mini-model. In short, the focus of this chapter is to provide examples of

structural transformation in an open economy. Thus, the model specification is here,

as in Chap. 5, that the total investment equation is determined by total saving, and

the allocation to the different industry sectors are influenced by the sector specific

rate of return, but now also in terms of endogenous obsolescence.

7.1 The New Specification

We now have to insert the sector ratio of foreign capital rent to domestic capital rent

and the exchange rate (and its adherent elasticity coefficients), according to the

discussion in Chap. 6, in the following equation of total depreciation expenditure

(5.32), thus:

DEPRECIA ¼ Σj;DEPRjpKj Kj

rjpKj

!εj1

ER

� �μj

(7.1)

DEPRECIA is, as before, the total depreciation expenditure, DEPRj is the depreci-

ation rate, Kj is the capital stock by sector, rj is the rate of foreign capital rent

(foreign rate of return), pKj is the rate of domestic capital rent (domestic rate of

return), and εj is the elasticity of sector ratio of foreign capital rent to domestic

capital rent. ER is the exchange rate, and μj is the exchange rate elasticity of

obsolescence. As the capital stock gets older, the quasi-rent in the Marshallian

sense falls. Following the preceding chapter, the economic decision is then taken

to scrap the capital object as obsolescent despite its continuing physical durability.



109

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As a consequence of these changes, the content of the CGE mini model is enhanced

by the incorporation of these variables affecting the transformation mechanism.

A change has here been done by adding three parameters (rj, εj and μj) and an

enlargement of one equation to comprise endogenous obsolescence. As described in

Chap. 5, the level of total investment is determined by savings behaviour. In the

total savings equation, Eq. 5.33, total depreciation expenditure is included.1

7.2 Re-computations of Numerical Experiments

The first task is to present Table 7.1. That table represents the computed benchmark

equilibrium data, i.e., we use the first equilibrium computation as a benchmark

dataset. The computed equilibrium is now used as the benchmark dataset because

variables, with adherent elasticity coefficients, have been added in the equation

representing the total depreciation expenditure (Eq. 7.1). That insertion influences

the basic numerical values of the model. In an empirical use of the model, a new

calibration must take place if we want to keep the original endogenous values.

Since we only use the model as an illustration, and not in any empirical study, our

computation of a benchmark equilibrium dataset is the easiest way out of the

problem. As is by now well known to the reader, the capital stock in this model is

subject to physical as well as economic deterioration. The physical deterioration,

depreciation rates (DEPRj), are assumed to be 6 % in agriculture, 15 % in industry,

and 15 % in services. The elasticity of sector ratio of foreign capital rent (foreign

rate of return) to domestic capital rent, and the elasticity of sector obsolescence of

capital equipment to the exchange rate are assumed to be different for the three

sectors. Thus, the values of the elasticity ratio of foreign capital rent relative

domestic capital rent (εj) are assumed to be 0.2 in the agriculture sector, 0.8 in

industry, and 0.5 in services, i.e., 1 % increase in the profit ratio above increases

obsolescence by the elasticity value. The exchange rate elasticities of obsolescence

by sector (μj) are here assumed to have the same numerical values, i.e., 0.2 in

agriculture, 0.8 in industry, and 0.5 in services, i.e., 1 % increase in the exchange

rate (devaluation of domestic currency) decrease obsolescence by the elasticity

value (note, the ratios are inversed in Eq. 7.1). Again, since we only use this model

as an illustration, the assumed values are without empirical significance. In all

experiments, the computations of the economy are assumed to start from the

computed benchmark equilibrium presented in Table 7.1 below.

We are now prepared again to draw attention to the elaboration of the

experiments, and in this context, evaluate and compare the results of the

computations with the computations presented in Chap. 5. The issue of structural

transformation naturally moves attention to the importance of investment as well as

1 The literature on endogenous disinvestment is rare, but see Abel (1981), and Epstein and Denny

(1980).

110 7 Back to the CGE Mini Model

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disinvestment. Hence, the focus of the presentation is principally directed to

depreciation by sector and investment by destination. The difference is now that

endogenous obsolescence of capital is included.2


Labour1 Labour2 Labour3

Agriculture 2,515.900 314.690 –


Services – 336.363 948.100




Labour supply 2,515.900 1,565.987 948.100

Table 7.1 Computed benchmark equilibrium





Composite commodity supply 664.409 1,030.307 441.152

Domestic output 642.561 922.150 451.280

Domestic sales 620.170 895.458 435.846

Exports 21.672 26.628 15.179

Imports 46.090 134.947 4.596

Capital stock 657.575 338.708 1,148.507















GDP 821.269

2 Readers familiar to the CGE mini-model will here notice the fall in the capital stock in services.

7.2 Re-computations of Numerical Experiments 111

7.2.1 A Change in the Real Exchange Rate

The exchange rate, factor prices, and the value of output are in the context of the

transformation process important variables. An undervalued currency increases

competitiveness, raises the rate of return, and thus, there is a risk that necessary

cost reductions will not be realised. Hence, the incentives to dismantling old

investments on obsolescence diminish. On the other hand, an overvaluation of the

domestic currency can imply, due to decreasing competitiveness and falling rate of

return, a risk of exaggerated cost cuts. The incentives to dismantling old

investments on obsolescence increase. In the first experiment we start with an

increase in the real exchange rate, i.e., a devaluation of domestic currency. We

arbitrarily assume once again devaluation by 20 %. Recall, we start from the

computed benchmark equilibrium data (Table 7.1). Table 7.2 presents the results

obtained.3

The first observation reveals a decrease in the depreciation expenditure and an

increase in the rate of capital rent (domestic rate of return). As expected, the

incentives to dismantling old investments on obsolescence decrease. Thus, a deval-

uation policy has an impact on economic obsolescence and the rate of return as

expected. If we compare Tables 5.2 and 5.3 with Tables 7.1 and 7.2 we will find an

obvious difference. Implementation of endogenous obsolescence has a clear effect

on depreciation in all sectors. Investment is decreasing. However, in terms of the

transformation model (Chap. 6) investment will increase because the increase in the

domestic rate of return (capital rent). The explanation is that the sector allocation of

investment, and thus domestic investment, in Chap. 6 is now only determined by the

domestic rate of return. The mechanism by which total saving, and thus its

transformation to total investment, is left unspecified. Only the sector allocation

of investment is specified. In the CGE mini model however, investment is deter-

mined by total saving. In the total savings equation, total depreciation expenditure

is included. For example, a decrease in total depreciation expenditure would

decrease savings, and thus the total level of investment.



Agriculture 2,515.900 325.432 –


Services – 334.925 948.100




Labour supply 2,515.900 1,565.987 948.100

3 See also Benjamin (1990).


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What will be the consequences in the long run? So far the model can not give us

any answer to that question. A guess is that the process of structural renewal will be

hampered, and thus, a slowdown in economic growth because of the decrease in

investment. However, to get a more specific answer, we must carry out a more

detailed empirical study over a longer period of time. That means that the capital

stock must be permitted to adjust. Second, we have to consider the activities in foreign

trade. The devaluation affects export and import prices uniformly. This is confirmed

in Table 7.2. In quantitative terms, the devaluation is expected to expand the

production of exportables, in other words, the current account may follow the

J-curve pattern. However, as noted in Chap. 5, the export demand function, discussed

in Chap. 4 (Eq. 4.35), is not included. Also the model must comprise subsequent

periods.

In the next experiment (Table 7.3 below) we have a decrease in real exchange

rate, i.e., an assumed appreciation of domestic currency by 20 %. Again, we start

from the computed benchmark equilibrium data in Table 7.1. As expected, the

reverse to the experiment above is the case, i.e., all of the features from the earlier

experiment are preserved but in an opposite direction. As expected, the incentives

to dismantling old investments on obsolescence (depreciation) now increase, as

also the initiative to invest despite the decrease in the rate of capital rent.

The explanations are the same as in the preceding experiment, Table 7.2.

Table 7.2 Devaluation of domestic currency






Domestic output 643.879 917.606 429.383

Domestic sales 609.073 878.156 432.496

Exports 30.956 38.733 22.889

Imports 31.122 116.195 4.158

Capital stock 657.575 338.708 1,157.175














savings 39.174, Net flow of foreign borrowing�4.954, Household tax revenue 68.279, and Private

GDP 766.525

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Agriculture 2,515.900 299.111 –


Services – 342.225 948.100




Labour supply 2,515.900 1,565.987 948.100


The experiments in this section have illustrated an important trade-off within the

open economy, more specifically the trade-off between increased import substitu-

tion versus domestic structural renewal, and hence, potential export expansion. The

change in the real exchange rate has an influence on that balance. Following the

Table 7.3 Appreciation of domestic currency





Composite commodity supply 697.644 1,066.646 443.570

Domestic output 640.229 927.863 448.309

Domestic sales 626.025 909.541 437.830

Exports 14.204 16.754 8.819

Imports 71.656 160.539 5.151

Capital stock 657.575 338.708 1,122.591















Private GDP 865.718


discussion above, transformation changes in strength due to different changes in the

exchange rate, particular in industry. Depreciation by sector has decreased or

increased, so also investment, i.e., in the same direction. The rate of capital rent

has gone in the opposite direction. In addition to these effects, consider the change

in net flow of foreign borrowing. That indicates changes in domestic absorption.

Remember, foreign savings and government consumption are both assumed con-

stant in these experiments.

In this model a balance between savings and investment is achieved by setting

total investment equal to the sum of domestic and foreign savings. Thus, total

investment is determined by total savings in the economy (saving determined

investment). A fixed fraction of the foreign capital inflow is assumed to enter

directly into savings. The rest being saved by the sectors and a portion ending up

as private consumption. Domestic savings is made up of government and private

savings. Private savings is in this model specified as a rising function of GDP. That

implies that a rising GDP will increase total savings and total investment, and a

falling GDP will decrease total savings and total investment. The change in GDP

will, of course, also influence total consumption, but the result may vary among

sectors. The CGE mini model comprises of a strategy designed for the study it was

constructed, namely the development strategies. To use the model for the study of

domestic relative foreign investment decisions, where the rate of return compared

to the rate of return of foreign countries is emphasised, an alternative design of the

model is recommended.4

Adjustment to equilibrium is a process where profitability (rate of capital rent) in

the different domestic sectors will adjust to a “normal” level of profitability for the

economy as a whole. Thus, a development which implies that a country adjusts is

characterised as an adjustment towards equalising the relative profitability between

sectors. This is the sector allocation mechanism in the CGE mini model in Chap. 5,

and the transformation model in Chap. 6. Once again, the mechanism by which total

savings, and thus total investment resources is determined, is left unspecified in

Chap. 6. On the other hand, investment by domestic sectors relative investment by

sectors abroad is specified in the transformation model by the variation of the

domestic rate of return to the assumed exogenous rate of return abroad, as specified

by the constant elasticity transformation (CET) function (6.1). For sectors where

domestic profitability is high relative to the level abroad, the adjustment to equilib-

rium implies an increase in domestic investment relative investment abroad. Logi-

cally, sectors where domestic profitability is low relative to the level abroad, an

adjustment to equilibrium implies a decrease in domestic investment relative

investment abroad. In this chapter the feature of endogenous obsolescence has

been included in the equation representing depreciation expenditure. In that

sense, the endogenous transformation process has been introduced in the CGE

mini model.

4 A review of the literature on business fixed investment spending, and assesses of the current state

of knowledge and future agenda, is presented by Chirinko (1992).


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Turning to export demand, standard trade theory assumes that a small country

faces a perfectly elastic demand for its exports. This profile of trade may not be

realistic for many countries. While they may not be able to affect the world market

prices with their exports, the countries may register a declining market share as

their domestic costs rise. The most satisfying way to reflect this situation would be a

specification were export demand is a decreasing function of the domestic export

costs (prices) in foreign currency. However, as noted in Chap. 5, that type of export

demand function is not included in the CGE mini model. An adjustment is here

recommended.

The elasticities of obsolescence (exchange rate and relative capital rent) by

sector are assumed to have the same numerical values. However, alternative

assumptions have been made. Namely, an experiment with no elasticity on the

relative return, only on the exchange rate, and vice versa.

No elasticity on the relative rate of return, only on the exchange rate:



Experiment depreciation:


Experiment appreciation:


No elasticity on the exchange rate, only on the relative rate of return:



Experiment depreciation:


Experiment appreciation:


In the CGE mini model and with this numerical specification, the numerical

values above expose that the change in the exchange rate is the dominant influence

on obsolescence in all three sectors, with specific emphasis in the industry sector.

The discussion has now come to an end and all we can establish here is that the

explicit recognition of the importance of endogenous disinvestment activities in

transition to a new equilibrium seems to be an interesting, and perhaps also an

important, contribution.

References

Abel A (1981) Taxes, inflation, and the durability of capital. J Polit Econ 89:548–560

Benjamin N (1990) Devaluations and credibility in structural adjustment policy. J Policy Model 12

(4):659–669


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Chirinko RS (1992) Business fixed investment spending: a critic survey of modelling strategies,

empirical results, and policy implications, vol 27, Working paper series. Center for Economic

Studies, University of Munich, Munich

Epstein Larry G, Denny Michael GS (1980) Endogenous capital utilization in a short-run produc-

tion model. J Econ 12:189–207

References 117

Chapter 8

Globalisation and Intermediate Activity

In this chapter we focus on production chains, i.e., on intermediate commodities, in

manufacturing. Based on input–output data for the 2 years 2000 and 2005, we

investigate the input change of the intermediate import shares. The result is that the

share of intermediate imports has increased in some important sectors. The value-

added chain has been heavily changed in later years. This is visible as an increase in

offshoring and fragmentation in some important production sectors of the economy.

The conclusion is that the globalisation process has affected tasks within the

production chain in the Swedish economy. Finally, adjustment and necessary policy

reforms are discussed.1

8.1 Introduction

The enlarged European Union (EU) together with the economic effects from

increasing global markets are now also on the political agenda in Sweden.2 Inter-

national flows of goods, services and capital have all increased relative to output.

An important aspect of the globalisation over the last decade is that the world’s two

most populous countries – China and India – have reintegrated into the world

economy. The enlarged EU is now China’s most important export market. On the

other hand, China is now the second most important market for Europe, after

1 See Noren (2010). This is from an article published in Journal of Policy Modeling # 2010

Elsevier. The journal title: Intermediate structure changed by globalisation – A study of Swedish

manufacturing 2000–2005. Volume 32, Issue 2, pp. 223–230. License Agreement Number:

2893110936588.2 Sweden is an export-oriented market economy featuring a skilled labour force. Sweden is since

1995 member of the European union, but the Swedes have rejected euro in a referendum 2003, and

thus, maintains its own currency, the Swedish krona.



119

the United States.3 The EU is selling China the inputs it needs for its expansion,

intermediate commodities as well as sophisticated consumer commodities.

EU companies have also become major foreign investors in China. EU companies

in China import components to assemble and re-export them to the West. All in all,

the process has resulted in China now being the seventh-largest economy in the

World in terms of GDP.4 This implies a shift in the location of economic activity,

with an increased proportion of world output produced in emerging Asian

economies.

So far the companies in Europe have been successful because they has been able

to outsource labour-intensive parts of their production chain to other countries.

EU’s eastward enlargement has to some degree obscured the impact of the eco-

nomic rise of China. West European companies have invested so far three times as

much in the Central and East European countries as in China. To maintain growth in

the long run in the whole EU implies that flexibility and adjustment of economic

policy to production-cost changes will be more important. Immobile labour and

sticky labour costs could lead to increasing unemployment, and in the long run,

lower growth.5 From this point of view, economic policy rules to affect economic

transformation will become most significant.

Globalisation, or more precisely, the geographic dispersion of industrial and

service activities and the process behind it, is not new. For example, the second

half of the nineteenth century and the years before the first World War was a great

era of international economic integration.6 Since the 1990s the pace of international

economic integration has accelerated. Factors behind the process are dismantling of

trade barriers and foreign direct investments. New technology has reduced the costs

for transportation and communication. These factors have exerted downward pres-

sure on prices and stimulated economic growth in the world economy. The eco-

nomic opening-up of China began in the late 1970s, and since the start of the 1990s

the country has been an important location for investment and trading on a global

scale. The long and strong expansion that started in 2000, ahead of WTO entry in

December 2001, has continued into 2007.7 This growth is having a big impact on

global trade, capital flows and hence a reorganisation of global economic activity.

As transportation costs fell industry structure became increasingly

internationalised because it was no longer necessary to have production activities

3 For details, see Barysch et al. (2005). See also the other interesting articles in this special issue

about China as the new global player.4 Per capita GDP, however, GDP is relatively low to China’s large population.5 See the discussion in Buti and Sapir (1998) Chaps. 12 and 13.6 As a proportion of GDP, world trade reached a peak just before the First World War. It is only in

the last decades that it has returned to these levels. See Begg et al. (2008).7 China has followed its WTO commitments but used implementation legislation and so-called

non-tariff barriers to keep its markets closed in practice. Thus, United States and the EU, insisted

that it remained classified as a non-market economy for a period of 15 years. Such a classification

makes it easier for other countries to impose anti-dumping duties on China. See Barysch et al.

(2005), p. 13.

120 8 Globalisation and Intermediate Activity

close to the place of consumption. Some sectors lost some or all of their production

to import competition, but other sectors could expand their export markets. This in

turn engendered an important reallocation of labour. That is known as horizontal

specialisation. Following Baldwin (2006), this may be called the first unbundling,

i.e., the geographic separation of production and consumption. More recently a

second unbundling, which has variously been called fragmentation, offshoring, and

slicing up the value-added chain, shares many similarities with the first, but it

differs in many important ways. The second unbundling, also knowing as vertical

specialisation, does not affect sectors. It affects tasks within the production chain

regardless of sector. Since we are discussing production chains we will focus on

intermediate commodities. In this particular case, we must have access to data over

inputs of domestic intermediate produced commodities and imported intermediate

commodities. We are here not preliminarily interested in volume but in the inter-

mediate shares.8

Thus, in this study we will take a closer look at the Swedish manufacturing

sectors, comparing the year 2000 with 2005. A closer look implies a study at the

sector level by using input–output data.9 2000 to 2005 was a period of accelerated

economic integration, in Sweden as well as in other countries.10 Sweden is to a

large degree dependent on foreign trade and its industry is highly internationalised.

Free trade and stronger integration in Europe is the central element of Swedish

foreign and trade policy.

8.2 Calculation Methodology and Results

The data used in this study is based on Swedish input–output statistics concerning

domestic output at basic prices for the year 2000 and 2005. The data is calculated in

millions of Swedish currency (SEK) in current prices. Since we only compare

relations we can use current prices.11 The source material for the sector balances

and the work of computations concerning the distribution by sectors and input

deliveries has been undertaken by the national accounts-unit at Statistics Sweden

(SCB).

8 From 1995 to 2000 the share of imported intermediate commodities in total inter-mediate

commodities has increased, according to EUROSTAT data discussed by Sinn (2006). Following

Sinn, the share has increased in Europe, measured in percentage points. Italy by 2, Denmark by 4,

Finland by 4, Netherlands by 1, Austria by 4, Sweden by 5, and Germany by 6.9 Tables for 2000 have been revised compared to previous publication, due to a general revision of

the time series. Tables for 2005 are published for the first time.10 Using input–output tables from 10 OECD and four emerging market countries Hummel et al.

(2001) calculate the use of imported inputs in producing goods that are exported.11We will calculate the intermediate relation in respective year, and then only compare the

intermediate relation between the 2 years 2000 and 2005.

8.2 Calculation Methodology and Results 121

The commodities are in this study classified according to input characteristics

rather than by using standard industrial classifications.12 From a theoretical point of

view, commodities should be set up in a way which would achieve internal homo-

geneity.13 A classification according to input characteristics in capital-intensive,

labour-intensive, and knowledge-intensive commodities is thus applied. The sector

classification is presented in Appendix 2. Using the above specification and assum-

ing the variables have been observed accurately, we can turn to Table 8.1 in

Appendix 1. Here we compare 2 years, 2000 and 2005. Both calculated in current

prices. Focus will now be the ratio of intermediate imports to intermediate domestic

production and its change (substitution) from 2000 to 2005 in percentage points. The

number before the sector definition is the SNA (Swedish National Accounts) code.14

The capital-intensive industry comprises Sweden’s traditional basic industry

and includes mining, pulp and paper, and the iron steel manufacturing. The

distinguishing feature of the production process is the relatively high capital-labour

ratio. Long-term investment decisions with large-scale investment, together with

high capital costs characterise the capital-intensive manufacturing industry. Struc-

tural rationalisation and economies of scale have induced a concentration of

establishments, and thus, the number of production units has been reduced. Invest-

ment opportunities, not fluctuations in capacity level, are the important focus.

Exports from this industry are considerable in most industrialised countries. In

Sweden in particular, since the traditional basic manufactures are of relatively great

importance for the whole economy. In 2000 this sector accounts for 32 % of total

manufacturing.15 Turning to our calculations, all manufacturing sectors show an

increased activity in the capital-intensive industry. The explanation for the increase

in input of intermediate import during the period in mining and quarrying (10–14)

is the sharp increase in demand for iron ore on the global markets, especially in

China. The shortage of domestic intermediate inputs has increased the input of

intermediate imports. The share of intermediate imports have strongly increased in

chemicals, rubber and plastic products, other non-metallic mineral products

(24–26), and in basic metal products (27). Increasing international competition is

the main explanation. In chemicals (24), research and development services16 are a

12We are following the input characteristics presented in Ohlsson and Vinell (1987, pp. 243–247).

These basic input characteristics are also used in the Swedish Medium Term Surveys, SOU

(2000):7 and SOU (2003):45.13 The homogeneity assumption requires that all commodities of a single sector should be

produced in strictly fixed proportions, that each sector should have a single input structure, and

that there should be no substitution between the commodities of different sectors.14 The level of detail in the tables is 53 industries and 53 products, classified according to NACE

Rev. 1.1 and CPA2002. Due to confidentiality issues SCB is not able to present products 13 and 14

separately. These products are presented within product aggregate 13. Nor SCB is able to present

products 15 and 16, 31 and 32 separately. These products are presented within product aggregates

15 and 31.15 Note, the mining and quarrying industry (10–14), and coke, petroleum products and nuclear

fuels (23) are included in the manufacturing sector.16 To study the input of research and development services (73) the reader must view the

input–output tables referred to in the reference list.


dominant input. That input show a strong increase in 2005, particularly the domes-

tic input. However, in rubber and plastic products (25), input from research and

development services demonstrates a strong decrease.

The labour-intensive industry includes sawmills, and textiles manufacturing.

There is a long tradition of strong competition from low-wage countries. This is an

important explanation for the long-run decline of employment in many parts of this

sector. The companies in the labour-intensive industry are in general small and

medium-sized. In 2000 this industry accounts for 29 % of total manufacturing.

Usually the companies in the labour-intensive industry are characterised by a

relatively strong concentration on import substitution (the share of intermediate

import is decreasing). Companies with high import dependence are represented in

the labour-intensive manufacturing sector. However, this structure is not now

reflected in the present calculations. We see now, in all sectors belonging to the

labour-intensive industry, an increase in the relative input of inter-mediate imports.

The explanation for this change is increased global competition, especially since

China in 2001 became a more prominent feature of the international landscape.

The knowledge-intensive industry includes a number of large international

engineering companies, for instance Ericsson, Volvo and ABB. The large propor-

tion of highly educated employees in this industry distinguishes it from other

industry sectors. New technology and new products are not only the driving forces,

but also strategy because of the competitive situation. Thus, a continuous renewal

of the process of production is necessary. To work with the latest technology is

important. As a consequence, the lifetime of capital will become relatively short.

The knowledge-intensive manufacturing industry comprises almost all manufacture

of fabricated metal products, machinery and equipment. The industry comprises a

large share of total manufacturing. From enterprises that work on a global market to

a small subcontractor on the local market. The different companies have, of course,

a different kind of dependence in their foreign relations. In 2000 this industry

accounts for 39 % of total manufacturing in Sweden.

The knowledge-intensive industry includes some of the largest and fastest grow-

ing sectors in Sweden. In this industry the included sectors demonstrate a strong

variation in intermediate inputs. Two manufacturing sectors suggest a relative

strong increase in the input share of intermediate domestic production. That is the

sector producing office machinery and apparatus (30) and the sector producing

medical, precision and optical instruments, watches and clocks (33).17 However,

an increase in intermediate import share, are registered for electrical machinery

and apparatus. Radio, television and communication equipment included (31–32).

What is more important, concerning these two manufacturing sectors, are the

demonstrated decrease in total activity for 2005. In addition, the share of domestic

17 Despite a sharp decrease of the price index for intermediate imports in sector 30, the input–output

statistics show no relative increase in the volume for intermediate imports, quite the contrary.

However, since the input–output statistics are in current prices the volume reported in the

input–output table are influenced by the price index. It also indicates that the short-term substitution

elasticity between intermediate imports and intermediate domestic production is very low.

8.2 Calculation Methodology and Results 123

intermediate input of research and development services decreased strongly. This

can have serious consequences in the long run, because it suggests a structural

decrease in Sweden of the main part of research and development of new products,

and perhaps a further outflow of production itself. Finally, a slight increase in

intermediate import ratio is also demonstrated in the sector manufacturing motor

vehicles, trailers and semi trailers and other transport equipment (34–35).

In several fast growing exporting sectors offshoring and outsourcing have been

an increasing alternative to parts of domestic production. By imports of

intermediates to relative low cost the companies have been more competitive,

and thus, can maintain itself, and growth on the international marketplace. This is

an example of specialisation according to comparative advantage within a specific

activity or company. The costs are lowered as productivity increases.

Consumers benefit directly from greater competition, which reduces prices and

sharpens incentives for innovation. The increase in the share of intermediate

imports in some important sectors is an indication that the Swedish production

structure has been affected by the economic integration process, both globally and

by the European integration process. The tasks within the production sectors, has

been affected, i.e., a second unbundling. However, different sectors change differ-

ently and a structural change will most likely take place. In the long run the

outcome can be a new structural profile of the Swedish economy.

8.3 Questions of Economic Strategy

In an open and growing economy globalisation is in most cases very positive,

particularly in the long run. Economic history has demonstrated that those countries

that try to cut themselves off from globalised markets lose out economically. In a

new study by the European Commission that examines the social impact of

globalisation for the EU economies18 the key message is that the EU as a whole

will gain from globalisation, but these gains will not be uniformly distributed across

individuals, regions and countries. The outcome will depend on adaptation and

policy responses. It will be a problem if the openness to the international market is

restrained, and as a consequence the activity in the international economy goes

down. As a result factories have been closed and economic activities have been

relocated abroad. Generally, low-skilled labour force has been negatively affected

by globalised competition, with falling relative wages of unskilled workers

contributing to widening of income inequalities. Thus, many people see little or

no benefit of globalisation. Following Verheugen (2006), the problem is that

benefits of an open and globalised integrated economy are visible at the aggregated

level, but the suffering is always local. If we are not very sensitive for such issues,

the growing international tendency towards national economic protectionism will

increase. The increase in imports in intermediate commodities is usually

18 Begg et al. (2008).


concentrated in relatively few product groups in the knowledge-intensive industry.

However, the labour-intensive industry also for the first time shows tendencies to

increase inter-mediate imports. The number of product groups has increased.

Growing imports of intermediate inputs implies a fall in the demand for

domestic labour. Needles to say; only if the growth in demand is increasing, new

jobs can be created. As we already know, in two important knowledge-intensive

manufacturing sectors (31–32) the total domestic activity have decreased very

seriously. The manufacturing in these sectors are increasingly being shifted to

lower-wage countries. This is a result of increased outsourcing. In other words,

vertical specialisation. From a business perspective this is of course a successful

strategy, so it can also be from an economist’s point of view. Without outsourcing

we perhaps would lose the whole domestic manufacturing sector. The economic

problem is to find new domestic activities that create new jobs. This raises the

question of structural transformation,19 and hence, of economic adaptation and

policy responses. In addition, also the question of economic policy and how

much economic policy we need.

An increased part of world output is produced at relatively low cost in Asian

countries. Demand is, so far, dominated by the established industrialised

economies. In other words, production moves to countries were labour cost is

low, but the main part of demand is to be found in relative high income countries

in the west, which guarantees a relative high price for the product. According to

economic theory the wage costs will narrow, but we cannot say when and how

much. However, if a large amount of production concentrates to low-cost regions

the unemployment will start to increase in the high-cost (high-income) regions.

Hence, the necessary demand from high-income regions for production in the

low-cost regions will be undermined. To get these forces into balance will be the

basic equilibrium problem in the globalised economy.

The strategy for the single European country is flexibility and adaptation to

the global equilibrium situation. The single European country has no potential to

influence the global equilibrium. However, if the single country is a member of

the European Union the situation may be different. Of course, it is still a question

of flexibility and adaptation, but the union has the potential to influence the

global equilibrium. The question in Europe is to find the balance between the

European social model and increasing its competiveness in the globalised

economy.

19 In an interesting article by Greenaway et al. (2008) transformation of industrial resources takes

one of three forms. Exit by closedown, exit by merger or acquisition, and switching to another

industry. Using a dataset of Swedish firms that extends over two decades, the authors find as the

level of international competition increased, that firms exited by merger or closed compared to no

change at all. They did not found a similar correlation regarding the probability of switching,

which tended to be higher in industries characterised by comparative disadvantage.

8.3 Questions of Economic Strategy 125

Appendix 1: 2000 and 2005 SNA Statistics

Million SEK in current prices

Appendix 2: Sector Classification

Capital-Intensive Industry

• 10–14: Mining and quarrying.

• 21: Pulp, paper and paper products.

• 22: Printed matter and recorded media.

• 24–26: Chemicals, rubber and plastic products, other non-metallic mineral

products.

• 27: Basic metal products.

Labour-Intensive Industry

• 15–16: Manufacture of food, beverages and tobacco.

• 17–19: Textiles. Wearing apparel and furs. Leather and leather products.

Table 8.1 Input of intermediate domestic production and imports

Column Q00 M00 M/Q Q05 M05 M/Q

M/Q substitution

00–05 percentage points

Capital-intensive industry

10–14 6,386 2,133 0.33 8,749 3,455 0.39 6.09

21 48,294 17,991 0.37 54,812 21,584 0.39 2.13

22 34,759 7,464 0.21 34,403 7,361 0.21 �0.07

24–26 45,194 35,531 0.79 53,699 49,889 0.93 14.28

27 37,578 21,972 0.58 52,948 37,242 0.70 11.87

Labour-intensive industry

15–16 65,037 16,461 0.25 69,529 20,263 0.29 3.83

17–19 4,437 3,562 0.80 4,168 3,588 0.86 5.80

20 38,301 7,160 0.19 44,557 9,375 0.21 2.35

28 34,831 14,962 0.43 40,737 20,227 0.50 6.69

36–37 15,573 7,803 0.50 16,131 9,576 0.59 9.25

Knowledge-intensive industry

29 52,790 34,324 0.65 71,370 46,634 0.65 0.32

30 1,287 1,673 1.30 1,872 1,627 0.87 �43.08

31–32 74,455 75,344 1.01 43,407 47,758 1.10 8.83

33 9,644 11,122 1.15 12,444 12,216 0.98 �17.16

34–35 77,467 57,414 0.74 108,778 83,086 0.76 2.27

Source: Statistics Sweden (SCB), Input–output tables for Sweden 2000 and 2005.

Q ¼ input of intermediate domestic production 2000 respective 2005, M ¼ input of intermediate

imports 2000 respective 2005


• 20: Wood and wood products, except furniture.

• 28: Fabricated metal products, except machinery and equipment.

• 36–37: Furniture, other manufacturing and recovered secondary raw materials.

Knowledge-Intensive Industry

• 29: Machinery and equipment.

• 30: Office machinery and apparatus.

• 31–32: Electrical machinery and apparatus. Radio, television and communica-

tion equipment included.

• 33: Medical, precision and optical instruments, watches and clocks.

• 34–35: Motor vehicles, trailers and semi trailers, other transport equipment.

References

Baldwin R (2006) Europe’s reaction to the challenge of globalisation. CESifo Forum 7(3):29–35

Barysch K, Grant C, Leonard M (2005) Embracing the dragon: can the EU and China be friends?

CESifo Forum 6(3):8–15

Begg I, Draxler J, Mortensen J (2008) Is social Europe fit for globalisation? A study on the social

impact of globalisation in the European Union. Centre for European policy Studies. Published

by The European Commission, Directorate-General for Employment, Social Affairs and Equal

Opportunities. Unit E1: social and demographic analysis

Buti M, Sapir A (1998) Economic policy in EMU, The European Commission Services. Oxford

University Press, Oxford

Greenaway D, Gullstrand J, Kellner R (2008) Surviving globalisation. J Int Econ 74:264–277

Hummels D, Ishii J, Yi K-M (2001) The nature and growth of vertical specialization in world

trade. J Int Econ 54:75–96

Noren R (2010) Intermediate structure changed by globalisation: a study of Swedish

manufacturing 2000–2005. J Policy Model 2:223–230

Ohlsson L, Vinell L (1987) Tillvaxtens drivkrafter: En studie av industriers framtidsvillkor.

Industriforbundets Forlag, Stockholm

Sinn H-W (2006) Welcome and introduction lecture to the 5th Munich Economic Summit 2006.

Europe and the new division of labour. CESifo Forum 7(3)

SOU 2000:7. Langtidsutredningen (Medium term survey) 99, Bilaga 3. Appendix A och B,

Finansdepartementet (Ministry of Finance), Allmanna forlaget, Stockholm

SOU 2003:45. Langtidsutredningen (Medium term survey) 2003, Bilaga 6. Appendix B. Finansde-partementet (Ministry of Finance), Allmanna forlaget, Stockholm

Verheugen G (2006) Europe’s answer to the global changes in the division of labour. CESifo

Forum 7(3):24–28

Statistical Sources

Statistics Sweden (SCB), The Swedish National Accounts, input–output tables for Sweden

according to the European System of National Accounts (ESA95). Input–output tables 2000

and 2005. Publication NR 10 SM 0701

By internet the tables can be found (Autumn 2008) at SCB web page: www.scb.se. See National

Accounts: http://www.scb.se/Pages/ProductTables____11040.aspx

References 127

http://www.scb.se

http://www.scb.se/Pages/ProductTables____11040.aspx

A Final Word

The equilibrium models are a logical system which must, in one way or another,

correspond to the real situation. Only the most relevant characteristics are included

in the models under discussion. In other words, an abstraction of the real system.

Such an abstraction is both necessary and effective in economics. However, all

equilibrium models presented in this study have their shortcomings. Hence, a sound

judgement must characterise the use of these models in applied work.

From an evolutionary point of view the equilibrium models are generally

inadequate to capture the specification of the mechanisms that creates incentives

for the entrepreneur to enforce new trans-formation activities to maintain the

capacity for growth. Besides imperfections in the competitive system, different

degree of active resistance to structural transformation may appear. A classical

study by Svennilson (1954)1 of the economic development of Europe between the

two world wars indicated that, in most cases, the resistance to a structural renewal,

i.e. a structural transformation directed to investments in new technology and

the establishment of new industries, was based not only on imperfections in the

competitive system but also on private agreements (vested interests). Thus,

increased competition from abroad is often not met with a necessary structural

renewal, but an increased rationalisation among the existing structure of produc-

tion. The result is an increase in capacity despite stagnating demand. In this way the

structural transformation of the economy as a whole is held back and the general

economic growth will slow down.

This book has been concerned with basic equilibrium models of industrial

structure and transformation. The workings of the presented equilibrium models

have been clarified. Thus, we have been able to examine the importance of different

initial conditions, resource endowments and the economic structure within a frame-

work that imposes intersectoral consistency. Not unexpected, the equilibrium

models alone is not sufficient to analyse or reflect the whole real situation.

1 Svennilson I, (1954) Growth and stagnation in the European economy. United Nations Economic

Commission for Europe, Geneva.


DOI 10.1007/978-3-642-34994-2, # Springer-Verlag Berlin Heidelberg 2013

129

The equilibrium models can more be seen as a request in terms of economic

efficiency. Had it be more productive to look at the historical and institutional

process? We don’t know. Sometime a modelling approach works out very well to

describe the situation in question. Sometime the approach is less useful. In addition,

every time period has its specific problem, although it is a reflection on earlier

periods. The best way is to use several approaches. Different approaches can

be seen as complements. There are different approaches, including models, for

different purposes.

130 A Final Word

Index

A

Abel, A., 110

Activity level, 10, 14

Additivity, 4

Adelman, I., 55

Allocative efficiency, 13

Armington assumption, 64

Armington, P., 41, 64, 74

Armour, J., 103

Arrow, K.J., 57

B

Baldwin, R., 121

Barysch, K., 120

Begg, I., 120, 125

Benjamin, N., 112

Bergman, L., 41, 55

Bodie, Z., 101

Borges, A.M., 55

Boter, H., 105

Buti, M., 120

C

Capital stock, 12

Carlsson, B., 99

CGE mini model. See also Computable

general equilibrium (CGE) models

computed benchmark equilibrium, 110, 111

domestic savings, 115

elasticity of sector, 110

export demand function, 116

GDP, 115

new specification, 109–110

no elasticity, 116

profitability, 115

real exchange rate

appreciation of domestic currency,

113, 114

depreciation expenditure, 112

domestic currency devaluation,

112, 113

summary matrix, 112, 114

sectoral and aggregate employment

results, 111

structural transformation, 110–111

trade-off, 114

CGE models. See Computable general

equilibrium (CGE) models

Chenery, H., xvii, 4, 73, 76, 96

Chiang, A.C., 7

Chirinko, R.S., 115

Clark, P.G., 4

Computable general equilibrium (CGE)

models, xiii, xv–xvii

aggregate employment results, 78

basic structure

aggregate labour, 58

degree of substitution, 57

domestic savings, 75

domestic supply, 58

duality theorem, 56

economic activities, 73

fundamental general equilibrium

links, 56

general characteristics, 74

index of domestic prices, 75

investments, 75

logical culmination, 57


DOI 10.1007/978-3-642-34994-2, # Springer-Verlag Berlin Heidelberg 2013

131

macro-econometric models, 56

market economy, 74

maximisation problems, 56

Norwegian economy, 57

numerical multisectoral economic

models, 57

process of production, 74

production function, 58

Walrasian model, 74

benchmark equilibrium, 76, 77

calibration procedure, 76

capital stock, physical deterioration, 77, 78

comparative benchmark, 77, 80

depreciation expenditure, 80

DEPRj, 79

domestic capital stock growth, 80, 81

summary matrix, 81

Chenery model, 76

construction

budget constraint, 58

Cobb-Douglas production function,

58, 59

conditional demand for capital, 60

conditional demand for labour, 59

exported and imported commodity,

60, 63

household income, 61

intra-industry trade, 63

open economy, 61–62

total cost, 59

unit profit equation, 60

value-added components, 61

world market prices, 62

data collection, 77

Dervis model, 76

development, 69

domestic capital stock, 83–84

domestic currency appreciation, 77, 80

domestic currency devaluation, 77, 79

foreign capital inflow, 79

foreign trade

aggregate and imports commodity, 64

CET function, 67

constant elasticity export demand

function, 66

cost minimization, 65

domestic production, 63

export demand, 65–66intra-industry trade, 64, 70

price-taker, 64

small-country assumption, 67

standard trade theory, 66

substitution elasticity, 65

supply side exports, 67

trade substitution elasticity, 68

world market prices, 63, 65

GAMS Program, 70

linear model, 69

market-clearing processes, 70

mathematical equations

activity prices, 87

capital commodity price, 87

capital formation, 94–95

CET function, 88

Cobb-Douglas production function,

87–88

composite commodity aggregation

function, 89, 90

cost minimisation, 89

domestic export prices, 86

domestic import prices, 86

domestic output/market value,

86–87

domestic production, indirect taxes, 93

domestic sales, non-traded sectors, 89

domestic sales value, 86

export supply, 88, 89

first order condition, profit

maximum, 88

general price level, 87

government consumption shares, 92

government revenue, 92

government savings, 92

household savings, 92

inventory investment, 90

labour market equilibrium, 88

Leontief matrix, 90

market equilibrium, 95, 96

parameters assignments, 96, 97

private consumption behaviour, 91

private GDP, 91

tariff revenue, 93

total import premium income, 93

total income, 91

optimum resource allocation, 75

quadratic model, 69

real exchange rate

arbitrarily devaluation, 81, 82

comparative benchmark, 77, 82

domestic currency, 80, 82, 83

elasticity export demand, 82

trade-off, open economy, 83

sectoral employment results, 78

won per dollar, 77

132 Index

Condon, T., 64, 76, 79

Constant elasticity of the transformation (CET)

function, 67

Cumming, D., 103

D

Dahl, H., 64

Dahmen, E., 99

Debreu, G., 10, 57

De Grauwe, P., xiii

de Melo, J., xvii, 73, 96

Denny Michael, G.S., 110

Depreciation expenditure rates (DEPRj), 79

Dervis, K., 34, 56, 64, 68, 75, 76

Devarajan, S., 64

Dinwiddy, C.L., 58

Dorfman, R., 26, 43, 44, 46, 47

E

Economic disequilibrium, xi

Economic transformation, xi

bankruptcy law, 103

capital stock, 103

elasticity of substitution, 101

entrepreneur framework, 100

foreign and domestic investments, 101, 102

geographical diversification, 102

long-term investments, 99

production costs reduction, 101

rate of return, 101, 102

Schumpeterian notion, 100

skills testing, 101

steady-state process

capital mobility, 105

disinvestment, 104, 105

golden rule level of capital, 104

real capital accumulation, 104

three phases, 105

vintage, 106

structural organization, 103

Enke, S., 23

Epstein Larry, G., 110

Euler’s theorem, 15

European Central Bank (ECB), xiii

European Monetary Union (EMU), xiii

F

Final demand, 11

Flam, H., 40, 41

Foreign trade

competitive imports, 29–30

foreign currency/imported amount, 30

foreign exchange constraint, 31

neoclassical model, 31

non-competitive imports, 30

transportation costs and tariffs effect, 30

G

Ginsburgh, V., 55

Globalisation process

capital-intensive industry, 123, 126

economic strategy, 125–126

European Union (EU), 119, 120

exporting sectors, 124

horizontal specialisation, 121

intermediate domestic production

and imports, 122

internation economic integration, 120

knowledge-intensive industry,

123–124, 127

labour-intensive industry, 123, 127

structural change, 125

Sweden, 121

Swedish input–output statistics, 121

transportation costs, 120–121

Greenaway, D., 126

H

Harrington, D.H., 22, 23, 26, 43, 44

Hayek, F., 100

Heady, E., 23

Henriksson, R.G.H., 99

Hoglund, B., 2

Horizontal specialisation, 121, xviii

Hotelling, H., 24

Hummel, D., 121

I

Identity matrix (I), 5, 7

J

Jaffe, W., 18

Johansen, L., 55, 57

Judge, G., 22–24, 26, 28, 29

K

Karlsson, A.-K., 105

Keynesian policy, xiii

Koopmans, T.C., 4, 13, 28

Krugman, P.R., 105

Kuczynski, M., 2

Kuhn, H.W., 14

Index 133

L

Labour resources, 12

Lancaster, K.J., 42

Leontief input–output model, xiv, xv

basic structure

additivity, 4arbitrary process, 5

final demand, 6

identity matrix, 5

input coefficients, 3

input–output transactions system, 3

matrix notation, 5, 6

process, 4produced commodities, 5

production activity, 5

proportionality, 4relative price of commodity, 4

total demand, 3

economy, 1

matrix form, 2

numeric model, 6–7

“Proprietary,” “Productive,” and “Sterile”

class, 2

Tableau Economique, 2Leontief matrix, 7

Leontief, W., 2, 3

Leon Walras, 43

Lewis, J., xvii, 73, 96

Linear numerical general equilibrium model

commodities and activities, 9

consumers, 10–11

feasible activities, 11–12

producers, 10

programming formulation

commodity price, 12, 13

competitive equilibrium, 19

consumer equilibrium, 18decentralized decision-making process,

16, 17

desired commodities, 13

Lagrangean multipliers, 14–15

marginal utility of income, 19

non-negative saddle point, 18

optimality conditions, Kuhn-Tucker

theorem, 14

Pareto optimality and efficiency, 13

producer equilibrium, 16profitability of investments, 16

shadow factor price, 15

state of equilibrium, 13

utility function, 15

Lofgren, H., 79

Lowstedt, E.-L., 105

M

Maddala, G.S., 46

Manne, A.S., 55

Marshall, A., 25

Meek, R.L., 2

Morishima, M., 18

N

Nickell, S., xiv

Noren, R., 22, 119

Norman, V.D., 38

O

Ohlsson, L., 122

P

Penrose, R., 46

Plessner, Y., 23

Primary commodities, 9

Private ownership economy, 10Produced commodities, 9

Q

Quesnay, F., 2

R

Reynolds, P., 105

Ricardo, D., xii

Robinson, S., xvii, 55, 73

S

Salgado-Banda, H., 100

Samuelson, P.A., 23, 25, 26, 43, 46, 47, 64

Sapir, A., 120

Scarf, H., 57

Schumpeter, J., 85, 100

Sheshinski, E., 100

Shoven, J., 57, 76

Sinn, H.-W., 121

Sodersten, 34

Solow, R.M., 26, 43, 46, 47

134 Index

State of economic balance, xii

Stern, N., xvii

Structural transformation, xiii

T

Tableau Economique, 2The Takayama judge activity model

comparative advantages, 41–42

demand and factor supply functions, 22

empirical findings

capacity expansion, 39

extreme specialisation, 41

least- and high-cost sectors, 38

maximum availability, 37

net private investment, 39, 40

next period optimization, 37

profitability, 37, 38

sectoral demand, 39

structural renewal process, 39

Swedish economy, 40

equilibrium prices, 21

linear activity model, 22

linear input–output structure, 21

optimal solutions, 21–22

programming formulation

demand and supply prices, 32

domestic economy, 33–34

economic equilibrium, 32

foreign exchange, 34

international trade, 35

Lagrangean point, 32

net benefit function, 31

optimum demand quantity, 32–33

pre-equilibrium price vectors, 32

shadow supply price, 33

quadratic programming problem

domestic production pattern, 24

feasible set, 23

Leontief input–output model, pricing

mechanism, 23

optimisation approach, 22

“quasi-welfare function,” 23

Samuelson model, 23

shadow prices, 24

two way feed-back, 22

sectors, 47, 48

specification

concave quadratic function, 27

consumers’ plus producers’ surplus, 24

consumer’s surplus, definition, 25

demand and factor supply, 26

demand curves, 27

demand-price function, 26

Engel curves, 29

factor supply curve, 25

final commodity, 26

foreign trade, 29–31

integrability conditions, 28

inverse factor, commodity, 27

market behaviour, 25

Marshallian quasi-rent, 25

net social monetary gain, 28–29

objective function, 24, 25

path-independence condition, 29

primary commodity, 27

total cost, 28

Walrasian system, private

expenditures, 24

temporary equilibrium, 47–52

capital commodities, 35

capital stock, 35, 36

inter-temporal optimization, 35

profitability, 36

replacement and net investment, 36

sectoral investment matrix, 36

Walras-Cassel model (see Walras-Cassel

model)

Takayama, T., 22–24, 26, 28, 29

Taylor, L., 56

Teal, F.J., 58

ten Raa, T., 1

Transaction matrix, 6

Tucker, A.W., 14

U

Unbundling, xv

V

Vaggi, G., 2

Varian, R.H., 28

Verheugen, G., 125

Vertical specialisation, xviii

Vinell, L., 122

von Friedrichs, Y., 105

W

Waelbroeck, J., 55

Wainwright, K., 7

Walras-Cassel general equilibrium model, xvi

Walras-Cassel model

income constraint on demand, 46

Leontief matrix, 45

Index 135

Walras-Cassel model (cont.)mathematical exposition, 44

matrix transforrmation, 44

non-substitution theorem, 46

price component of rewards, 45

quadratic input–output model, 44

Walrasian factor supply and commodity

demand functions, 43

Werin, L., 2, 30, 41

Whalley, J., 57, 76

White, S., 105

Y

Yaron, D., 23

136 Index

equilibrium models in an applied framework: industrial structure and transformation

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