INTERNATIONAL TRADE, INDUSTRIAL POLICY AND

INITIAL CONDITIONS

Leopoldo Yanes∗

School of Economics, University of Queensland

Abstract

This paper develops a two-country, general equilibrium, model of oligopoly in international

trade. The model brings forth an analysis of how technological capability and market structure

relate to economic development. In a symmetric equilibrium a gains-from-trade-theorem is ob-

tained. Allowing for asymmetric initial conditions, a backward economy may lose from free-trade

with an advanced economy, if the gap in initial conditions is too wide. However, the advanced

economy always gains by trading. This provides positive and normative criteria for the choice of

trading partners and the formation of trade blocks. We also consider the feasibility and welfare

effects of industrial policy, we particular reference to catching-up. In this model, catching-up is

always feasible and welfare improving.

KEYWORDS: Oligopoly, international trade, industrial policy, technological capability.

JEL CODES: D43, F12, F15, L13, L52, O14, O24.

∗I am indebted to John Sutton for his help and encouragement. I would also like to acknowledge insightful discussions

with and suggestions by Tim Besley, Mark Schankerman, Anthony Venables and seminar participants at the London

School of Economics and Universitat Pompeu Fabra. STICERD and Universitat Pompeu Fabra provided infrastructure

and a stimulating research environment. Any errors or shortcoming are my own responsibility. Correspondence address:

School of Economics, University of Queensland, St. Lucia, Brisbane, QLD 4072, Australia. Email: L.Yanes@uq.edu.au.

Tel: 61-7-3365 6619. Fax: 61-7-3365 7299.

1

I. INTRODUCTION

Disappointing results from structural reforms based on prescriptions of the ‘Washington consen-

sus’ (particularly in Latin America and Sub-Saharan Africa) and studies detailing how East Asian

economies diverged from such prescriptions and yet achieved outstanding performance [Nelson and

Pack, 1999; Amsden, 1988 and Wade, 2003], have sparked a search in the economics profession for a

better understanding of how such heterodox policies could have worked, and whether they did in fact

work. Rodrik [2004, p.1] puts the problem succinctly:

“Perhaps the disappointments in Africa are due to special circumstances: the ravages

of civil war and crises in public health. But how can one explain the Latin American

story, which is one of poor growth and productivity performance in the 1990s–much worse

than in the 1950-1980 period? Fiscal discipline, privatization and openness to trade have

produced an economic performance that does not even begin to match the performance

under import substitution. And that is a puzzle of major proportions.”

This paper contributes by providing theoretical insight into the analysis of industrial and trade

policy, within a model that captures some salient features of the East Asian experience, in a framework

which is standard in economic analysis. Nelson and Pack [1999] come to the conclusion that the theories

we have so far are lacking in their microfoundations:

“Economic analysis in general, but development economics in particular, needs a better

theory of firm behaviour...it needs a realistic theory, that is consistent with what we have

learned empirically, about the processes of firm, industry and national learning, that have

been behind The Asian Miracle” [p. 435]

Without a clear, positive theory of policy intervention, one is left with little foundation on which to

pursue such crucial decisions. What are the precise mechanisms by which these policies worked? Did

they work at all or is there some other underlying process? To use Robert Wade’s terminology [2003,

p. 348], after a few decades of ‘inductive policy analysis’, it is time to apply the lessons we can draw

from this literature to build a theory which takes into account some of the most relevant features of the

process. It is in this spirit that we find a need for formal, testable theories of industrialization. Before

enumerating these features, it is convenient to define some key concepts, which we will use extensively.

The first is that of technological capability. This term refers to the knowledge of workers within

the firm, which determines the levels of productivity and product quality [Fransman and King, 1984;

Lall, 1992 and Sutton, 2004]. In this study we will use the term in the narrow sense of ‘product

quality’. The second notion is that of initial conditions. Usually, this is taken to reflect the status

quo, including sociopolitical, as well as economic, structure. Here we will use this notion in the

restricted sense of initial conditions pertaining to technological capability. More generally, these may

be interpreted as encompassing all initial conditions which are relevant to the production process.

The framework we build incorporates the following features:

1) Oligopolistic behavior and the associated strategic interaction.

2) An endogenous treatment of technological capability and market structure.

3) A general equilibrium framework.

2

4) A dualistic structure (characteristic of many developing countries).

Features 1 and 2 emphasize the importance of large, oligopolistic enterprises which successfully

embarked upon technologically advanced projects, by learning and sometimes developing indigenous

technological capability, with particular reference to the cases of South Korea and Japan [Amsden,

1989]. Features 3 and 4 are essential to analyze the impact of structural change as the economy

industrializes. After we develop the model incorporating these features, we will be in a position to

introduce:

5) Asymmetries in initial conditions.

This will bring forth a coherent analytical framework which will allow us to analyze the role of

industrial and trade policy, building on solid micro foundations. The model features two countries,

each of which has two industries. One of the industries (labeled Y ) produces a homogeneous good

under constant returns to scale. The other industry (labeled X) produces a vertically differentiated

product with increasing returns to scale and an oligopolistic market structure. The terms of trade are

determined endogenously, whence each country is treated as a large economy1 . Both economies have

identical structures, although we allow for asymmetry in all parameters except σ (the degree of product

substitutability). We assume free trade in the goods market and zero transport costs. Consumers

maximize a (quadratic) utility function over goods X and Y . Consumers’ income is constituted by

their wage receipts, by profits accruing from shares owned in firms, and by the value of an endowment

of good Y . The output of industries X and Y is consumed by workers, and there are no intermediate

inputs. Consumers have a constant labour supply, which has been normalized to unity. Labour is

perfectly immobile across and perfectly mobile within countries. Labour is the sole input and is used

by industries X and Y (with the latter absorbing any surplus labour).

Industry X is characterized by a three stage game. In stage 1 firms decide whether to enter or not,

and a zero profit condition emerges. In stage 2, firms compete in technological capabilities by investing

in sunk costs, taking market structure as given. Stage 3 portrays (Cournot) competition in quantities,

taking market structure and technological capabilities as given. In this industry, the presence of fixed

costs is associated with increasing returns to scale. In principle, industry X could use labour to

generate technological capability (fixed costs) and to produce type X goods (variable costs). We will

simplify matters by assuming that variable costs are zero (the analysis can be readily extended to non-

zero variable costs). Hence, industry X uses labour exclusively to generate technological capability.

The assumption that all fixed costs are sunk becomes reasonable when we consider that these take the

form of wages paid to workers: If the firm exits, it cannot get any of the wage payments back from its

workers. That industry X does not have any variable production costs can be justified by the following

allegory: Imagine that this industry uses labour to build ‘solar powered robots’. Once the robots are

built, they then produce output in the Cournot stage of the game, at a variable cost of zero.

Industry Y features a freely available 1:1 technology. The output of industry Y is equal to em-

ployment in that industry. This implies a very simple form of constant returns to scale. Good Y is

treated as the numeraire, so its price is normalized to unity. Thus the marginal product of labour in

1The term ‘large economy’ is used in the traditional trade theoretic sense: changes in the individual economies affectthe world (general) equilibrium. The alternative case would be that of a small economy, where changes in an individualeconomy do not affect the world (general) equilibrium. In the latter case, terms of trade are usually assumed to beexogenous.

3

industry Y will also be unity. We will see that this effectively constitutes the outside option of workers

employed in industry X, and it implies that the economy has a minimum wage equal to 1.

We find the usual result that, under symmetry, autarky is not welfare improving. Comparative

statics results lead us to some interesting conclusions regarding development configurations. The no-

tion of a ‘development configuration’ refers to the characteristics an economy may exhibit in terms of

its technological capability and market structure. In particular, a high-tech configuration features

an economy with few firms, each with high technological capability. By contrast, a proliferation

configuration features an economy with many firms, each with low technological capability. These

characterizations lead to the following question: Under which circumstances (i.e., parameter values)

will a high-tech configuration generate a higher wage rate (and welfare) than a proliferation configu-

ration? There is a trade-off for labour demand when choosing whether to opt for few firms with high

technological capability or for many firms each with low technological capability. A-priori, it is not

clear which leads to the higher level of income and welfare. We find that, unless type X goods are

poor substitutes, it is always welfare improving to have a high-tech configuration.

We also consider various types of industrial policies under symmetry, with different financing

schemes (all of which feature lump-sum taxes). The first finding is that if the government adopts

a financing scheme whereby it pays for all of the change in firms’ expenditure relative to the original

equilibrium outcome, then consumers earn the same income and have the same welfare, with or without

intervention (the net social benefit of intervention is zero). Other financing schemes result in either

taxes or subsidies being optimal, depending on parameter values. The restrictions on parameter values

provide a positive and normative basis for decisions regarding which industries should feature which

type of policy. Whence, we provide a formal basis for industrial targeting, under the assumption of a

symmetric equilibrium.

The assumption of symmetry is, clearly, a strong one. Hence, we address the impact of asymmetries

in initial conditions and the question of whether, given this asymmetry, catching-up is feasible and

welfare improving. We find that a technologically advanced nation benefits from free trade with all

nations of lower or slightly higher technological capability. However, a nation with a significantly

lower technological capability will not benefit from free trade with an advanced nation, and is better

off either in autarky or trading with nations whose technological capabilities are not much higher than

its own. Thus, there exists a range of admissible technological capabilities within which free trade is

welfare improving for both nations. Outside of this range, only the advanced nation reaps the benefits

of free trade. This provides an answer to the question of Who should trade with whom? That is, which

countries should be chosen as partners for the formation of trading blocks? Such results are particularly

relevant to the analysis of the recent wave of (bilateral) free-trade agreements between the USA and

Australia and many of their smaller (backward) trading partners, particularly Latin American (for

the USA) and Asian economies (for Australia). Regarding the issue of catching-up in the presence

of asymmetries in initial conditions, we find that a subsidy to enhance technological capability is an

effective instrument which allows the backward economy to match the advanced economy’s wage rate.

Moreover, if the subsidy is funded via a lump-sum tax, it will be welfare enhancing.

Another finding sheds light in a persistent puzzle in Taiwanese and South Korean development.

In particular, in a comment on Rodrik [1995], Victor Norman notes that in these nations the export

4

boom occurred prior to the investment boom. The received view proposes the reverse: Investment

leads to expansion of output, which is then exported. How, then, do we explain that in these nations

exports preceded investment? Our model elucidates this pattern: When the economy is opened, firms

are exposed to overseas competition and a larger market size. Firms then have to either exit or match

rival’s technological capabilities by increasing fixed outlays, and this (may) lead to an investment

boom.

[discuss social planner here]

The literature on strategic interaction in international trade [Brander, 1981; Brander and Spencer,

1985; Venables, 1985] has been extended by considering the effects of innovation (i.e., technological

capability). Spencer and Brander [1983] analyze the case of R&D rivalry across nations. This branch

of the literature on trade under imperfect competition highlights the interaction between governments

which are deciding how to support their industries. Our focus of attention lies in the strategic inter-

action between firms, rather than governments.

Murphy and Shleifer [1997] provide a model where differences in human capital affect product

quality. The model assumes a perfectly competitive setting and a taste for quality (but not for

variety). An advanced economy has no incentive to trade with a backward economy, since consumers

in the advanced economy (high in human capital) have high income levels and prefer the quality good.

In the backward economy, consumers have low income levels and cannot afford the quality good. Thus

the backward economy has nothing to offer to the advanced economy, while the rich economy finds it

unprofitable to produce low quality goods to sell to the backward economy.

Motta [1992] is one of the closest works to our study. He introduces a model of oligopoly with tech-

nological capability (originally created by Sutton [1991, ch. 3]) into an international trade framework.

Motta’s framework is partial equilibrium, and he allows for differences in technological capabilities

between countries. In that framework, when backward nations engage in free trade with advanced

nations, trade losses may arise in the short run (i.e., for fixed technological capability). This is due

to exit of the low capability firms. Conversely, in the long run (when technological capability can be

adjusted) both nations benefit from trade. This result is similar to what we find below (Proposition 3),

where symmetric economies with Cournot industries benefit from free trade. Like Motta, our model

endogenizes technological capability in international trade. Additionally, we also endogenize market

structure, wage rates, the sectorial distribution of employment and the terms of trade, in order to

develop a general equilibrium analysis.

The paper is structured as follows. In Section II we develop the model. In Section III we char-

acterize a symmetric equilibrium. Section IV presents a gains-from-trade-theorem (Proposition 3)

and comparative statics for the symmetric equilibrium. In Section V we consider industrial policy of

various forms and guises, for the symmetric equilibrium. Section VI considers the consequences of

introducing asymmetries in initial conditions and whether, given some difference in initial conditions,

industrial policy aimed at catching-up is effective and welfare improving. Section VI presents social

planner analysis [pending]. Conclusions are offered in Section VII.

5

II. THE OPEN ECONOMY GENERAL EQUILIBRIUM MODEL

We begin by solving the consumers’ problem and then present the structure of industry X. Subse-

quently, the labour market is discussed together with industry Y and the trade balance. An informal

overview of the model is offered in Appendix 1. We refer to two types of equilibrium. Firstly we

have a symmetric equilibrium within each economy (but not necessarily across economies). In this

case all firms within a given country choose identical quantities and technological capability. This

type of equilibrium allows countries to have different equilibrium outcomes if their parameter values

differ. The other type of equilibrium features symmetry across economies. In this equilibrium both

countries feature identical parameter values, and resulting equilibrium outcomes are identical in both

economies. Subscripts ‘d’ and ‘f ’ denote domestic and foreign economy variables, respectively. To

avoid duplication of equations, it will be convenient to use subscripts i, j = d, f with i �= j to label

expressions which are identical for both economies. The corresponding expressions for autarky will be

distinguished by the superscript ‘A’ (open economy expressions will bear no superscript).

1. CONSUMERS

In each economy there is a population of Li representative consumers, indexed by li = 1, ...,Li for

i = d, f . Consumers allocate their labour endowment between industries X and Y . Since there is no

labour mobility across countries, consumers earn the (labour market clearing) wage rate prevalent in

their country. There is free trade in goods of type X and Y , and zero transport costs.

In industry X, the kth firm in country i produces one good only, labelled xki and production of

the kth firm from either country is indexed by xk. In each economy, there is a finite number of firms,

denoted by ni+1. The worldwide number of firms is denoted by N +1 = nd +nf +2. We denote the

number of firms by nd +1, nf +1 and N +1, rather than the usual notation of nd, nf and N . This is

adopted purely for aesthetic convenience, since it will make the equations somewhat more organized.

We introduce the following vector notation: xd = (x1d, ..., xnd+1 d), xf = (x1f , ..., xnf+1 f ) and

x = (xd, xf ). Each good in the X industry has a ‘quality level’ associated to it, denoted by uki

(and uk denotes technological capability in either country). The quality level represents the producer’s

technological capability. In vector notation, we have: Ud = (u1d, ..., und+1 d), Uf = (u1f , ..., unf+1 f )

and U = (Ud, Uf ). The representative consumer’s problem can be stated as

maxx, Y

Vi =

N+1∑k=1

(xk −

x2k

u2k

)− 2σ

N+1∑k=1

xk

uk

N∑l �=k

xl

ul

+ Yi (1)

subject toN+1∑

k=1

pkxk + qiYi � wi + qiY i +

ni+1∑

k=1

shkiΠki for i = d, f (2)

where σ ∈ (0,1) measures the substitutability between X-type goods (and is identical for both

economies), pk is the price of the kth X-type good (in either country), qi is the price of the Y -type

good in economy i, wi is the wage rate in economy i, Yi is the consumption of type Y goods in country

i, Y i represents a per-capita endowment of type Y goods for country i, shki is the ownership share of

consumer h in firm k in country i (with the usual restriction that∑

Li

h=1shki = 1), and Πki denotes

net profits of firm k in country i. Note that firm ownership is restricted to a consumer’s economy (i.e.,

6

foreign ownership is ruled out). The endowment of type Y goods, Y i, is introduced to allow for the

possibility that a rich economy may demand more type Y goods than the poor economy produces (in

which case the poor economy depletes its endowment of type Y goods).

Consumer income comes from wages (wi), the value of their endowment of type Y goods (qiY i) and

dividends generated by the consumer’s shares in industry X firms (∑

ni+1

k=1shkiΠki). In equilibrium we

will see that net profits are zero (by free entry), thus the dividend term in the budget constraint will

drop out. The (quadratic) utility function in equation (1) is the underlying utility for the standard

linear demand model, with some modifications (see Sutton, 1998, ch. 2). To move from the open

economy case to autarky, each economy is considered in isolation. Thus the world number of firms

(product varieties) becomesN+1 = nAi +nAj +2. To perform welfare analysis we substitute equilibrium

solutions into Vi, and we label this welfare indicator ‘Wi’ for economy i = d, f. Since the wage rate

determines welfare (see Appendix 6 for further details), looking at the former will be sufficient to

draw conclusions about the latter. From the consumer’s problem, we obtain the inverse demand facing

domestic producers (pkd) and foreign producers (pkf )

pki = 1− 2xki

u2ki−

2σ

uki

⎛⎝

ni∑l �=k

xli

uli

+

nj+1∑

l=1

xlj

ulj

⎞⎠ for i, j = d, f and i �= j (3)

Per-capita demand functions for good Y are obtained as a residual from the budget constraint (equation

2). Good Y is the numeraire, hence its price is set to 1 in both economies (qi = 1). Agents in economy

i will be net consumers of Y when their demand is above their endowment. Otherwise, they are net

suppliers (exporters) of Y .

2. INDUSTRY X

Firms in this industry face competition not only from their local rivals, but also from their overseas

rivals (since there is free trade in consumer goods), and hire workers exclusively from the local work-

force. We will consider two types of symmetric equilibria. Firstly we consider a symmetric equilibrium

within each economy, without restricting parameters or solutions to be identical across economies.

This will allow us to set out the conditions for a general equilibrium. Secondly, we consider symmetry

both within and across the economies. In this case we impose the restriction that each parameter

takes the same value in both economies. We shall refer to the latter case as a symmetric equilibrium.

Firms play a three stage game. In the first stage the entry decision is made. In the second stage, firms

invest in building technological capability (by choosing their level of sunk costs). In the final stage,

firms compete in quantities, à la Cournot. We look for a Subgame Perfect Nash Equilibrium [Selten,

1975]. In keeping with backward induction, we proceed to the description of the final stage in the

firms’ decision problem.

In the final (Cournot) stage, gross profits of firm k in country i are equal to revenue (pkixki)

minus variable production costs. For simplicity, when solving the final stage we follow Sutton [1998]

in assuming that such costs are zero. Whence gross profits are πki = pkixki (for i = d, f). The first

order condition for the kth firm in country i is given by

pki +∂pki

∂xkixki = 0 for i = d, f (4)

7

Each economy features ni + 1 such equations in x. In Appendix 2, we solve this system of (N + 1)

equations, and find a symmetric Nash equilibrium. We obtain solutions for xd and xf in terms of

the number of domestic and foreign firms (nd + 1 and nf + 1) and the vectors of firms’ technological

capabilities, Ud and Uf . Using the solutions for xd and xf (after calculations shown in Appendix 2),

we obtain a solved-out payoff function, which will be used to solve the second stage of the game. This

solved-out payoff is:

πki(U) =u2

ki

2 (2− σ)2

[1−

σ

2 + σ (ni + nj + 1)

(ni+1∑

l=1

uli

uki

+

nj+1∑

l=1

ulj

uki

)]2(5)

Note that πki(U) is per-capita gross profit earned by the firm. Since population is Ld in the domestic

economy and Lf in the foreign economy, and the firm faces a unified world market for consumer goods,

total gross profit of the kth firm in country i is given by (Ld+Lf )πki(U). Solved-out payoffs in autarky

can be easily obtained by setting nj + 1 and Lj equal to zero in (5).

In the second stage firms choose their investment in technological capability. Sunk investment

determines technological capability via a fixed outlays function, F (.). The firm’s net profit is given by

Πki = (Ld + Lf ) πki(U) −F (uki,wi) for i = d, f (6)

F (uki,wi) denotes the fixed outlays function: F (uki,wi) = wi f(uki), where wi is the wage rate

prevailing in country i, and f(uki) = εi

(uki

uoi

)βiis a convex mapping from technological capability

in country i (uki) to labour units required to achieve such capability. εi is an exogenous set-up cost.

uoi represents an initial (inherited) value of technological capability, which is an exogenous parameter.

In section 5, uoi is used as a means of modelling differences in initial conditions across countries.

βi > 2 is required for second order conditions to hold (see Appendix 3). We also assume εi > 0, and

uki > uoi � 1. It is important to note that we allow each country to have different values for the

following parameters: βi, Li, εi, uoi (i = d, f). The value of σ has been constrained to be the same in

both economies. This appears to be a reasonable assumption for it seems hard to justify that the same

goods should have different degrees of substitutability in different countries. The first order conditions

to maximize (6) with respect to uki are:

(Ld +Lf )∂πki

∂uki=

wiεiβiuki

(uki

uoi

)βi

for i = d, f and k = 1, ..., ni + 1 (7)

which is a system of N + 1 equations in Ud and Uf .

For the entry stage, assume there is a sufficiently large pool of potential entrants. Firms enter so

long as net profits are positive. This leads to the following non-negative-profit condition

(Ld + Lf )πki � wiεi

(uki

uoi

)βi

for i = d, f (8)

Ignoring integer effects, entry occurs until (8) holds with equality.

8

3. THE LABOUR MARKET, INDUSTRY Y AND THE TRADE BALANCE

Each consumer supplies a fixed amount of labour which has been normalized to 1. Hence, total

labour supply is fixed at each country’s population (Li). Labour is perfectly mobile within each

economy but internationally immobile. Thus, demand for labour stems exclusively from the local

industries (X and Y ). Employment in industry X is given by Lxi =

ni+1∑

k=1

f(uki). Any surplus labour

not employed in industry X is absorbed by industry Y . Employment in industry Y in country i is

labelled Lyi. Labour market clearing requires

Li = Lxi +Lyi where Lxi,Lyi ∈ [0,Li] and i = d, f (9)

The wage rate adjusts to ensure that the labour market clears in each economy, given that labour

is internationally immobile and that industry Y offers a (de-facto) minimum wage rate equal to the

marginal product of labour in industry Y . We now discuss industry Y .

On the supply side, industry Y has a simple 1:1 (constant returns to scale) technology: One

unit of labour produces one unit of type Y good. The 1:1 technology in industry Y means that the

marginal product of labour in industry Y is equal to the price of type Y good, qi. This good is the

numeraire, so its price is set to unity. Aggregate supply of good Y is composed by production of good

Y (which is identical to employment in the sector) and by the economy’s endowment of this good

(LiYi). Aggregate demand for good Y in each country is obtained by multiplying per-capita demand

by Li. This sector constitutes a worker’s outside option: in the worst scenario the worker can always

resort to transforming his/her labour endowment with a (freely available) 1:1 technology, and earn

an income of qi = 1. Thus we obtain that in (general) equilibrium wi � 1. If Lyi > 0 then wi = 1.

However, if demand for labour from sector X is high enough to make Lyi = 0 (in which case Lxi = Li),

then industry Y is inactive, and industry X uses all the available labour in the economy. In this case

we have that wi > 1 (otherwise workers would shift to industry Y and earn wi = 1).

We now discuss net exports (the trade balance). In sector Y the difference between aggregate

supply and aggregate demand for type Y good gives the trade balance for good Y (labelled TByi).

Since there are only two countries, we have that TByd = −TByf . Exports of good X in country

i are given by Lj (ni + 1) pixi, while imports are Li (nj +1) pjxj . From these it is clear that there

will always be intra-industry trade, unless either country has ni + 1 = 0, Li = 0, pi = 0 or xi = 0

(for i = d, f). The trade balance for industry X is labelled TBxi. The (overall) trade balance for

each economy is given by TBi = TBxi + TByi. In this model the overall trade balance is always

zero, hence the trade balance for type X goods must be equal to the negative of the trade balance

for type Y good (TBxi = −TByi). Moreover, because there are only two countries in the model, the

domestic trade balance for type X goods must be equal to the negative of the foreign trade balance

for type X goods (TBxd = −TBxf ), which in turn is the negative of the foreign trade balance for

type Y good (TBxf = −TByf ), leading to the conclusion that TByd = −TByf . Thus we have that

TByd = −TByf = TBxf = −TBxd.

In Appendix 4, we provide a discussion of value added and the trade balance in the context of this

model, which complements the above discussion. We now proceed to characterize a symmetric general

equilibrium for the world economy.

9

III. CHARACTERIZATION OF GENERAL EQUILIBRIUM

We begin by considering a symmetric equilibrium within each economy, such that uki = uli = ui,

for i = d, f . After setting out the conditions for such an equilibrium, we proceed to obtain explicit

solutions for a symmetric equilibrium across both countries, such that all parameters take identical

values in both economies (as well as technological capabilities, the number of firms and the wage rates).

We will refer to the latter as a ‘symmetric equilibrium’.

In the case of a symmetric equilibrium within each economy, we have nine parameters (βi, σ,

εi, Li, uoi for i = d, f) and six key variables which determine the rest of the system (ui, ni

and wi). A general equilibrium is characterized by the functions ui(βi, βj, σ, εi, εj ,Li, Lj, uoi, uoj),

ni(βi, βj, σ, εi, εj ,Li, Lj , uoi, uoj) and wi(βi, βj, σ, εi, εj ,Li, Lj, uoi, uoj), which can be derived explic-

itly in a symmetric equilibrium. We will simplify notation by dropping the arguments, so we write

ui(.), ni(.) and wi(.). The solutions will depend on whether Lyi > 0 or Lyi = 0.

A Symmetric General Equilibrium has the following features:

a) World market clearing for goods of type X and Y .

b) Labour market clearing in each economy.

c) A Symmetric Subgame Perfect Equilibrium in IndustryX in each economy, which is characterized

by:

i) Firms choosing (Nash) symmetric equilibrium quantities in stage 3 of the game, taking as

given technological capabilities of domestic and foreign rivals and market structure in both economies.

ii) Firms choosing (Nash) symmetric equilibrium technological capabilities in stage 2 of the

game, taking market structure in both economies as given.

iii) Free entry in stage 1 of the game for both economies.

The corresponding equilibrium for autarky features goods markets clearing at the national level,

and no links to the overseas economy.

Equilibrium Conditions:

The general equilibrium of the world economy is characterized by three conditions for each country

(as well as the standard market clearing conditions for goodsX and Y ). We write these for a symmetric

equilibrium within each economy.

The first equilibrium condition is a mapping from uj to ui, such that along this mapping no

individual firm wishes to deviate from its strategy. The mapping is defined by the first order conditions

for technological capability, ∂Πki

∂uki= 0 for i = d, f and k = 1, ..., ni + 1 (given by 7). Symmetry within

each economy allows us to write the mapping as follows:

(Ld +Lf ) [2 + σ (ni + nj)]

(2− σ)2 [2 + σ (ni + nj + 1)]

⎧⎨⎩1−

σ

[(ni + 1) + (nj + 1) uj

ui

]

2 + σ (ni + nj + 1)

⎫⎬⎭ = wiεiβi

uβi−2

i

uβi

oi

(10)

Secondly we have the free entry condition, as stated in (8). After substituting gross profits from (5),

10

in a symmetric equilibrium within each economy the free entry condition becomes

(Ld + Lf )

2(2− σ)2

⎧⎨⎩1−

σ

[(ni +1) + (nj +1) uj

ui

]

2 + σ (ni + nj + 1)

⎫⎬⎭

2

= wiεi

uβi−2

i

uβi

oi

(11)

Thirdly we have labour market clearing, from (9). In a symmetric equilibrium (whether it be across

or within economies) this is written as:

Li = Lyi + Lxi = Lyi + (ni + 1)εi

(ui

uoi

)βi

(12)

where symmetry allows us to simplify Lxi =

ni+1∑

k=1

f(uki) to Lxi = (ni + 1)f(ui). Market clearing

for type Y and type X goods is ensured by construction. These conditions determine the general

equilibrium values for technological capability (ud, uf ), for the number of firms (nd + 1, nf + 1) and

for the wage rate (wd, wf ). Autarky counterparts are obtained by setting nj +1 and Lj equal to zero.

Equilibrium condition (10) embeds the following result:

Proposition 1: On how the technology gap affects technological capability

The net marginal benefit of investment in technological capability is decreasing in the technology

gap between countries, i.e., in the ratio of technological capabilities (ui/uj). Whence there exists

a threshold level of ui/uj above which investment in technological capability is not optimal for the

laggard economy.

Proof: By inspection of (10)�.

The consequence of Proposition 1 is that if the distance between equilibrium levels of technological

capability (the ‘technology gap’) is sufficiently large, then one of the economies will cease to invest

in technological capability: It is simply not optimal to try to catch up with the advanced economy.

However, in equilibrium, we find that in order to achieve a positive market share, firms must match

rivals’ technological capability. Nonetheless, this does not imply catching-up in terms of income, since

the technology gap affects market structure and hence the wage rate. When we come to analyze the

effect of differences in initial conditions (uoi) or ‘history’, the result in Proposition 1 will drive some

of our conclusions.

In a symmetric equilibrium across both economies, we can find explicit solutions as follows. Let

all parameters take identical values in both economies and let ud = uf = u, nd = nf = n and

wd = wf = w. We obtain an expression for u from (10), given by

u =

{Luβowεβ

4 (1 + σn)

(2− σ) [2 + σ (2n+ 1)]2

} 1

β−2

(13)

Noting that under symmetry n =N−1

2, we can express the above expression in terms of the world

number of firms, as follows

u =

[2Luβowεβ

2 + σ(N − 1)

(2− σ)(2 + σN)2

] 1

β−2

11

The autarky counterpart to this is given by

uA=

[Luβowεβ

2 + σ(nA − 1)

(2− σ)(2 + σnA)2

] 1

β−2

The next step is to use condition (11) to obtain the number of firms. In a symmetric equilibrium, this

simplifies toL

[2 + σ (2n+1)]2= wε

uβ−2

uβo

(14)

Substituting u from (13) and solving for n gives the equilibrium number of firms:

n+ 1 =β (2− σ)− 4

4σ+1 (15)

Noting that n = N−1

2, the (world) number of firms simplifies to

N + 1 =(β − 2) (2− σ)

2σ+ 1 (16)

which is the same as the autarky number of firms for each economy (nA+1): In a symmetric equilibrium,

when moving from a two-country autarkic world to a two-country free-trade world, the world number

of firms is halved. Substituting n+ 1 from (15) into (13) we obtain the (symmetric) equilibrium level

of technological capability, as a function of parameters and the wage rate:

u =

{uβo

w

L

ε

1[β(1−

σ2

)+ σ

]2} 1

β−2

(17)

which is the same result as in autarky, with double the population (i.e., in autarky L is replaced

by L/2). This completes the description of the symmetric Subgame Perfect Nash Equilibrium for

industry X. To find a symmetric general equilibrium, we now determine the equilibrium wage rate.

In a symmetric equilibrium the labour market clearing condition (12) simplifies to

L = Ly + (n+ 1)ε

(u

uo

)β(18)

The wage rate is obtained by substituting (17) and (15) into (18) and solving for w. This yields

w = max

⎧⎪⎪⎨⎪⎪⎩1, u2o

(L

ε

) 2

β

[β(2−σ)−4

4σ + 1

]β−2β

[β(1−

σ

2

)+ σ

]2

⎫⎪⎪⎬⎪⎪⎭

(19)

where the minimum wage of 1 is attributable to the presence of an outside option for workers, namely,

12

the 1:1 technology. In autarky, similar substitutions yield the following wage rate:

wA =max

⎧⎪⎪⎨⎪⎪⎩1,u2o

2

(L

ε

) 2

β

[(β−2)(2−σ)

2σ + 1

]β−2β

[β(1−

σ

2

)+ σ

]2

⎫⎪⎪⎬⎪⎪⎭

(20)

The general equilibrium solution for technological capability is obtained by substituting (19) into (17)

for the open economy. In autarky, replace L by L/2 in (17) and substitute (20) into this. If Ly = 0

(such that w > 1), then we have:

u = uo

[L

ε

1

β(2−σ)−44σ + 1

] 1

β

uA= uo

[L

ε

1

(β−2)(2−σ)2σ + 1

] 1

β

(21)

If, on the other hand, Ly > 0 (and hence w = 1), general equilibrium technological capability is

obtained by simply setting w = 1 in (17) for the open economy. In autarky, replace L by L/2 in (17).

This yields:

u =

{uβoL

ε

1[β(1−

σ

2

)+ σ

]2} 1

β−2

uA=

{uβo

L

2ε

1[β(1−

σ2

)+ σ

]2} 1

β−2

(22)

This completes the description of a symmetric general equilibrium in the open economy. Equilibrium

outcomes for all remaining variables are obtained by substituting the solutions obtained above. The

symmetric general equilibrium outcomes for the open economy and autarky are summarized in the

following table:

Open Economy Autarky

a) If Ly = 0 (w > 1) a) If Ly = 0 (w > 1)

w = u2

o

(Lε

) 2

β [β(2−σ)−44σ +1]

β−2β

[β(1−σ

2 )+σ]2

u = uo

[L

ε

1

β(2−σ)−44σ +1

] 1β

n+ 1 =β(2−σ)−4

4σ+ 1

wA =

u2o2

(L

ε

) 2

β [ (β−2)(2−σ)2σ +1]β−2β

[β(1−σ

2 )+σ]2

uA= uo

[L

ε

1

(β−2)(2−σ)2σ +1

] 1β

nA+ 1 = (β−2)(2−σ)

2σ+1

b) If Ly > 0 (w = 1) b) If Ly > 0 (w = 1)

w = 1

u =

{uβoLε

1

[β(1−σ

2 )+σ]2

} 1

β−2

n+ 1 =β(2−σ)−4

4σ+ 1

wA = 1

uA =

{uβo

2

Lε

1

[β(1−σ2 )+σ]

2

} 1

β−2

nA+ 1 =

(β−2)(2−σ)2σ

+1

Table 1: Symmetric General Equilibrium Outcomes in Autarky and in the Open Economy Case.

An interesting feature of the results on market structure is that concentration depends only on β and

σ. Thus market size (L), initial conditions (uo) and set-up costs (ε) do not affect concentration. This

is a common feature of vertical product differentiation models, and is related to the ‘non-convergence

property’ discussed in Sutton [1991, 1998], that is, that concentration does not fall to zero as market

size increases indefinitely.

13

Since we have focussed on symmetric equilibria (be they within or across economies), a natural

question to pose relates to the existence of asymmetric equilibria. We can in fact rule out a class of

such equilibria, as is shown in the following proposition.

Proposition 2: Non-existence of a type of asymmetric equilibria

Consider the following type of equilibrium: Both economies have identical parameter values and

firms set a symmetric level of technological capability within each economy, which is not necessarily

symmetric across economies. Then there no equilibria exist where firms in one economy set a different

level of technological capability to firms in the other economy.

Proof: See Appendix 5.

This proposition can be extended to rule out all asymmetric equilibria, provided one is willing

to assume that the zero profit condition holds exactly for each firm (as opposed to holding for each

economy). The proof is along the same lines to the proof of Proposition 2, but now we consider a

partition of the industry into two groups of firms. One can then show that the constituent firms in

both groups must be identical.

IV. ANALYSIS OF THE SYMMETRIC EQUILIBRIUM

We can identify two mechanisms which determine the demand for labour and thereby the wage

rate. Firstly, we have the technological capability effect, which refers to how changes in technological

capability affect the demand for labour at the level of the firm: If technological capability rises, this

will increase f(u) and thus labour demand at the firm level. Secondly, we have the market structure

effect, which refers to how industry-level labour demand is affected by market structure: As the

number of firms rises, the demand for labour at the industry level will expand —there are more firms

with labour requirement f(u). The key notion is that the two effects never go in the same direction:

As technological capability rises, fixed costs increase, and concentration does not fall. Conversely, if

technological capability falls, so do fixed costs and concentration does not rise.

The outcomes in Table 1 contain the following result:

Proposition 3: Consequences of free trade for the wage rate, technological capability

and market structure

In a symmetric equilibrium with wage rates above unity, free trade results in a higher wage rate,

higher technological capability and a smaller number of firms. If w = wA = 1, free trade still implies

higher technological capability and a smaller number of firms.

Proof: By comparing symmetric equilibrium outcomes under free-trade and autarky (see table

1)�.

Corollary 3:

In a symmetric equilibrium with wage rates above unity, free trade results in higher welfare. If

w = wA= 1, free trade does not imply a welfare loss.

Proof: By substituting symmetric general equilibrium outcomes (table 1) into welfare indicators

(equations A6.2 and 24) and then comparing these for the open and closed economy�.

14

Proposition 3 and its corollary are familiar results from the literature on trade under imperfect

competition (see Brander, 1981 and the survey by Chui et al., 2002). Furthermore, equating the free

trade and autarky wage rates for the case when these lie above unity, we find that they are equal

along the following locus: σ∗ = (2β−4)β−4 . σ∗ defines a boundary or separation locus in (β,σ)-space. The

wage rate in the open economy is lower than under autarky above the σ∗ locus. Conversely, the wage

rate in the open economy is higher than under autarky below the σ∗ locus. As β goes to infinity, σ∗

converges to its lower asymptote of 2. However, σ ∈ (0,1), so the open economy features a higher wage

rate than autarky (hence Proposition 3). The wage separation locus emerges because there are two

effects generating the difference in wages between the closed and the open economy. On the one hand,

opening the economy yields a larger market size (a doubling of population). The increase in market

size raises demand for labour via higher technological capability, and thus tends to raise wages, ceteris

paribus. On the other hand, in a symmetric equilibrium half of the firms in each economy exit as the

economy is opened. This reduces labour demand and tends to lower the wage rate, ceteris paribus. σ∗

defines the locus where the two effects exactly offset each other. Since welfare is determined by the

wage rate, there also exists a separation locus for welfare.

We now analyze how key variables change with parameters, in the case of a symmetric equilibrium

with wage rates above unity. This is, in essence, a comparative statics analysis. However, we not only

specify the first, but also the second derivatives of the symmetric equilibrium outcomes. The results

are reported in Table 2.

15

CS1. Effect of Changes in β: CS3. Effect of Changes in ε:

Wage rate: Wage rate:∂w∂β

< 0, ∂wA

∂β< 0, ∂

2w∂β2

> 0,

∂2wA

∂β2> 0

∂w∂ε< 0,

∂wA

∂ε< 0,

∂2w∂ε2

> 0,

∂2wA

∂ε2> 0

Technological capability: Technological capability:∂u∂β< 0, ∂uA

∂β< 0, ∂2u

∂β2> 0, ∂2uA

∂β2> 0

∂u∂ε< 0, ∂uA

∂ε< 0, ∂2u

∂ε2> 0, ∂2uA

∂ε2> 0

Number of firms: Number of firms:∂(n+1)∂β

>0,∂(nA+1)

∂β>0,

∂2(n+1)∂β2

=0,∂2(nA+1)

∂β2=0

∂(n+1)∂ε

=0,∂(nA+1)

∂ε=0,

∂2(n+1)∂ε2

=0,∂2(nA+1)

∂ε2=0

Welfare: Welfare:∂W∂β< 0,

∂WA

∂β< 0,

∂2W∂β2

> 0,

∂2WA

∂β2> 0

∂W∂ε< 0,

∂WA

∂ε< 0,

∂2W∂ε2

> 0,

∂2WA

∂ε2> 0

Exports and Imports of Good X: Exports and Imports of Good X:∂XX∂β

< 0, ∂2XX∂β2

> 0∂XX∂ε

< 0, ∂2XX∂ε2

> 0

CS2. Effect of Changes in σ: CS4. Effect of Changes in uo:

Let σ∗

=

4−8β+3β2−√

16−64β+24β2+β4

2β(β−4)Wage rate:

Wage rate: For ∂w∂uo

> 0,

∂wA

∂uo> 0,

∂2w

∂u2o

> 0,

∂2wA

∂u2o

> 0

1) σ = σ∗

,

∂w

∂σ= 0,

∂wA

∂σ= 0 Technological capability:

2) σ > σ∗, ∂w

∂σ> 0, ∂w

A

∂σ> 0

∂u

∂uo> 0, ∂u

A

∂uo> 0, ∂

2u

∂u2o

= 0,∂2uA

∂u2o

= 0

3) σ < σ∗

,∂w

∂σ< 0,

∂wA

∂σ< 0 Number of firms:

For all σ ∈ (0, 1), ∂2w

∂σ2>0, ∂

2wA

∂σ2>0

∂(n+1)∂uo

=∂(nA+1)∂uo

=∂2(n+1)∂u2

o

=∂2(nA+1)∂u2

o

=0

Technological capability: Welfare:∂u

∂σ> 0,

∂uA

∂σ> 0,

∂2u

∂σ2< 0,

∂2uA

∂σ2< 0

∂W

∂uo> 0,

∂WA

∂uo> 0,

∂2W

∂u2o

> 0,∂2WA

∂u2o

> 0

Number of firms: Exports and Imports of Good X:∂(n+1)∂σ

<0,∂(nA+1)

∂σ<0,

∂2(n+1)∂σ2

>0,∂2(nA+1)∂σ2

>0 ∂XX

∂uo> 0,

∂2XX

∂u2o

> 0

Welfare: For CS5. Effect of Changes in L:

1) σ = σ∗, ∂W

∂σ= 0, ∂W

A

∂σ= 0 Wage rate:

2) σ > σ∗, ∂W

∂σ> 0, ∂W

A

∂σ> 0

∂w

∂L> 0, ∂w

A

∂L> 0, ∂

2w

∂L2 < 0,

∂2wA

∂L2 < 0

3) σ < σ∗

,∂W

∂σ< 0,

∂WA

∂σ< 0 Technological capability:

For all σ ∈ (0, 1), ∂2W

∂σ2>0, ∂

2WA

∂σ2>0

∂u

∂L> 0, ∂u

A

∂L> 0, ∂

2u

∂L2 < 0, ∂2uA

∂L2 < 0

Exports and Imports of Good X: For Number of firms:

1) σ = σ∗, ∂XX

∂σ= 0

∂(n+1)∂L

=∂(nA+1)

∂L=∂2(n+1)∂L2 =

∂2(nA+1)∂L2

=0

2) σ > σ∗

,

∂XX

∂σ> 0 Welfare:

3) σ < σ∗, ∂XX∂σ

< 0∂W

∂L> 0, ∂W

A

∂L> 0, ∂

2W

∂L2< 0,

∂2WA

∂L2< 0

For all σ ∈ (0, 1), ∂2XX

∂σ2>0, ∂

2XX

∂σ2>0 Exports and Imports of Good X:

∂XX

∂L> 0, ∂

2XX

∂L2 < 0

Table 2: First and Second Order Comparative Statics

From these comparative statics results we obtain the following conclusion regarding development

configurations.

Proposition 4. Development configurations

Under free trade and autarky, for wage rates above unity, a high-tech configuration is associated

with a higher wage rate (and welfare) than a proliferation configuration, unless σ < σ∗.

16

Proof: Let p = β,σ, ε,uo,L. In all comparative statics (Table 2: CS1-CS5), except for σ < σ∗

(CS2), we have that sign[∂w∂p

]= sign

[∂u∂p

]. In turn, ∂u

∂pis never of the same sign as ∂n+1

∂p(that is,

they are either of opposite signs or ∂n+1∂p

= 0). Similarly for autarky�.

A Replication Argument

The model is constituted by a single oligopolistic industry. This feature is an extreme simplification

of a real economy. Nonetheless, under some simplifying assumptions, the mechanisms at work readily

extend to the multiple industry case. Consider an economy composed by a traditional sector like the

one we have described, and multiple industries similar to sector X (indexed by r = 1, ..., R). Let

the products of these industries be non-substitutable with the products of other industries (although

each firm’s product is substitutable with those of other firms within the same industry). Assume

further that there are no supply-side linkages between industries (i.e., there are no intermediate goods

or economies of scope). The absence of demand and supply linkages between industries implies that

they are only linked via the labour market. Each of these industries will be characterized by a set

of parameters (βr, σ

r, ε

r, u

or,L)2 , which vary according to the characteristics of each industry. Then

we can consider the net effects on the demand for labour of having different mixes or proportions of

industries with high or low technological capability (respectively, concentration). The reasoning is

straightforward and extends Proposition 4 to the multiple industry case: Having a high proportion of

high-tech industries will result in a higher wage rate than having a high proportion of proliferation

industries, with the exception of those industries for which σr is low. In the latter case, proliferation

will constitute an effective way of expanding the demand for labour (and the wage rate).

V. INDUSTRIAL POLICY I: THE SYMMETRIC CASE

We now address the following question: Can industrial policy improve income, in the case of a

symmetric equilibrium? The model allows us to set up a variety of designs for industrial policy. We

envision a policy maker who can implement different types of taxes or subsidies, and finances these with

lump sum transfers to or taxes on consumers. In this section we focus on the symmetric equilibrium.

Whence, any policy is implemented in unison by both nations.

We consider two financing schemes for such interventions. Equilibrium outcomes under interven-

tion are superscripted with a prime. In Scheme 1, the government pays/charges for any change in

firms’ expenditure from the original equilibrium outcome. Consumers in the open economy will then

pay/receive the per-capita sum of

T1 =1

L[(n′

+ 1)F ′ (u′)− (n+1)F (u)]

where F′(u′) = w

′ε′(u′)β

′

denotes the fixed outlays function under intervention. Thus, the deviation

of fixed outlays from their original equilibrium values is paid by (transferred to) consumers in a lump-

sum, per-capita manner. If T1 > 0, firms receive a subsidy and consumers are taxed. Conversely for

T1 < 0. In autarky, we have TA1=

1

L

[(nA ′ + 1)F ′(uA ′) − (nA +1)F (uA)

]. Under this scheme we can

show the following result.

2Population size (L) is assumed to be an economy-wide variable, and so does not vary between industries.

17

Proposition 5:

Under financing Scheme 1, consumers earn identical income with or without intervention, in

both the closed and open economy.

Proof of Proposition 5: We will present the proof for the open economy. The same structure

can be used to prove the closed economy case. Net (per-capita) income under intervention is given

by w′− T1. We will show that w′

− T1 = w. Zero profits imply that F (u′) = 2LΠ′ = 2Lp′x′ and

F (u) = 2LΠ = 2Lpx. From consumers’ budget constraint we have that 2(n′ + 1)p′x′ = w′ and

2(n+ 1)px = w. Plugging these results into T1 we obtain the equality we seek �.

Corollary 5:

Under financing Scheme 1, consumers achieve identical welfare with or without intervention,

in both the closed and open economy.

Proof of Corollary 5: Noting that welfare is a constant times the wage rate, the proof follows

immediately �.

To analyze financing Scheme 2 it is convenient to consider each type of intervention. The policy

maker can affect expenditure on technological capability through two types of intervention. Firstly,

set-up costs can be modified by setting ε′= δε. Secondly, the elasticity of the labour requirement with

respect to technological capability can also be modified by setting β′= δβ. δ > 1 represents a tax on

firms, δ < 1 a subsidy, and δ = 1 implies no intervention3.

First we look at the case of industrial policy affecting set-up costs. The financing constraint in

Scheme 2 is given by

T2ε =n

′+ 1

L

[w

′ε(u

′

uo)β − w

′ε

′(u

′

uo)β]

In this case, the (per-capita) tax/transfer is given by the difference between fixed outlays evaluated at

the equilibrium outcome under intervention using unmodified set-up costs, and fixed outlays evaluated

at the equilibrium outcome under intervention using modified set-up costs. In autarky, we have TA2ε =

nA ′+1

L

[wA ′

ε(uA ′

uo)β −wA ′

ε′(u

A ′

uo)β]. Since ε

′= δε, T2ε reduces to

n′+1

Lw

′ε(u′)β(1− δ). We can now

compare net income after taxes/transfers (w′−T2ε) against income without intervention (w). To this

end, we recalculate the equilibrium solutions as in section III with ε′= δε substituting ε, and find

the following relationship between the wage with intervention (w′) and the wage without intervention:

w′=

(1

δ

) 2

βw, which also holds under autarky. After simplifying, we find the following result.

Proposition 6a:

Under financing Scheme 2, intervention in the form of modifications of ε yields higher net

income if and only if 2 > 1

δ+ δ

2

β, in both the open and closed economy. Otherwise intervention does

not yield higher net income. Moreover, δ∗

=

(β2

) β

β+2

> 1 (a tax) maximizes the net income gain from

intervention.

3We also explored a third type of intervention, which modifies how technological capability enters the fixed outlays

function. Instead of F (u) = wε

(uuo

)β, the fixed outlays function is then written as F ′(u′) = w

′ε

(δu

′

uo

)β. This yields

qualitatively similar results to intervention via set-up costs. Full results are available upon request.

18

Proof of Proposition 6a: We show the open economy case, autarky proceeds along the same

lines. Substituting w′=

(1

δ

) 2

βw into T2ε yields T2ε = w

′ 1−δ

δ. Setting up the inequality w′

−T2ε > w and

simplifying yields the result. Maximizing w′−T2ε−w = 2−

1

δ−δ

2

β with respect to δ gives δ∗

=

(β2

) β

β+2

which is strictly greater than 1, provided β > 2 �.

Corollary 6a:

Under financing Scheme 2, consumers achieve higher welfare with a tax on set-up costs, in

both the closed and open economy.

Proof of Corollary 6a: As in Corollary 5 �.

The next type of intervention affects the elasticity of the labour requirement to technological

capability (β). The financing constraint is now given by

T2β =n

′ + 1

L

[w

′ε

(u

′

uo

)β

−w′ε

(u

′

uo

)δβ]

Under autarky, we have TA2β =

nA ′+1

L

[wA ′

ε

(uA ′

uo

)β−w

A ′ε

(uA ′

uo

)δβ]. Again, we recalculate equilib-

rium outcomes as in section III, replacing β by β′

= δβ. Substituting these yields T2β = w′

[(L

ε

1

n′+1

)1

δ−1

− 1

]

(likewise in autarky). We then compare net income with and without intervention: w′−T2β versus w.

The following proposition states the results.

Proposition 6b:

Under financing Scheme 2, intervention in the form of modifications of β yields higher net

income if and only if

2 >

(L

ε

) 2

β (1− 1

δ ) (n +1)β−2

β

[δβ

(1−

σ

2

)+ σ

]2

(n′ + 1)δβ−2δβ

[β(1−

σ

2

)+ σ

]2 +(L

ε

1

n′ + 1

) 1

δ−1

(23)

in the open economy. Otherwise intervention does not yield higher net income.

Condition (23) holds with equality at δ = 1 and at δ∗

∈ (0, 1). For δ ∈ (δ∗, 1), a subsidy to firms

yields strictly greater net income. Otherwise, a tax yields (weakly) greater income. Moreover, there

exists a δ∗∗

∈ (δ∗,1) which maximizes w′− T2β − w.

The corresponding analysis for autarky is obtained by replacing n′ with nA ′.

Proof of Proposition 6b: We focus on the open economy, the analysis for autarky follows the

same steps. Substituting T2β, w′ and w into w′− T2β > w and simplifying yields condition (23). This

condition can be plotted against δ on the horizontal axis, as shown in figure 1.

19

δ

2

0 1δ∗ δ∗∗

Figure 1: Condition (23). The dotted horizontal line shows the left hand side of condition (23). The

continuous curve shows the right hand side of condition (23). The crossings indicate where the

condition holds with equality.

The horizontal dotted line plots the left hand side of condition (23), while the continuous curve plots

the right hand side. Two intersections at δ = 1 and δ = δ∗ are apparent, as well as the minimum at

δ∗∗

�.

Corollary 6b:

In the open economy, under financing scheme 2, consumers achieve (strictly) higher welfare

with δ ∈ (δ∗,1). Welfare is maximized at δ = δ∗∗.

Proof of Corollary 6b: As in Corollary 5 �.

The corresponding analysis for the closed economy is qualitatively identical.

VI. INDUSTRIAL POLICY II:

ASYMMETRIC INITIAL CONDITIONS AND CATCHING UP

In this section, we focus on the consequences of changing initial technological capability for one

country (uoi), while holding all other parameters constant. We examine the case of ‘large’ changes in

uoi. An explicit solution is not possible in this case, and the results reported are based on extensive

numerical analysis. After analyzing the impact of asymmetry in initial conditions, we proceed to

investigate the effects of industrial policy to allow the backward economy to catch-up with the advanced

economy. The policy we will consider takes the form of a subsidy which reduces the marginal cost of

technological capability. More specifically, industrial policy will imply that a fraction of the cost of

technological capability will be borne by the government. The subsidy will be financed via a lump-sum

tax on consumers. We then ask about the welfare properties of such a scheme.

1. ASYMMETRIC INITIAL CONDITIONS

Starting from a symmetric equilibrium, let uod diverge from its initial (symmetric) value, and track

the general equilibrium solutions of the model by using the equilibrium conditions: (10), (11) and (12).

We have six conditions (three for each economy) which determine the general equilibrium values for

technological capability (ud, uf ), the number of firms (nd + 1, nf +1) and the wage rate (wd, wf ). In

20

the case of asymmetric initial conditions, the equilibrium conditions can only be solved numerically.

The algorithm is as follows:

(0) Start from a symmetric equilibrium.

(1) Let uod change by a small amount.

(2) Obtain a numerical solution such that (10)-(12) hold, taking the previous equilibrium as the

starting point for the equilibrium search.

(3) Note the new equilibrium values and use these as the new starting point. Go to step (1).

This procedure was iterated until we had tracked the general equilibrium of the model for a wide

range of uod. For robustness purposes, we tried a wide range of combinations of the remaining para-

meters. A graphical representation of the results is offered in Figures 5.1 and 5.2. In these figures,

the horizontal axis shows the ratio of domestic initial technological capability (i.e., domestic ‘initial

conditions’) to foreign initial technological capability (i.e., foreign ‘initial conditions’): uod/uof . For

the analysis that follows we introduce the following notions:

Horizontal Symmetry: Two schedules are said to be horizontally symmetric if we can find a point

through which we can draw a horizontal benchmark line such that the schedules are symmetric around

this line.

Vertical Symmetry: Two schedules are said to be vertically symmetric if we can find a point through

which we can draw a vertical benchmark line such that the schedules are symmetric around this line.

We will see that the some of the schedules presented below exhibit horizontal symmetry, but

not vertical symmetry. The reference point around which we draw the benchmark lines will be the

symmetric equilibrium.

It is useful to bear in mind three points depicted in Figures 5.1 and 5.2. Firstly we have the

threshold uod/uof wd=1, which is defined as the level of uod/uof at which wd reaches its lower bound of

1. Secondly we have uod/uof wf=1, which is the level of uod/uof at which wf reaches its lower bound of

1. Finally we have the initial symmetric equilibrium, identified by uod/uof = 1. This value of uod/uof

is associated with the crossing of the domestic and foreign (open economy) wage schedules, as well as

the crossing of schedules for the number of firms, per-capita demand of good Y , exports and imports

of type X goods and the trade balances.

The figures show three regimes, which will be determined by the values taken by the wage rates in

both economies. The first regime is characterized by values of uod/uof such that uod/uof � uod/uofwd=1. The second regime is characterized by values of uod/uof such that uod/uof � uod/uof wf=1.

The third regime lies between regimes 1 and 2, and is characterized by values of uod/uof such that

uod/uofwd=1 < uod/uof < uod/uof

wf=1. In this regime, both wage rates lie strictly above their lower

bounds: wd > 1 and wf > 1.

We use the notion of the ‘shadow-value’ of a variable. This refers to the value the variable would

have taken had the wage rate not had a lower bound equal to 1. The counterpart to the shadow value

of a variable will be labelled the ‘actual’ value, or simply referred to by the name of the variable.

21

u w

n+1

uod /uof

LLx

Ly

1

Lyf

LxfLxd

Lyd

Open Domestic Open Foreign Closed Domestic Closed ForeignOpen Domestic Open Foreign Closed Domestic Closed Foreign

od~cdof~cf

uod /uofwf=1uod /uof

wd=1 1

uod /uofuod /uofwf=1uod /uof

wd=1 1

uod /uofuod /uofwf=1uod /uof

wd=1 1

uod /uofuod /uofwf=1uod /uof

wd=1 1

Tec

hnol

ogic

al C

apab

ilit

y

Wag

e R

ate

Num

ber

of F

irm

s

Em

ploy

men

t

Figure 5.1. The Impact of Changes in Relative Initial Conditions on: Technological Capability,

Market Structure, Income and the Distribution of Employment.

A higher level of uoi reduces the marginal cost of achieving technological capability level ui for firms

in country i. On the other hand, firms in the other country now face a disadvantage, and must choose

their optimal response to the change of technological capability in the advantaged country. In the

top left graph, we find that both the domestic and the foreign economies choose identical levels of

technological capability (shown by the continuous thick line). While one economy is improving its

relative initial conditions (in this case the domestic economy), firms in the other economy must match

technological capability in order to maintain a positive market share.

For values of uod/uof � uod/uof wf=1, technological capability has a flatter slope. To see why this

occurs, note that for these values of uod/uof the foreign wage rate is at its lower bound of 1. Con-

sequently foreign technological capability becomes increasingly more expensive relative to its shadow

value. Firms in the domestic economy are content to match foreign firms’ technological capability

and thereby spend less on fixed outlays than would have been the case had the foreign wage rate not

reached its lower bound. An optimal deviation from this outcome is ruled out by equilibrium condition

(10).

For uod/uof � uod/uof wd=1, we find that technological capability has a steeper slope. For this

range, the domestic wage rate is 1 and the shadow wage rate lies below the actual wage rate. As uod/uof

grows, the gap between the shadow marginal cost of technological capability and its actual counterpart

22

is shrinking, and thus actual technological capability catches up with shadow technological capability.

Correspondingly, firms in the foreign economy match (actual) domestic technological capability.

The number of firms is shown in the bottom left graph. We can see that as uod/uof grows the

number of domestic firms increases, while the number of foreign firms contracts. This reflects the

increase in fixed outlays in the foreign economy, which drives out foreign firms, while domestic entrants

fill in the gaps left by exiting foreign firms. This replacement process is accelerated when uod/uof �

uod/uofwf=1. In this case the foreign wage rate is fixed at 1, and the foreign industry X contracts

at a faster rate, allowing the domestic industry X to expand. Meanwhile, the world number of firms

remains constant (not shown). For uod/uof � uod/uof wd=1, we find that as uod/uof rises the number

of domestic firms rises (and the number of foreign firms falls) at a steeper rate relative to the case when

uod/uofwd=1 < uod/uof < uod/uof

wf=1. This reflects the same mechanism as for uod/uof � uod/uofwf=1: For uod/uof � uod/uof wd=1 the domestic wage rate is fixed at 1 and lies above the shadow wage

rate for the domestic economy. Moreover, the further to the left we are from uod/uof wd=1, the greater

the distance between the actual wage rate of 1 and the shadow wage rate. Correspondingly, this implies

that as uod/uof grows, the number of domestic firms expands faster as the gap between the domestic

shadow wage rate and its actual counterpart is reduced. Meanwhile, in the foreign economy the number

of firms falls in order to adjust so that the world number of firms is constant. We can see that the

schedules for the number of firms are horizontally symmetric around the symmetric equilibrium.

Turning now to the wage schedules, we have that the increase in foreign labour demand associated

to the rise in technological capability is insufficient to offset the fall associated with the contraction

of the number of foreign firms. Accordingly, the foreign wage rate contracts as uod/uof rises. On the

other hand, the domestic industry X is enjoying an increase in both technological capability and in

the number of firms, leading to a rise in the domestic wage rate.

In the wage diagram we have also shown the wage rate for the closed economies: the domestic

economy as the dotted thin line and the foreign economy as the continuous thin line. We can see

that these lines intersect those of the corresponding open economy. The intersection of the domestic

open economy wage with that of the domestic closed economy is labelled od˜cd, and we will refer to

this point as uod/uof od˜cd. On the other hand, the intersection of the foreign open economy wage

with that of the foreign closed economy is labelled of˜cf , and we will refer to this point as uod/uofof˜cf . The implication is that for values of uod/uof lower than that associated with point od˜cd

(uod/uof < uod/uof od˜cd) the domestic economy achieves a higher wage rate (and welfare) in autarky,

while the foreign economy achieves a higher wage rate under free trade. Similarly, for values of uod/uof

above that associated with point of˜cf (uod/uof > uod/uofof˜cf ) we find that its now the foreign

economy which achieves a higher wage rate under autarky, while the domestic economy achieves higher

wages under free trade.

This raises an important issue: The notion that one economy (the one with relatively better initial

conditions) could seek to impose on the other economy a trade regime which is not welfare enhancing

for the disadvantaged economy. This may shed some light on the nature of bilateral trade negotiations

between advanced and backward economies. This important result is summarized in the following

proposition:

23

Proposition 5. Initial conditions, free trade and the wage rate

i) For uod/uof < uod/uof od˜cd the domestic economy achieves a strictly higher wage rate under

autarky, and the foreign economy achieves a strictly higher wage rate under free trade.

ii) For uod/uof > uod/uof of˜cf the foreign economy achieves a strictly higher wage rate under

autarky, and the domestic economy achieves a strictly higher wage rate under free trade.

iii) For uod/uof od˜cd < uod/uof < uod/uof of˜cf both economies achieve a strictly higher wage

rate under free trade.

iv) For uod/uof = uod/uof od˜cd the domestic wage rate is equal under autarky or free trade.

v) For uod/uof = uod/uof of˜cf the foreign wage rate is equal under autarky or free trade.

This proposition states precisely the conditions under which different trade regimes will generate

higher wage rates in different economies. If the two economies are not too different regarding their

initial conditions, free trade will generate higher wage rates in both economies. However, if initial

conditions are too dissimilar across economies, the backward economy will achieve a higher wage rate

in autarky. On the other hand, the advanced economy will achieve a higher wage rate under free

trade. Hence the advanced economy has incentives to negotiate free trade agreements which do not

necessarily benefit both parties.

Finally we analyze the bottom right diagram, showing employment in industries X and Y . For

uod/uof wd=1 < uod/uof < uod/uof wf=1, labour demand is sufficiently high to ensure that all of

the economies’ labour endowment is employed in industry X. For uod/uof � uod/uofwd=1 labour

demand from the domestic industry X is smaller than the domestic labour endowment. Consequently,

as uod/uof falls, employment in the domestic industry X falls below the labour endowment. Parallel

to this, employment in the domestic industry Y expands as it absorbs surplus workers. Meanwhile,

the foreign economy still features sufficiently high labour demand in industry X to employ all of the

labour endowment. For uod/uof � uod/uof wf=1 it is the foreign industry X which cannot generate

sufficient labour demand to employ all of the foreign labour force, so as uod/uof rises, employment in

the foreign industry X contracts. Accordingly, employment in the foreign industry Y rises to take in

any redundant workers.

The next figure depicts per-capita demand for type Y goods (left panel), exports and imports of

type X goods (center panel) and the trade balance in type X goods (right panel).

24

TBxY Xx

Mx

0__

Y

Domestic ForeignDomestic Foreign

Xxd=MxfXxf=Mxd

uod /uofuod /uofwf=1uod /uof

wd=1 1 uod /uofuod /uofwf=1uod /uof

wd=1 1 uod /uofuod /uofwf=1uod /uof

wd=1 1

Demand for Good Y Exports/Imports of Good X Trade Balance for Good X

a

b

Figure 5.2. The Impact of Changes in Relative Initial Conditions on: Per-Capita Demand of Good

Y , Exports and Imports of Type X Goods and the Trade Balance.

In the central panel of Figure 5.2 we observe that exports and imports of typeX goods closely resemble

the pattern displayed by the wage rate. When either of the wage rates reach their lower bound of 1

(that is, when either uod/uof � uod/uof wd=1 or uod/uof � uod/uof wf=1), exports of that country fall

more steeply, reflecting the increased rate of contraction in the country’s number of firms. Conversely,

the other country’s exports expand more rapidly as a consequence of the increased rate of expansion

in that country’s number of firms. This is reflected on the trade balance (right panel), which is given

by the distance between a country’s exports and imports of type X goods.

Per-capita demand of type Y goods is shown on the left panel. For uod/uof wd=1 < uod/uof <

uod/uofwf=1, demand for good Y exhibits similar behavior to the corresponding trade balance. The

high wage country is a net consumer of type Y goods, while the low wage country is a net supplier.

The low wage country depletes its endowment of type Y goods in order to finance its negative trade

balance in type X goods. For uod/uof � uod/uof wd=1, we find that as the domestic wage rate reaches

its lower bound, production of type Y goods expands as uod/uof shrinks. This allows the domestic

economy to cover its trade deficit in type X goods, and to eventually become a net consumer of type

Y goods too, as evidenced by the crossing of the demand for type Y goods and the endowment line, Y

(point ‘a’ in Figure 5.2). For uod/uof � uod/uof wf=1, the pattern is similar, with the roles of domestic

and foreign reversed.

2. INDUSTRIAL POLICY AND CATCHING UP

Suppose an economy faces a historically given asymmetry in initial conditions, to its disadvantage.

In our analysis this corresponds to a location leftward of the symmetric equilibrium in Figures 5.1 and

5.2. We now ask the following questions:

1) Is it possible for this economy to subsidize industryX and catch-up with the advantaged economy

(in terms of income and welfare), taking into account the strategic response by foreign rivals?

2) If catching-up is possible, is it welfare improving to do so?

We consider the perspective of the domestic economy (the identity of the disadvantaged economy is

not important). A lump-sum tax is imposed on consumers, and then redistributed to firms in industry

25

X via a reduction in the marginal cost of technological capability. The reduction in the marginal cost of

technological capability can be achieved by reducing εd or βd. As we reduce either of these parameters,

firms in the domestic economy will increase their technological capability, relative to their optimal level

in the absence of industrial policy. This generates higher demand for labour, and thus a rise in the

wage rate. Concentration does not change in the domestic economy, since fixed outlays actually paid

by firms are not altered by the subsidy: The difference between fixed outlays with industrial policy

and those obtained without intervention will be covered by the subsidy (financed with a lump-sum

tax). Thus, industrial policy operates via the ‘technological capability effect’.

βd

εd

uod /uof

symd

symd

ε

β

1

1

0

wf > wd

wf < wd

catching-up

is beneficial

for laggard

uod /uof

(Relative Initial Conditions)

(Relative Initial Conditions)

Required βd or εd for Catching-Up

Net Welfare Gain from Catching-Up

Figure 5.3. The Backward Economy’s Response to Differences in Initial Conditions: Catching-Up

Given some asymmetry in initial conditions, the top panel in Figure 5.3 shows a schedule depicting

the level of βdor εd required to ensure that the backward economy catches-up with the advanced

economy, in terms of wages. As the foreign economy’s initial conditions improve relative to the domestic

economy’s (uod/uof falls), the domestic economy must reduce its values of βd or εd if it is to maintain

a wage rate equal to the foreign economy’s. Levels of βd or εd lying above the schedule imply that

the foreign wage rate will be higher than the domestic wage rate. Levels of βd or εd lying below the

schedule imply that the foreign wage rate will be lower than the domestic wage rate4.

The bottom diagram shows the net welfare gain of catching up with the foreign economy, as

measured by the welfare indicator (expression 24 in Appendix 6). The net welfare gain will depend on

4Both parameters generate similar behaviour in the diagrams depicted in Figure 5.3, although their effect on other

variables is not always identical. Full results are available upon request.

26

whether the higher wage rate associated with industrial policy is higher than the wage rate without

intervention (net of the lump-sum tax associated with industrial policy). Whenever the domestic

economy is lagging behind, it is always welfare improving to impose a lump-sum tax in order to

finance a subsidy to technological capability, in the form of paying for the difference between the

non-intervention fixed outlays benchmark and the fixed outlays outcome with industrial policy.

We summarize these results in the following proposition.

Proposition 6. On the feasibility and welfare consequences of catching-up

A subsidy to technological capability (financed with a lump-sum tax on consumers), which takes

the form of reducing the marginal cost of technological capability via reductions in εi or βiin the

backward economy:

1) Can always equate the wage rate of the backward economy to that of the advanced economy

(catching-up is always feasible).

2) Is always welfare improving for the backward economy.

VII. THE SOCIAL PLANNER

[under construction, full results are already available]

VIII. CONCLUSIONS

In this paper we presented a two-country, two-sector, general equilibrium model of the world econ-

omy, together with the autarky benchmark. The main features of the model are oligopolistic inter-

actions (à la Cournot) and endogenous technological capability, market structure, sectorial allocation

of labour and terms of trade. We found a symmetric (general) equilibrium, such that each country’s

industry X features subgame perfection. With identical parameter values in both nations, we can

rule out asymmetric equilibria in which firms have different technological capability to overseas rivals

(Proposition 2). This lends some robustness to the analysis of the symmetric equilibrium, lessening

the need to worry about multiplicity of equilibria. The following results emerged from the analysis:

Firstly, the marginal benefit of technological capability is decreasing in the overseas rivals’ techno-

logical capability. The implication of this is that there exists a threshold for the ratio of technological

capabilities (that is, the technology gap), above which the marginal benefit becomes negative. This in

turn means that in the absence of industrial policy, catching up will be feasible only if the technological

gap is not too wide. In other words, a precondition for catching-up (without industrial policy) is that

the technology gap be sufficiently small (Proposition 1).

The model exhibits intra-industry trade, and in a symmetric equilibrium free trade does not reduce

welfare. Moreover, free-trade implies a (weakly) higher wage rate and (strictly) higher technological

capability, as well as a more concentrated market structure. In particular, the number of firms in a

symmetric equilibrium under free-trade is half of that under autarky. The opening of the economy to

foreign competition forces domestic firms to either match their foreign rivals’ technological capability

or exit. Thus, in facing a larger market, firms in both nations raise their technological capability. This

leads to an increase in sunk investments with the associated rise in concentration. This mechanism

27

sheds light on how the export boom preceded the investment boom in South Korea and Taiwan (see

the comment by Victor Norman in Rodrik [1995]).

Two development configurations emerged from the analysis. In a high-tech configuration the

economy is characterized by few firms, each with high technological capability. In a proliferation

configuration the economy is characterized by many firms, each with low technological capability.

The question is then, which path will deliver the highest the demand for labour and hence the highest

wage rate? Proposition 4 summarizes the result: Unless type X goods are poor substitutes (σ < σ∗),

a high-tech configuration is associated with a higher wage rate (and welfare). If type X goods are

poor substitutes, then a proliferation configuration is associated with a higher wage (and welfare).

Essentially this means that the technological capability effect always dominates the market structure

effect, except when goods are poor substitutes (i.e., there is a high degree of horizontal product dif-

ferentiation). This proposition is easily extended to encompass an economy composed by multiple

industries, which are only linked via the labour market. This rules out inter-industry demand linkages

(goods are not substitutes across industries), and supply-side linkages (there are no intermediate prod-

ucts or economies of scope). In this simple (but enlightening) case, if a planner chooses policies such

that all industries except those with low within-industry product substitutability achieve maximum

technological capability, maximum demand for labour will ensue (thus the wage rate and welfare will

be maximized). On the other hand, if a planner chooses policies so that concentration is minimized in

industries with highly horizontally differentiated products, then labour demand from these industries

will also be maximized. Moreover, in considering the symmetric equilibrium, what is good for the

closed economy is even better for the open economy (since the latter will feature an even higher wage

rate and welfare).

We analyzed various forms of industrial policy, under differing financing schemes for the symmetric

equilibrium. We found that if the government pays for all of the change in firms’ expenditure relative

to the original equilibrium outcome, consumers are indifferent to intervention. Alternative financing

schemes suggest either taxes or subsidies, depending certain restrictions on parameter values. The

restrictions constitute a formal basis for industrial targeting, under the assumption of a symmetric

equilibrium.

With few exceptions, symmetric equilibrium analysis is of little relevance to actual economies. To

raise the relevance of the model, we introduced asymmetric initial conditions. This changed matters

substantially. We found that a backward economy (with low technological capability) will benefit from

trade with an advanced economy (with high technological capability), provided the gap between their

initial conditions is not too large. If the gap is too wide, the backward economy achieves a higher

wage rate (and welfare) in autarky. On the other hand, the advanced economy always benefits from

trading with the backward economy. Thus, the gains-from-trade-theorem needs to be qualified. This

result clarifies the incentives in bilateral free trade agreements between an advanced and a backward

economy. The possibility of incompatible interests gives rise to issues of unfair trade negotiations, in

which an advanced country pressures a backward nation into a trade agreement from which it will not

reap welfare gains. The lesson that can be taken from this result is that before exposing domestic

industry to foreign competition, it is important to compare the initial conditions of both industries. If

the local industry is lagging too far behind, then rather than expose it to trade straight away, it may

28

be more convenient to enhance its technological capability first to ensure the gap in initial conditions

is reduced sufficiently to ensure that the domestic economy benefits from the trade agreement. This

result is summarized in Proposition 5, which provides a positive basis for the choice of trade partners.

We have thus provided positive and normative criteria for the formation of trading blocks.

Bhagwati [1988] has discussed at length the trend in the USA during the mid-eighties to spouse

a kind of ‘strategic’ trade policy. The policies proposed amount to little less than coercing small

economies into trade diversion towards the USA. The support of such policies often calls upon some

variant of the infant industry argument, whereby temporary interventions may generate a permanent

advantage to the small nation. The small nation would then presumably overtake the USA in a

particular industry. In order to prevent this overtaking, interest groups in the USA support removing

interventions (industrial policies) in foreign economies, which could give rivals an ‘unfair’ advantage.

The problem with this prescription, as embodied in the 1988 Trade Act, is that the USA would have

itself decide whether foreign rivals enjoy such ‘unfair’ advantages. Given the bargaining power of the

USA, it is likely that politically weaker rivals can be coerced into trade-distorting measures, such as

voluntary import expansions, where they divert trade from other nations to the USA. Proposition 4

states the circumstances in which these incentives arise, and pins down parameter values identifying

when it will (or will not) make sense for the backward nation to engage in free trade with the advanced

nation. The basic thrust of the proposition is that free trade is always welfare enhancing, provided the

technological capabilities of the two nations are not too dissimilar. It is when technological capabilities

become very different that the laggard nation could be better off remaining closed (although free trade

will still be welfare improving to the advanced nation). Only when technological capabilities of the

backward economies expand (possibly as a result of free trade within a ‘backward trading block’)

and the gap in initial conditions with the advanced nation is reduced, may it be optimal to engage

in free trade with the advanced nation. The last decade has seen the USA embark upon a series of

bilateral free trade agreements with small nations (particularly within Latin America). The theoretical

findings we have developed here lead us to predict that these small nations will not benefit from such

agreements.

Once asymmetries in initial conditions are introduced, the question arises of whether catching-up

is feasible and welfare enhancing. We analyze this issue by introducing industrial policy in the form

of a subsidy to technological capability, funded via a lump-sum tax. The subsidy takes the following

form: The government pays for the extra investment in technological capability required to ensure

that the backward economy achieves the same wage rate as the advanced economy. We find that with

this policy catching-up is both feasible and welfare enhancing (after accounting for lump-sum taxes

and for any strategic response by overseas firms).

Future Research and Limitations

An extension of the model to multiple time periods is a necessary step towards a full assessment

and reconsideration of the infant industry argument, especially regarding the role of expectations and

intertemporal strategic interaction (first mover advantages, preemption, entry deterrence, etc.). An-

other promising avenue is to translate this framework into a dynamic general equilibrium setting with

dynamic oligopoly. In general, the model developed in this paper would benefit from dynamic analy-

sis, and it is in this direction that our efforts are being directed. We have obtained some preliminary

29

results, which (thus far) support the present analysis.

In this study we have uncovered various justifications for government intervention, be it in the

form of preferential trade agreements or subsidies for catching-up. Our conclusions run the risk of

being misinterpreted as supporting government intervention in the form of closing the economy and

subsidizing industries. It is important to stress that closure of the economy is not what is being

suggested. Instead, the conclusion should be that trade agreements between economies that are not

too dissimilar in their initial conditions will be beneficial. The focus that emerges is: How can we

transform the economy so that it will benefit from free trade? The transformation implies ensuring

that the gap in initial conditions is sufficiently small to achieve welfare gains from free trade, and this

will invariably be associated with higher wages than permanent closure of the economy. Moreover,

the developing world is full of examples of failed industrial policies, which are ripe for capture by

rent-seekers. Once the subsidies are instituted, the resources devoted to such directly-unproductive

rent-seeking activities [Bhagwati, 1982] can constitute a heavy burden on the economy. We also assume

that the subsidies can be transformed into technological capability without efficiency loss. However, it

is likely that the effectiveness of subsidies in raising technological capability is less than that of private

efforts. In particular, if the subsidy loses efficiency as the technological capability gap widens, it is

likely that industrial policy will be welfare improving only when the gap in initial conditions is not too

wide. Furthermore, our calculations assume that the opportunity cost of the subsidy is unity (forgone

consumption). If the subsidies are being financed, not by reductions of consumption, but by social

investment (public health or education), their opportunity cost is likely to be higher than unity.

APPENDIX

A1. Informal Overview of the Model

For expositional purposes, the structure of the model is summarized in a flow-chart diagram in

Figure A1. The corresponding diagram for autarky is obtained by isolating the economies.

Consumers:max V s.t. B.C.

R&D

Industry XIRTS

3 Stages Lxd

Ld

Industry YCRTS

1:1 Technology

Lf

Lyd=Ld-Lxd

Domestic Economy Foreign Economy

xd, ud

Cournot:πd=F(ud)

ud

Numeraire: Yd

R&D

Industry XIRTS

3 StagesLxf

Industry YCRTS

1:1 Technology

Lyf=Lf-Lxf

xf, uf

Cournot:πf=F(uf)

uf

Numeraire: Yf

Figure A1: The structure of the open economy model

30

A2. Solving the Final Stage Subgame for Industry X

In this Appendix, we solve the final stage subgame (Cournot competition), in order to obtain

‘solved-out payoff’ functions for domestic and foreign firms. Recall the first order conditions for this

stage of the game (equation 4):

(Ld +Lf )∂πki

∂uki=

wiεiβiuki

(uki

uoi

)βi

for i = d, f and k = 1, ..., ni + 1

Let us begin by substituting the inverse demand functions (equation 3) and its derivative ( ∂pki∂xki

for

i = d, f) into the first order conditions. Adding and subtracting 2σ xkiu2ki

, we obtain

1− 2(2− σ)xki

u2

ki

−

2σ

uki

(ni+1∑

l=1

xli

uli

+

nj+1∑

l=1

xlj

ulj

)= 0 for i, j = d, f and i �= j (A2.1)

We multiply (A2.1) through by uki and re-organize the expression as follows

xki

uki=

uki − 2σ(∑

ni+1

l=1

xli

uli+∑nj+1

l=1

xlj

ulj

)

2(2− σ)for i, j = d, f and i �= j (A2.2)

The next step is to sum (A2.2) over k and solve for∑

ni+1

l=1

xli

uli

. This yields

ni+1∑

l=1

xli

uli

=

∑ni+1

l=1uli − 2σ(ni +1)

∑nj+1

l=1

xlj

ulj

2 (2 + σni)for i, j = d, f and i �= j (A2.3)

The equations in (A2.3) constitute a pair of linear equations in∑

ni+1

l=1

xli

uliand∑nj+1

l=1

xlj

ulj. Solving for

these we obtain

ni+1∑

l=1

xli

uli

=

(2 + σnj)∑ni+1

l=1 uki − σ (ni + 1)∑nj+1

l=1 ukj

2 (2− σ) [2 + σ (ni + nj +1)]for i, j = d, f and i �= j (A2.3′)

To obtain the solution for xki, substitute expression (A2.3′) back into (A2.2). This yields the following

solution for xki

xki =

u2

ki

2(2− σ)

[1−

σ

2 + σ (ni + nj +1)

(ni+1∑

l=1

uli

uki

+

nj+1∑

l=1

ulj

uki

)](A2.4)

Symmetry between firms within each country, such that uki = uli = ui and ukj = ulj = uj , yields the

following simplification

xi =u2

i

2(2− σ)

{1−

σ

2 + σ (ni + nj +1)

[(ni +1) + (nj +1)

uj

ui

]}(A2.4′)

With symmetry across countries, such that ud = uf = u, and noting that N = 2n+1, this expression

31

becomes

x =u2

2 (2 + σN)(A2.4′′)

where N represents the worldwide number of firms minus one. To solve for prices (pki), add and

subtract 2σ xki

u2

ki

to the inverse demand functions (equation 3), to obtain

pki = 1− 2 (1− σ)xki

u2

ki

−

2σ

uki

(ni+1∑

l=1

xli

uli

+

nj+1∑

l=1

xlj

ulj

)for i, j = d, f and i �= j (A2.5)

Next substitute xki from equation (A2.4) and the expressions in (A2.3′) into (A2.5). This yields the

solution for pki:

pki =1

2− σ

[1−

σ

2+ σ (ni + nj + 1)

(ni+1∑

l=1

uli

uki

+

nj+1∑

l=1

ulj

uki

)]for i, j = d, f and i �= j (A2.6)

By imposing symmetry between firms within each economy (such that uki = uli = ui and ukj = ulj =

uj), we obtain the following simplified solution

pi =1

2− σ

{1−

σ

2 + σ (ni + nj +1)

[(ni +1) + (nj +1)

uj

ui

]}(A2.6′)

If there is symmetry across economies, such that ud = uf = u, and noting that 2n + 1 = N , this

expression becomes

p =1

2 + σN(A2.6′′)

The solved-out payoff is given by the product of equations (A2.4) and (A2.6). This yields

πki(U) =u2

ki

2(2− σ)2

[1−

σ

2 + σ (ni + nj +1)

(ni+1∑

l=1

uli

uki

+

nj+1∑

l=1

ulj

uki

)]2(A2.7)

The solved-out payoff is written as equation (5) in the text. With symmetry across economies, this

simplifies to

π =u2

2(2 + σN)2

which is the expression derived by Sutton [1998, p. 512, equation 2.2.17′], but now N represents the

world number of firms minus one.

A3. Second Order Conditions for the Second Stage Subgame

The second order conditions are obtained by differentiating the first order conditions (equation 7)

with respect to uki for i = d, f. We obtain the following

(Ld +Lf )1

(2− σ)2

[2+ σ (ni + nj)

2 + σ (ni + nj +1)

]2�wiεiβi(βi − 1)u

βi−2

ki

uβi

oi

(A3.1)

for i = d, f and k = 1, ..., ni +1

32

If we substitute out uki, ni and wi with their equilibrium values, (A3.1) provides a restriction on

(σ,βi)-space. This restriction implies that σ cannot be too high and βi cannot be too low (in any case

we require βi > 2). If any one of these parameters crosses its bound, the other will need to compensate

by moving inward from its bound.

A4. Value Added and the Trade Balance

Value added is identical to the wage rate because labour is the only production factor, profits

are zero and there are no international monetary transfers. We can trace value added generated by

industry X and by industry Y . We consider measurement of value added on the production, income

and expenditure side. Consider first industry X.

Since there are no intermediate goods, value added in industry X measured on the production side

is equal to world-wide revenue from good X, which is given by (Ld + Lf ) (ni + 1)pixi for i = d, f .

Dividing by Li yields per-capita value added (as measured by production):

V APxi = V Axi =(Ld +Lf )

Li

(ni + 1)pixi for i = d, f (A4.1)

As measured by income, value added in industry X is given by workers’ wages (V AIxi = wiLxi

for i = d, f). Moreover, employment in industry X (Lxi) is given by (ni + 1)fi(ui) (where fi(ui) was

defined in section 2.2 as fi(ui) = εi

(ui

uoi

)βi

). The free entry condition can be written as (Ld +Lf )πi =

wifi(ui), so fi(ui) = (Ld +Lf )πi/wi. Gross profits in industry X are πi = pixi. Substituting this

into V AIxi, yields the same result as above: V AIxi = V Axi =(Ld+Lf )

Li(ni + 1)pixi for i = d, f .

As measured by expenditure, value added in industry X is made up by consumption expenditure

and net exports of good X (i.e., the trade balance in industry X), since there are no savings (invest-

ment) in this model. Consumption of good X is Li [(ni + 1) pixi + (nj + 1) pjxj] in country i. Exports

of good X are equal to Lj (ni +1) pixi, while imports of good X are Li (nj + 1) pjxj for i, j = d, f

and i �= j. The trade balance for industry X can be written as

TBxi = Lj (ni +1) pixi − Li (nj +1) pjxj for i, j = d, f and i �= j (A4.2)

By adding consumption expenditure and the trade balance, dividing by population (Li) and simplifying

we obtain the same result previously found in per-capita terms: V AExi = V Axi =(Ld+Lf )

Li(ni+1)pixi.

Value added in industry Y (as measured by production) is V APyi = qi(Li − Lxi). Noting that

qi = 1 (good Y is the numeraire), hence value added in industry Y is the supply of Y goods, which

(from the 1:1 technology) is the same as employment in industry Y (Lyi). Per-capita, this is given by:

V APyi = V Ayi = (Li − Lxi) /Li = Lyi/Li for i = d, f (A4.3)

Measured by income, value added in industry Y is equal to wages obtained by workers in industry

Y , V AIyi = wiLyi. From section 2.3 we have that whenever Lyi > 0, the wage rate is unity. So

we obtain: V AIyi = V Ayi = Lyi/Li (the same result as measured by production). Measured by

expenditure, value added in industry Y is constituted by consumption and net exports of good Y .

33

Consumption expenditure is obtained as a residual from the consumer’s budget constraint:

Li [wi − (ni + 1) pixi − (nj + 1) pjxj]

Net exports (i.e., the trade balance for industry Y ) are given by the difference between aggregate

supply and aggregate demand of good Y :

TByi = Lyi︸︷︷︸

Aggregate

Supply

− Li [wi − (ni +1) pixi − (nj +1) pjxj ]︸ ︷︷ ︸

Aggregate

Demand

for i, j = d, f and i �= j (A4.4)

and we obtain the same (per-capita) value added as measured by production and income: V AEyi =

V Ayi = Lyi/Li.

Total (per-capita) value added is the sum of value added for both industries: V Ai = V Axi+V Ayi.

The trade balance for each economy is given by TBi = TBxi + TByi with the following relationships

holding: TBi = −TBj, TBxi = −TBxj and TByi = −TByj for i, j = d, f and i �= j.

A5. Proof of Proposition 2.

The proof proceeds by obtaining an expression which makes it clear that any asymmetry of the

kind described in Proposition 2 is inconsistent with the general equilibrium conditions of the model.

We attain this by working with the equilibrium conditions for each economy: (10), (11) and (12). To

simplify these expressions, define:

A = 2 + σ (nd + nf + 1)

We can then re-write the equilibrium conditions as follows.

The first equilibrium conditions are given in expression (10):

(Ld + Lf )(A− σ)σ

(2− σ)2A2

[A

σ− (ni +1)− (nj +1)

uj

ui

]= wiεβ

uβ−2i

uβo

i, j = d, f , i �= j (A5.1)

Secondly we have the zero profit (free entry) conditions, from (11), which simplifies to

(Ld + Lf )σ2

2 (2− σ)2 A2

[A

σ− (ni + 1) − (nj + 1)

uj

ui

]2= wiε

uβ−2i

uβo

i, j = d, f , i �= j (A5.2)

Thirdly we have the labour market clearing conditions

Li = Lyi + (ni +1) ε

(ui

uo

)β

i = d, f (A5.3)

If Lyi > 0, then wi = 1. Otherwise wi > 1. For the case of wi > 1, we can divide the labour market

clearing condition for economy i by that for economy j to obtain the following expression:

ui

uj=

(nf + 1

ni +1

)1/β

i = d, f (A5.4)

34

Squaring (A5.1) we obtain:

[(Ld + Lf )

(A− σ)σ

(2− σ)2 A2

]2 [A

σ− (ni + 1)− (nj + 1)

uj

ui

]2=

(wiεβ

uβ−2i

uβo

)2

i, j = d, f , i �= j (A5.5)

Dividing (A5.5) by (A5.2) we obtain the following relationship:

(Ld +Lf )(A− σ)2

(2− σ)2A2= wiεβ

2 uβ−2i

uβo

i = d, f (A5.6)

Dividing the expression in (A5.6) for economy i by the corresponding expression for economy j we

obtain: (ui

uj

)β−2

=

wj

wi

(A5.7)

We now proceed to divide expression (A5.1) for economy i by its counterpart in economy j5 :

A

σ− (ni + 1) − (nj + 1) uj

ui

Aσ− (nj +1)− (ni + 1) ui

uj

=wi

wj

(ui

uj

)β−2i, j = d, f , i �= j (A5.8)

Substituting (A5.7) into (A5.8) we can simplify the latter to:

(ni + 1) + (nj + 1)uj

ui

= (nj + 1) + (ni + 1)ui

uj

i, j = d, f , i �= j (A5.9)

We now substitute expression (A5.4) in (A5.9) and we obtain an expression relating ni to nj :

(ni +1)

[1−

(nj + 1

ni + 1

)β−1

β

]= (nj + 1)

[1−

(ni +1

nj +1

)β−1

β

]i, j = d, f , i �= j (A5.10)

From this expression it is clear that if ni �= nj the left hand side will be of opposite sign to the right

hand side, which is a contradiction. It follows that for both economies to have the same number of

firms they must also have identical technological capabilities and wage rates.

It remains to consider the case when Lyi > 0. In this case wi = 1 and (A5.7) tells us that ui = uj,

and the result follows through as before�.

A6. A Note on Welfare

The welfare indicator is denoted by Wi. Substituting equilibrium solutions into the utility function

(equation 1) yields the indicator. The utility function contains the term: 2σ∑N+1

k=1

xk

uk

∑N

l �=kxl

ul. This

poses the following difficulty: When we impose within-country symmetry (xki = xi, uki = ui for i = d,

f) the term∑

N

l �=kxl

ulcan be written as either (ni + 1) xi

ui+ nj

xj

ujor as ni

xi

ui+ (nj + 1)

xj

uj, depending

on whether the good we drop is produced by the domestic or the foreign economy. Whence we write

5The same result obtains if we divide the expressions in (A5.2).

35

the welfare measure as follows

Wi =

[(ni +1)

(xi −

x2i

u2i

)+ (nj + 1)

(xj −

x2j

u2j

)]−min(Ai,Bi) + Y where, (A6.1)

Ai = 2σ

[(ni + 1)

xi

ui

+ (nj +1)xj

uj

] [(ni + 1)

xi

ui+ nj

xj

uj

]

Bi = 2σ

[(ni + 1)

xi

ui+ (nj +1)

xj

uj

] [nixi

ui+ (nj +1)

xj

uj

]

In a symmetric equilibrium this simplifies to W = 2 (n+ 1)(x−

x2

u2

)− 4σ (n+ 1) (2n+ 1)

(x

u

)2+ Y .

In autarky we have:

WA=

(nA+ 1

)[xA−

(1+ 2σnA

) (xA)2

(uA)2

]+ Y

A (A6.2)

For welfare analysis it is important to note that consumer welfare is determined by the wage rate.

Indeed, substituting the decentralized (symmetric) equilibrium outcomes into the welfare indicator,

yields W = (3/2)w + Y . Thus, to obtain the welfare consequences of any change in parameter values

all we need to observe are the changes in the wage rate, for given Y . This result also comes through

for the closed economy case.

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