09 advanced economic analysis negt i 2011
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Advanced Economic Analysis
Lecture 9:
The New Endogenous GrowthTheory I
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Contents Background Basic Structure The AK models and optimal growth Two examples of AK models: Romer
1986 and Lucas 1988
Entrepreneurial efforts and innovation
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Background
Main objectives of the NEGT: Explain the Solow residual Make the economic growth rate
dependent on the saving decision ofindividual agents
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The basic structure of NEGT models
nacrawa +=
)/()('
)(''cc
cu
ccu
r
=
=
0
)]([ tCUU e nt e - t dt (1)
The Ramsey model:
(3)
))(/1()/( =
rcc
(2)
(5)
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The basic structure of NEGT modelsThe basic AK model:
Y = AK (6)
dK(t)/dt = sY(t) (equation (2) Solow model)
dK(t)/dt = sAK (7)
long term growth rate depends on saving(investment rate): scale effect
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ComparisonHarrod-Domar - Solow - AK
Harrod-Domar gw = s/c
where c = incremental capital-output ratio
dttdY
dttdK
/)(
/)( YK/
yk/
ky/
c =K/Y
Hence, also :
= 1/c.
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ComparisonHarrod-Domar - Solow - AK
Solow model:= s (k) nk (equation 4 Solow model)
/k = s (k)/k nSince y = (k):
/k = s y/k n
Assuming = 0
s y/k = n, or
gw = s/c = n
gw = s/c = n +where stands for exogenous technical progress
k
k
k
k
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ComparisonHarrod-Domar - Solow - AK
AKmodel,:y = Ak, (6.1)
where y = Y/L and k = K/L,= sAk (7.1)
/k = sA
gw = s/c = s/(1/A) = sA
k
k
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Comparison
Harrod-Domar - Solow - AK
Harrod-Domar Solow AK models
gw
= s/c n + sA
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Basic AK model Growth rate of consumption (per capita):
A = r +d. Therefore:
R = A - d
/k =
What is the meaning of constant returns tocapital?
k )))((/1()/( =
dAcc
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Romer 1986 One-sector model Learning-by-investment Firm knowledge is a public good If Ai denotes all knowledge controlled
by a firm, then changes in Ai correspond
to learning-by-doing across economyand this is proportional to changes incapital stock
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Romer 1986Yi = F (Ki, K(Li)) (9)
Yi = A (Ki) (KLi)
1- (10)
Yi/Ki = AL1- Therefore:
/k =
y/k = AL1-.Therefore:
/kPLANNER= (11a)
k ))(/1()/(1
=
LAcc
k ))(/1( 1 AL
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Romer 1986Actual growth rate of decentralised
economy is below optimal growth rate
due to knowledge externalities Perfect competition prevails since
producers remain unaware of positive
externality (firm-external) Space for government policies
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Lucas 1988 Two-sector model: capital accumulation and
investment in education
Constant rate of growth derived frominterpretation of growth of labour efficiencyas a combination of a given accumulation ofknowledge with an explanation of its growth
in terms of a societys preferences betweenpresent and future consumption
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Lucas 1988 (12)
where ay is a positive constant (i.e. a parameterfor technical progress) Ly is labour employed inthe process of the production of real output, Hicorresponds to individual human capital, and Hadenotes the general state of education
(13)
where aH is a positive constant, H is the givenstock of human capital, and LH is labour employedin the process of building human capital
Y = a K ( L H ) Hy y i1-
a
HH
HLa=H
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Lucas 1988 Firms face constant returns to capital and labour Overall production function characterised by
increasing returns to scale
Formation/accumulation of human capital (13)characterised by exactly constant returns
Existence of steady-state balanced growth attributedto human skills and knowledge (of human capital)
acquired through intentional learning process Equation (13) effectively transforms labour from a
scarce resource into an accumulable factor
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Entrepreneurial efforts: R&D
Microeconomic explanation forendogenisation of technical progress
Increasing returns to scale andimperfect competition
Constant returns to some type of capitalor accumulable factor of productionremain central
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Romer 1990
Product differentiation Knowledge is non-rivalrous and partially excludable IRS (research-intensive production) and imperfect competition 3-sector model: final goods, intermediate goods, research sector
Intermediate goods sector: monopolistic competition (high productvariety and each individiual good is produced by a monopolist), freeentry into the sector, returns to production of intermediate goodscan be made firm-specific
Research sector: perfect competition that determines theequilibrium number of intermediate inputs (A) and ensures zero
profit for marginal entrant; researches make free use of knowledgestock A
In the long run, general knowledge is both an input into and anoutput of the production of intermediate goods (blue-prints), i.e.positive knowledge externality in both intermediate and researchsector
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Romer 1990
Aggregate Production Function(14)
where Ly is labour employed in the production process.
The production of ideas and designs (A) is a function ofthe aggregate research effort (Li) and the rate of
discovery of new ideas () in the following form:
(15)
Y = K (ALy )1
ALAI
=
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Romer 1990
The rate of technological progress (or the growthrate of A) is:
(16)
Productivity of research is exactly proportional tothe existing stock of ideas, i.e. externality due to
past innovations exhibits constant returns
ILA
A=
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Romer 1990
The steady-state growth rate for the decentralisedeconomy is:
(17)
where = total labour supply, 1/ monopoly mark-up
Equilibrium growth rate of decentralised economy willbe less than social optimum
+
=Lgw
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Jones 1998
Adjusted R&D equation:
(15a)
where 01 and 01. denotes an additional externalityreflecting the likely duplication of research efforts.
Therefore, the rate of growth of the stock of ideas Anow is:
(16a)
I
1-
I L)L(A=A
I-1
1-
IL
A
L
A
A
b
=
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Jones 1998
Solving the model in the same way asRomer, the steady state growth rate of thestock of ideas or design becomes:
(17a)
where n denotes the population growth rate.
=
1
ng
w
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Jones 1998
A growing population rises the level oftechnology (conscious research efforts
resulting in non-rivalrous ideas)
Growth rate independent of the savingsrate: Solowian dynamics
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Schumpeterian innovationmodels
Vertical product innovation with obsolence(creative destruction)
Imperfect (monopolistic) competition and IRSin research-intensive and innovation sectors
Aghion and Howitt 1998: Constant returns to research activities arise from
the assumption that every innovation generates aproportionate increase in A and that the marginalproductivity of research is independent of thenumber of researchers in the economy
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Schumpeterian innovationmodels
Aghion and Howitt 1998 contd: IRS generate externalities so that optimal and
equilibrium growth paths differ (as in Romer 1990) In addition to positive intertemporal spillover
effect from innovation, there is a negativebusiness stealing effect and a positiveappropriability effect.
The relationship between the optimal and theequilibrium growth paths, and the design ofgovernment policies to promote innovation,depends on sizes of the two positive and thenegative externalities.
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