Post on 20-Dec-2015
transcript
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 11
Endogenous Technological ChangeEndogenous Technological Change
Schumpeterian Growth Schumpeterian Growth TheoryTheory
By
Paul Romer
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 22
OrganizationOrganization
Paul Romer’s (1990) article is one of the most influential papers in the theory of endogenous growth.
This topic will provide an overview of the paper by developing a simple version of Romer’s model. Readings
Romer (1990), “Endogenous Technological Change”, JPE, pp. S71-S101.
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 33
Introduction and motivationIntroduction and motivation
Significance of technological change (process or product innovations) it lies at the heart of economic growth. It arises in large part because individuals
take intentional actions based on market incentives.
It involves fixed costs. It generates nonconvexities which exclude
perfectly competitive markets.
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 44
The Economic Nature of TechnologyThe Economic Nature of Technology
One useful way to think about technology is to treat it as a collection of designs (blue prints).
Each design contains detailed instructions of how to produce a new product or a new process.
As such, technology can by produced, copied, transferred and traded.
There are two fundamental attributes of technology: It is non-rivalrous. It is excludable.
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 55
The Economic Nature of TechnologyThe Economic Nature of Technology The use of a purely rival good by one firm or
person precludes its use by another; The use of a purely nonrival good by one firm or
person does not limit its use by another. A good is excludable if the owner can prevent
others from using them. Conventional economic goods are rivalrous and
excludable. Public goods are nonrivalrous and
nonexcludable. Technology is nonrivalrous but excludable.
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 66
Technology and Market StructureTechnology and Market Structure
The excludable nature of technology allows the private sector to produce designs based on market incentives.
The nonrivalous nature of technology allows the accumulation of designs and creates noncovexities (e.g., fixed costs) in the structure of production.
Nonconvexities generate internal scale economies and increasing returns.
Increasing returns reguire imperfectly competitive market structures.
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 77
Sectoral Structure of the ModelSectoral Structure of the Model
There are three sectors in the economy The final good sector consists of a
homogeneous good produced with labor and intermediate goods under perfect competition.
The intermediate good sector produces capital goods with capital only under monopolistic competition.
The research sector produces designs (varieties) with labor.
Factor markets are perfectly competitive.
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 88
Description of the ModelDescription of the Model
Final output, Y, is given by
i
a
i
a
YYxHxHY1
),(
Where HY is labor devoted to manufacturing of final good Y, and xi is the quantity of a typical intermediate good.
Intermediate goods can be thought of as capital goods.
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 99
Description of the ModelDescription of the Model
It is convenient of work with a continuum of goods. Therefore denote with A(t) the measure of designs produced by time t.
Final output can be written as
)1()())(,,()(
0
1 diixHtAxHYtA
aa
YY
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 1010
Evolution of Physical CapitalEvolution of Physical Capital
Following the usual approach to growth, it is useful to define an accounting measure of total capital.
The aggregate measure of capital, K, is cumulative forgone output.
Thus, in the absence of depreciation ( a simplifying assumption), K evolves according to
)(
0
)(,tA
diixKCYK Where C is aggregate consumption.
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 1111
The Evolution of DesignsThe Evolution of Designs
Designs are produced in the research sector, which utilizes only labor.
Romer assumes that anyone engaged in research has free access to the entire stock of designs, A(t). This is feasible under the assumption that
knowledge is a nonrival good. The output of researcher j is HJA dt, where dt
is an infinitesimal period of time. During that period researcher j produces dAj
designs.
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 1212
The Evolution of Designs and the Full The Evolution of Designs and the Full Employment of Labor ConditionEmployment of Labor Condition
Aggregating over researchers we obtain an equation for the flow of designs:
Where HA is the amount of labor devoted to R&D.
The full employment of labor condition is
)2(AHAA
)3(HHHYA
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 1313
Firm Behavior: The Final Good SectorFirm Behavior: The Final Good Sector
Notation to be used: Output Y is used as the numeraire, so all
prices are measured in units of Y. PA denotes the spot price of a design. Let r denote the instantaneous interest rate.
Because goods can be converted to capital, the spot price of capital is equal to one and the rate of return (wage of capital) is equal to r.
Let w denote the wage of labor, H.
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 1414
The Demand for Intermediate InputsThe Demand for Intermediate Inputs
Because perfect competition prevails in the final good sector, the representative firm solves the following problem:
Differentiating under the integral sign leads to the inverse demand function:
diixipixHtA
aa
Yx
)(
0
1 )]()()([max
)4()()1()( aa
YixHaip
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 1515
Intermediate Goods ProducersIntermediate Goods Producers
A producer for a specialized good x (assuming symmetry) faces demand p(x) and chooses x to maximize its profits.
This firm has already incurred the fixed costs to discover the design.
)5()1(max
)(max
1 rxxHa
rxxxp
aa
Yx
x
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 1616
Intermediate Goods ProducersIntermediate Goods Producers
The solution to the above maximization problem is given by
)8(**
)7()1(
*
)6(})1){(1(
xap
a
rp
rxHaa aa
Y
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 1717
The Market Valuation of DesignsThe Market Valuation of Designs
At every point in time, the instantaneous profit flow should be sufficient to cover the interest cost on the initial investment (fixed costs) of a design.
The cost of a design is simply its spot price PA.
)9()(
)(
,)()(
tr
tPor
Ptrt
A
A
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 1818
Intertemporal Consumer MaximizationIntertemporal Consumer Maximization
Consumers have an intertemporal utility with constant elasticity of substitution and choose consumption expenditure optimally.
The representative consumer’s problem is :
1
0
1[ ]1max t
C
Ce dt
subject to Z rZ w C
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 1919
Intertemporal Consumer OptimizationIntertemporal Consumer Optimization
The solution to the consumer’s problem implies
)10()(
r
C
Cg
Where g is the long-run growth of the economy. Equation (10) defines a positive relationship
between the growth rate and the rate of interest.
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 2020
Balanced Growth Equilibrium SolutionBalanced Growth Equilibrium Solution
Substitute p* in the expression of profits = ap*x* to obtain = a(1-a)Hy
a x*(1-a). This results in an expression for the price of
designs PA = /r = {a(1-a)Hy
a x*(1-a)} / r (11)
Equalization of wage for workers in the research sector and manufacturing of final goods implies equalization of the value of marginal product of labor in these activities.
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 2121
Balanced-Growth EquilibriumBalanced-Growth Equilibrium
Free mobility of labor between the final output and R&D sectors requires
)12(*
*
)1(1
)(
0
)1(1
aa
Y
tAaa
YA
AxaH
dixaHAPw
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 2222
Balanced Growth EquilibriumBalanced Growth Equilibrium
Substitute PA from (11) to (12) and simplifying yields:
)13()1(
1
a
rH
Y
Using the full employment condition H = HA + HY and knowledge creation equation yields another equation that relates the growth rate to the interest rate
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 2323
Balanced Growth EquilibriumBalanced Growth Equilibrium
In the balance growth equilibrium the growth rate g is equal to
)14()1(
}{
a
rH
HHHA
Ag
YA
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 2424
Balanced Growth EquilibriumBalanced Growth Equilibrium
Equation (10) defines a positive relationship between g and r:
)10()(
r
C
Cg
Combining (14) with equation (10) yields an explicit solution for g.
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 2525
Balanced Growth EquilibriumBalanced Growth Equilibrium
In the balanced growth equilibrium C, Y, K and A all grow at the same rate g.
Any policy that shifts resources to research, increases g.
)15(1)}1/({
)}1/({
a
aH
HA
A
K
K
Y
Y
C
Cg
A
Endogenous Endogenous
Technological ChangeTechnological Change Slide Slide 2626
ConclusionsConclusions
The model provides an elegant formalization of endogenous technological change.
Romer’s claims that human capital matters do not alleviate the problem of scale effects.
Dinopoulos and Thompson (JIE, forthcoming) have generalized the Romer model by removing the scale effects property and tested its implications.
Jones (JPE, 1995) has removed the scale effects by making the level of technology endogenous and g proportional to the exogenous rate of population growth.