endogenous technological change slide 1 endogenous technological change schumpeterian growth theory...

Endogenous Endogenous

Technological ChangeTechnological Change Slide Slide 11

Endogenous Technological ChangeEndogenous Technological Change

Schumpeterian Growth Schumpeterian Growth TheoryTheory

By

Paul Romer



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.



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.



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.



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.



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.



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.



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.



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



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.



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.



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



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.



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



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



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



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



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



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.



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.



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



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




In the balance growth equilibrium the growth rate g is equal to

)14()1(

}{

a

rH

HHHA

Ag

YA




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.




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



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.

endogenous technological change slide 1 endogenous technological change schumpeterian growth theory...

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