Schumpeterian Growth
Theory
Endogenous Technological Change
By
Paul Romer
Endogenous Technological Change
Slide 1
Organization


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 Technological Change
Slide 2
Introduction 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 Technological Change
Slide 3
The 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 Technological Change
Slide 4
The 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 Technological Change
Slide 5
Technology 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 Technological Change
Slide 6
Sectoral 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 Technological Change
Slide 7
Description of the Model

Final output, Y, is given by

Y ( H , x)  H  x
a
Y


Y
i
1 a
i
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 Technological Change
Slide 8
Description 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
A(t )
Y ( H , x, A(t ))  H  x(i) di
a
Y
1 a
Y
(1)
0
Endogenous Technological Change
Slide 9
Evolution 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

K  Y C ,
A(t )
K   x(i)di
0

Where C is aggregate consumption.
Endogenous Technological Change
Slide 10
The 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 Technological Change
Slide 11
The Evolution of Designs and the Full
Employment of Labor Condition

Aggregating over researchers we obtain an
equation for the flow of designs:

A  H A
A


(2)
Where HA is the amount of labor devoted to
R&D.
The full employment of labor condition is
H H H
A
Y
Endogenous Technological Change
(3)
Slide 12
Firm 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 Technological Change
Slide 13
The Demand for Intermediate Inputs

Because perfect competition prevails in the
final good sector, the representative firm
solves the following problem:
A(t )
max  [ H x(i)  p(i ) x(i)] di
a
x

1 a
Y
0
Differentiating under the integral sign leads to
the inverse demand function:
p(i)  (1  a) H x(i)
a
a
Y
Endogenous Technological Change
(4)
Slide 14
Intermediate 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.
  max p( x) x  rx
x
 max (1  a) H x  rx
a
x
1 a
Y
Endogenous Technological Change
(5)
Slide 15
Intermediate Goods Producers

The solution to the above maximization
problem is given by
(1  a){(1  a) H x }  r
a
a
Y
r
p* 
(1  a )
  ap * x *
Endogenous Technological Change
(6)
(7 )
(8)
Slide 16
The 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.
 (t )  r (t ) P ,
 (t )
A
or
P 
A
r (t )
Endogenous Technological Change
(9)
Slide 17
Intertemporal Consumer Maximization


Consumers have an intertemporal utility with
constant elasticity of substitution and choose
consumption expenditure optimally.
The representative consumer’s problem is :

C1  1   t
[
]e dt
max

1
C
0

subject to Z  rZ  w  C
Endogenous Technological Change
Slide 18
Intertemporal Consumer Optimization

The solution to the consumer’s problem
implies

C
(r   )
g 
C



(10)
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 Technological Change
Slide 19
Balanced Growth Equilibrium Solution

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Substitute p* in the expression of profits  =
ap*x* to obtain  = a(1-a)Hya x*(1-a).
This results in an expression for the price of
designs
PA =  /r = {a(1-a)Hya 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 Technological Change
Slide 20
Balanced-Growth Equilibrium

Free mobility of labor between the final output
and R&D sectors requires
w  P A  aH
A
a 1
Y
A(t )
 x * di
( 1 a )
0
 aH
a 1
Y
( 1 a )
Ax *
Endogenous Technological Change
(12)
Slide 21
Balanced Growth Equilibrium

Substitute PA from (11) to (12) and simplifying
yields:
1
r
H 
 (1  a)
Y

(13)
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 Technological Change
Slide 22
Balanced Growth Equilibrium

In the balance growth equilibrium the growth
rate g is equal to

A
g   H   {H  H }
A
r
 H 
(14)
(1  a )
A
Endogenous Technological Change
Y
Slide 23
Balanced Growth Equilibrium

Equation (10) defines a positive relationship
between g and r:

C
(r   )
g 
C


(10)
Combining (14) with equation (10) yields an
explicit solution for g.
Endogenous Technological Change
Slide 24
Balanced Growth Equilibrium




C Y K A
g      H
C Y K A
H  { /(1  a)}

{ /(1  a )}  1


A
(15)
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.
Endogenous Technological Change
Slide 25
Conclusions

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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 26