Endogenous Technological Change

1
Endogenous Technological Change
Schumpeterian Growth Theory

• By
• Paul Romer

2
Organization

• Paul Romers (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 Romers model.
• Readings
• Romer (1990), Endogenous Technological Change,
  JPE, pp. S71-S101.

3
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.

4
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.

5
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.

6
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.

7
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.

8
Description of the Model

• Final output, Y, is given by

• 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.

9
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

10
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

• Where C is aggregate consumption.

11
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.

12
The Evolution of Designs and the Full Employment
of Labor Condition

• Aggregating over researchers we obtain an
  equation for the flow of designs

• Where HA is the amount of labor devoted to RD.
• The full employment of labor condition is

13
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.

14
The 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

15
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.

16
Intermediate Goods Producers

• The solution to the above maximization problem is
  given by

17
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.

18
Intertemporal Consumer Maximization

• Consumers have an intertemporal utility with
  constant elasticity of substitution and choose
  consumption expenditure optimally.
• The representative consumers problem is

19
Intertemporal Consumer Optimization

• The solution to the consumers problem implies

• 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.

20
Balanced Growth Equilibrium Solution

• Substitute p in the expression of profits ?
  apx 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.

21
Balanced-Growth Equilibrium

• Free mobility of labor between the final output
  and RD sectors requires

22
Balanced Growth Equilibrium

• Substitute PA from (11) to (12) and simplifying
  yields

• Using the full employment condition H HA HY
  and knowledge creation equation yields another
  equation that relates the growth rate to the
  interest rate

23
Balanced Growth Equilibrium

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

24
Balanced Growth Equilibrium

• Equation (10) defines a positive relationship
  between g and r

• Combining (14) with equation (10) yields an
  explicit solution for g.

25
Balanced 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.

26
Conclusions

• The model provides an elegant formalization of
  endogenous technological change.
• Romers 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.