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Endogenous Technological Change

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### Endogenous Technological Change

By

Paul Romer

Endogenous Technological Change

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.

- Readings

Endogenous Technological Change

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

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

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

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

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

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.

Endogenous Technological Change

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

Endogenous Technological Change

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.

Endogenous Technological Change

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

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 R&D.
- The full employment of labor condition is

Endogenous Technological Change

Firm Behavior: The Final Good Sector Condition

- 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

The Demand for Intermediate Inputs Condition

- 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:

Endogenous Technological Change

Intermediate Goods Producers Condition

- 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.

Endogenous Technological Change

Intermediate Goods Producers Condition

- The solution to the above maximization problem is given by

Endogenous Technological Change

The Market Valuation of Designs Condition

- 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.

Endogenous Technological Change

Intertemporal Consumer Maximization Condition

- Consumers have an intertemporal utility with constant elasticity of substitution and choose consumption expenditure optimally.
- The representative consumer’s problem is :

Endogenous Technological Change

Intertemporal Consumer Optimization Condition

- The solution to the consumer’s 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.

Endogenous Technological Change

Balanced Growth Equilibrium Solution Condition

- 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

Balanced-Growth Equilibrium Condition

- Free mobility of labor between the final output and R&D sectors requires

Endogenous Technological Change

Balanced Growth Equilibrium Condition

- 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

Endogenous Technological Change

Balanced Growth Equilibrium Condition

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

Endogenous Technological Change

Balanced Growth Equilibrium Condition

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

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

Endogenous Technological Change

Balanced Growth Equilibrium Condition

- 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

Conclusions Condition

- 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

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