Neoclassical Growth Theory Chapter 15 Neoclassical Growth Theory

Introduction Growth theorists concentrated on documenting the sources of growth - population - capital stock - new discoveries and innovations - others (human capital, R&D, …) Robert Solow and T.W. Swan the leading contributors (1950s)

Introduction Robert Solow and T.W. Swan - Investment in new capital and the growth of population cannot lead to continued growth in per capita income. They attributed growth to the invention of new technologies. The source of these innovations was unexplained in their models. (exogenous growth theory)

Introduction From the 1950s until the late 1980s, the theory of economic growth was a stagnant area for economic research. All of this changed for two reasons: 1. The Penn World Table. 2. A comprehensive source of data.

Introduction Two theoretical papers were instrumental in the resurgence of growth theory. Romer (1986) & Lucas (1988) - they searched for an explanation of the sources of technological progress. - one of the main ideas is human capital, accumulation of knowledge. - endogenous growth theory.

The Sources of Economic Growth Growth theory begins with the assumption that GDP is related to aggregate capital and labor through a production function. For simplicity, suppose the output is produced from a single (compound) input. Ex. k = K/L. Figure 15.1 -- input and output person for the U.S. economy from 1929 through 1995. -- more input leads to more output.

Inputs and Outputs in the United States, 1929–1999 Figure 15.1 ©2002 South-Western College Publishing

Exogenous v.s Exogenous Growth Theory Ex. growth theory -- the state of technology does not remain constant over time. -- the production function satisfies CRS. -- The slope is a measure of productivity. -- because the points in Figure 15.1 do not lie on a straight line through the origin, the slope of the production function must have changed from one year to the next.

Exogenous v.s Exogenous Growth Theory Ex. growth theory (cont.) -- Because early work in growth theory did not try to explain the influence of invention and innovation, productivity was left exogenous. Endogenous theory -- rejects the assumption – CRS. -- allows for the possibility that the points in Figure 15.1 may all come from the same production function.

Production Function and Returns to Scale Frequently used production function :

Production Function and Returns to Scale Constant Returns to Scale (CRS) -- if all the inputs are increased by a fixed multiple, than output should increase by the same multiple. -- in the Cobb-Douglas production fun., CRS means that the exponents on capital and labor add up to 1.

The Neoclassical Theory of Distribution How the output is distributed to the owners of the factors of production, labor and capital. The theory asserts that factors are paid their marginal products. ( Euler Theorem ) We can measure how much labor and capital contribute to growth by observing how much they are paid.

The Theory of Distribution and the Cobb-Douglas Function The representative firm maximize F.O.C. yields

The Theory of Distribution and the Cobb-Douglas Function 1-α (α) measures the percentage increase in output that will be gained by a given percentage increase in labor (capital) input, and is so called the labor (capital) elasticity. 1-α (α) can be estimated to calculate how much of the growth in GDP per person is due to growth in labor and capital per person.

Labor’s Share of National Income Figure 15.2 ©2002 South-Western College Publishing

Growth Accounting Output per person equals input per person multiplied by a term called “total factor productivity”.

Growth Accounting If we construct the aggregate input as described by this equation, the graph of the production function is a straight line through the origin. On this graph, GDP per person is plotted against input per person, and total factor productivity corresponds to the slope.

Growth Accounting In figure 15.1, we found that if we plot points on the production function for different years, these points do not follow the same straight line through the origin. Solow took this as evidence of the fact that productivity has increased, i.e. the slope of the production function has been increasing over time.

Inputs and Outputs in the United States, 1929–1999 Figure 15.1 ©2002 South-Western College Publishing

Growth Accounting Growth in labor and capital would be represented as a movement along the production function. Part of GDP growth per person must be due to changes in total factor productivity as measured be increases in the slope of the production function. Economists call total factor productivity the “Solow residual”.

The Solow Residual in the United States Figure 15.3 ©2002 South-Western College Publishing

Growth Accounting Suppose growth rates of GDP per person, capital per person and labor per person are 10%, 5%, 3% respectively, then growth in the Solow residual is 10%-1/3*6%-2/3*3%=6%.

The Sources of Growth in GDP per Person Figure 15.4 ©2002 South-Western College Publishing

The Neoclassical Growth Model We have described the factors that account for growth in GDP per person and one of these factors is the growth in capital per person which can be increased by increasing investment. Can we increase growth by investing more as a nation? Neolcassical spells out the link between investment and growth.

The Neoclassical Growth Model Increases in productivity are necessary if a nation is to experience sustained growth in its standard of living. The neoclassical growth model shows that an economy with a fixed production that is subject to constant returns to scale cannot grow forever. ( due to diminishing returns to capital )

Three Stylized Facts The neoclassical growth model begins with three stylized facts that characterize the U.S. data to a first approximation. GDP per person has grown at an average rate of 1.89% over the past century. The share of consumption in GDP have remained approximately constant. The labor’s share of income have remained approximately constant.

Three Facts Used To Construct the Neoclassical Growth Model Figure 15.5A ©2002 South-Western College Publishing

Three Facts Used To Construct the Neoclassical Growth Model Figure 15.5B ©2002 South-Western College Publishing

Three Facts Used To Construct the Neoclassical Growth Model Figure 15.5C ©2002 South-Western College Publishing

Three Stylized Facts The neoclassical model builds these constants into an economic model based on a competitive theory of production and distribution. It uses this model to explain the per capita GDP growth rate.

Assumptions

Assumptions

Simplifying the Model We make three assumptions that are not strictly necessary, but that will simplify the exposition. Each person in the economy supplies exactly one unit of labor to the market. The population is constant. (N) There are no changes in the efficiency of labor, i.e. Q is constant over time.

Diminishing Marginal Product Divide both sides of the production function by population, N. This leads to the per capita production function, which expresses the relationship between output per person and capital per person.

Diminishing Marginal Product Diminishing marginal product of capital means that if capital changes by a fixed percentage, holding the input of labor constant, then output will change by a smaller percentage as k increases.

The Per Capita Production Function Figure 15.6 ©2002 South-Western College Publishing

Three Steps to the Neoclassical Growth Equation

Steady State Let

Convergence When the Economy Begins with Too Little Capital Figure 15.7 ©2002 South-Western College Publishing

Convergence When the Economy Begins with Too Much Capital Figure 15.8 ©2002 South-Western College Publishing

Dynamics

Steady State An economy with a very high saving rate should also have very high levels of capital and GDP per person. The economy always grows to the point at which new investment is just sufficient to replace worn-out capital. Higher depreciation will tend to lower the steady state stock of capital and per capita GDP.

The Effects of Productivity Growth We have learned that per capita output cannot grow forever. A key to understanding growth is in being able to explain how the input of labor per person can grow. The neoclassical growth model explains how labor can grow by distinguishing labor supply measured in hours from labor supply measured in efficiency units.

Measuring Labor in Efficiency Units E is equal to the number of people, N, each of whom supplies one unit of time, multiplied by their efficiency, Q. Although we have assumed that the population is constant and each person supplies a fixed number of hours, it will still be possible for the labor supplied by each person to increase as long as we measure labor in efficiency units.

Table 15.1 ©2002 South-Western College Publishing

The Neoclassical Growth Equation

The Neoclassical Growth Equation

The Neoclassical Growth Equation

Homework Question 6, 7, 11

END