Chapter 10: The Theory of Economic Growth

Introduction

1. We measure growth as sustained change in real GDP per person. Does this reflect a welfare gain? How does this related to the LRAS curve?

2. Why the rate of compounding results in substantial differences in welfare gain? What is the ‘rule of 72’?

3. Why we study growth theory. Several important questions in chapters 10-11:

a. What determines economic growth in natural real GDP per person? (Ch. 10)

b. Why are some countries ‘rich’ and others ‘poor’? (Ch. 11)

c. What explains the ebb and flow of productivity growth in the U.S.? (Ch. 11)

Standards of Living as a Consequence of Economic Growth

1. How does U.S. per capita income compare to the United Kingdom?

2. Why can we conclude that Minor differences in economic growth rates over a long period build up into substantial differences in relative living standards.

3. How does economic growth shift the production possibility curve to avoid a ‘zero sum’ game.

The Production Function and Economic Growth

1. How does neoclassical theory explains output as a function of labor, capital, and exogenous total factor productivity?

2. How is this converting to output per worker as a function of capital per worker?

3. Why are the sources of growth per person dependent on capital per person and autonomous growth factor, A?

4. What sources of growth are included in A?

Example of Cobb-Douglas production function

1. If the Cobb-Douglas production specification is used, variables are expressed as an index. (See appendix to chapter 10).

2. Cobb-Douglas Y = A Kb L1-b assumes constant returns to scale.

3. Suppose initially 1.0 = 1.0(1.0 0.25 1.0 0.75)

a. Suppose labor input increases 4% to 1.04, then Y increases to 1.03 (or 3%).

b. Suppose capital input increases 4% to 1.04, then Y increases 1.01 (or 1%).

c. If both input increase 4%, then Y increases 4%

d. uppose A increases 4% to 1.04, then Y increases to 1.04 (or 4%).

4. (Note that exponents are elasticity of real GDP with respect to a change in an input (0.75 for labor, 0.25 for capital).

5. Assume that L can be estimated by total population, N, then the Cobb-Douglas specification after dividing by N, gives the following relationship: Y/N = A (K/N) b Note that the function results in diminishing returns from capital, since MPPk = Ab(K/N) b-1 = Ab(K/N)b)/(K/N) decreases as K/N increases. (see figure 10-1)

The Theory of Economic Growth

Goal: To understand forces causing differences in income over time and across countries.

· Why is economic growth is based upon the production function of the economy?

· Why must differences in income and growth over time come from differences or changes in capital, labor, and/or technology?

· Why do changes in the production function result in shifts in the aggregate supply curve (to the right) so that higher output occurs for a given price level?

Our Primary Task in chapter 10 is to develop the Solow model of economic growth.

Our Secondary Task is to examine how economic policy can influence the level and growth in our standard of living.

Finally, we will look at some endogenous forces that may affect economic growth.

The Solow Growth Model without Technology Change

1. What determines the supply of goods in the economy?

a. The Solow model assumes that the supply of goods and services depends upon a production function with constant returns to scale. zY = F(zK, zN)

b. Hence, with substitution if z = 1/N, then Y/N = F(K/N, 1), i.e. output per worker depends upon capital per worker.

c. The marginal productivity of capital MPK will diminish if the amount of labor and technology is fixed. (See Figure 10-1)

d. Clearly changes in the stock of capital will result in an increase in the supply of goods and services, even with the supply of labor and technology fixed.

2. What determines the link between investment and the growth in capital?

a. The Solow model assumes that the demand for goods depends upon consumption and investment. This rate of income equates the savings rate per capita with the rate of investment per capita.

c. For a given propensity to save, s, this occurs when I/N = s (Y/N), i.e. investment is proportional to income.

d. Hence, the savings rate determines the allocation of Y/N between consumption and investment for every value of K/N.

e. Net investment adds to the capital stock. This occurs only if gross investment is greater than depreciation. If depreciation is given by d (K/N), then change in the capital stock is = s f(Y/N)) - d (K/N)

4. What is the Steady State?

a. The steady state occurs when net investment equals zero, i.e. investment equals depreciation. Then s f(Y/N) = d (K/N).

b. Output and capital grow at the same rate, so that Y/K is fixed.

c. Also, Y/N and K/N are fixed, so that the growth rate in capital, k, and the growth rate in labor, n, are the same, i.e. k = n.

f. At this Steady State I = (n + d)K or s(Y/K) = n + d

5. What is the impact of a higher savings rate on income per capita?

a. A higher savings rate increases the rate of investment and adds to net investment, K/N and Y?N.

b. It results in a higher Steady State equilibrium income and higher economic welfare of a country.

c. Is a higher domestic savings rate always desirable?

6. What is the impact on income per capita of population growth?

a. Population growth increases output but lower income per capita

b. The change in capital must now be sufficient to meet depreciation plus the erosion in the productivity of capital due to less capital per worker as the number of workers increase.

c. Hence, the steady state level of capital per worker falls with more population as population growth widens (as opposed to deepens) the capital stock and in effect ‘depreciates’ the amount of capital available to each worker.

d. Graphically, this causes the depreciation plus population growth function to rotate upwards compared to its value if population is fixed.

e. This lowers steady state output per capita and consumption per capita in populated countries.

7.. What is the impact of technological Progress in the Solow Model?

a. Solow explains technological progress as the residual between the rate of growth in output and the amount explained by the rate of growth in capital and the rate of growth in labor inputs. This is called the “Solow Residual.”

b. The growth in autonomous growth factors, a, is the amount that is not explained by capital and labor inputs, so that (with small letters representing rates of change) If Y/N – A (K/N)b , then

a = (y – n) – b(k – n)

c. Since, k and n face diminishing returns only technological progress (changes in a) can explain persistently rising living standards .

d. Neutral technological change makes labor and capital more efficient, so that the growth factor A grows over time. Education, innovations, and research increase A every year so that GDP per capita increases with a constant output per capital ratio. K/N and Y/N both rise in the steady state at the same rate, supported by statistical evidence in developed economies, such as the U.S.

What insight does the Solow Model give regarding growth, and economic policy?

1. What does the model predict to be the impact of policies to change the rate of savings?

2. What about polices to allocate investment?

3. What about policies that control population growth?

4. What about policies to encourage advances in technology and education?

What are some Puzzles that Solow’s Theory Cannot Explain

1. Long-run economic growth per capita depends primarily on the ‘Solow residual’ (rate of change in A) that is exogenous to the model. We are left with little understanding of the principal determinants of differences in long-term growth rates among countries.

Conflict 1: Income per capital varies too much across countries to be explained by neoclassical theory which depends primarily on savings rate or slope of steady-state investment line. Obviously, all countries do not have the same production function in terms of technology and knowledge.

Conflict 2: Poor countries do not have a higher rate of return on capital. Again, poor countries do not operate on the same production function as rich countries.

Conflict 3: Convergence of income is not occurring among ‘rich’ versus ‘poor’ countries or even within regions in the same country. Convergence occurs among regions in the same ‘club’ but not among regions outside the ‘club’.

Beyond the Solow Model: What are the elements of new (endogenous) growth theory?

1. The basic model: Y/N= A (K/N)b

What determines A?

2. What is the role of human capital with constant or increasing returns. How are ideas tuned into innovations? Adding human capital to capital in the production function substantially increases the value of b to b + c where c is the rate of return on human capital. (An Increase of b + c to 0.9 rather than b only of 0.25 adds to percent growth explained by the production function, while increasing returns allows output to increase more than proportional to inputs.)

3. What determines the production of ideas?: “standing on shoulders” versus “stepping on toes”. Technology relates to innovation in production, including business and organization, development of intellectual property rights, public infrastructure, research and development, market structure to reinforce patents and copyrights, political stability

Chapter 11. The Big Questions of Economic Growth

The Big Questions (revisited):

1. Why is the disparity of income among countries so large when the neoclassical model predicts convergence of income?

2. What creates a growth ‘miracle’ that elevates countries from the ranks of the poor?

Why are we so rich and they so poor?

1. The groupings of countries among the consistently rich (U.S. Britain, etc.), the rapidly growing countries achieving income convergence with the rich (Korea, Taiwan, Hong Kong, and Singapore), and the poor nations that have failed to converge India, Bangladesh, African and Latin American countries).

2. What are the Solow model predictions?

a. Higher income per person due to higher capital per person, achieved through savings and investing.

b. But, the differences between countries’ income per capita is several times larger than differences in both the amounts of capital per person and rates of return on capital investment.

c. Part of the difference can be explained by differences in human capital per worker, but then how can a migrant worker earn so much additional income in a ‘rich’ country with no change in their education?

d. The answer is a shift upward in the production function or higher total factor productivity allowing countries to be much more productive than others in using the capital that they have.

What creates a growth miracle?

1. How have countries been able to catch up to the technological frontier established by rich countries?

2. Solow model predictions:

a. Assume a production function with diminishing returns that allows a higher income (output) per person to be reached by increasing the rate of capital per person through higher rates of savings and investment, including human capital.

b. But, the economy eventually slows to its stationary state without expansion of its technological frontier.

How does the standard of living relate to labor productivity?

1. The Solow Model assumes that ‘output per person’ is the same as labor ‘productivity’ symbolized as y – n, where y is the rate of change in output and n is the rate of change in population.

2. But, if q is the rate of change in work hours and n is the rate of change in population, then it is possible for q > n or q < n to exist and the rate of change in standard of living may not be the same as the rate of change in labor productivity.

3. In Europe, labor productivity has grown faster than their standard of living because hours of work have grown more slowly than population.

4. Europe has longer vacations, a lower labor force participation rate, and a higher average unemployment rate than in the United States.

Growth rate in labor’s share = (w – p) – (y – n)

Why has convergence not occurred?

Recall that the Solow model without technological change predicts convergence of income per person at a steady state based on the country’s production function and savings rate. A poor country differs from a rich country only because it has a lower capital per labor ratio, since there is no difference between the per person production function of rich versus poor nations.

Technology does not alter the conclusions of the Solow model if assumed that it is freely available to all countries. The key empirical prediction is that poorer nations have lower capital per person ratios, but they also have higher subsequent growth rates that eventually converge at the same capital per person and income per person.

The facts show that the prices of labor-intensive services (like haircuts) are much higher in rich countries, but prices of high-tech goods (like computers) tend to be lower in rich countries. If prices were the same, poor countries would improve their relative standing to rich countries, but even if adjusted for prices convergence is not universal. (See fig. 11-3 and Table 11-1 that shows indexes of relative income of countries to U.S. income)

Despite the failure to converge among all countries, among rich countries the negative relationship between initial income per person and subsequent growth in income per person is quite strong. The prediction toward convergence breaks down when poor countries are included.

What are some solutions to the issues of convergence suggested from a study of the Solow Model?

1. The Solow model is unrealistic because it assumes the production function does not shift.

a. Even higher saving rates that speed up the rate of growth toward the stationary state may not explain differences in income per person among countries that have different production functions.

b. Investment in human capital shifts up the production function for a given amount of physical capital. Poor countries cannot afford high levels of investment in physical and human capital.

c. Technological change shifts up the production function for a given amount of physical capital and also requires greater human capital to operate modern equipment and software.

2. At the stationary state the only increase in growth comes from TFP that is gained from innovation higher technology.