Intermediate Macroeconomics Sample Problems
3. Long-Run Economic Growth
1. Given the neoclassical growth model production function Y = A f ( K, L) and assuming constant returns to scale, the contribution of the growth rate of capital to the growth rate of total output can be estimated by:
a. dividing the growth rate of capital by the elasticity of output with respect to capital.
b. multiplying the growth rate of capital by the elasticity of output with respect to capital.
c. subtracting the growth rate of labor from the growth rate of total output.
d. multiplying the capital-labor ratio by the level of output.
2. Given the neoclassical growth model production function Y = A f ( K, L) and assuming constant returns to scale, the elasticity of output with respect to labor is 0.7, and the elasticity of output with respect to capital is 0.3. If there is no technological change, capital grows at 1.5% per year, and labor doesn't grow at all, what is the growth rate of total output?
Answer: A. The growth rate of total output = rate of technological change (= 0) plus the elasticity of output with respect to labor (= 0.7) times the growth rate of labor (= 0) plus the elasticity of output with respect to capital (= 0.3) times the growth rate of capital (= 1.5). Thus, the growth rate of output = 0 + (0.7 0) + (0.3 1.5) = 0.45 % per year.
3. Which of the following would be a source of increase total factor productivity?
a. technological progress
b. an increase in the average level of education
c. an increase in the capital stock
d. improved resource allocation
e. growth in the labor force
f. an increase in on-the-job training
Answer: A, B, D, and F. Multifactor productivity represents the increase in output that is not explained by increases in the quantities of labor and capital. In other words, an increase in multifactor productivity represents the increase in the quality of labor such as from better education (B) or on-the-job training (F) or increase in the quality of capital such as from technological progress (A). Productivity can also improve when the existing quantities of labor and capital are used more efficiently (D) such as might happen when governments eliminate trade barriers and protections or subsidies for inefficient industries.
1. In the neoclassical growth model, when current saving and investment are just enough to replace depreciated capital and equip new entrants into the labor force with the same amount of capital that the average person already in the work force uses, then
a. the economy is in a steady state.
b. output per worker is constant.
c. capital per worker is constant.
d. capital is growing at the same rate as the employed labor force.
e. all of the above.
Answer: E. This question can easily be modified to give only one correct answer.
2. In the neoclassical growth model, an increase in the population growth rate with an unchanged savings rate will
a. raise the growth rate of total output.
b. improve the standard of living.
c. increase the level of output per worker.
d. increase the steady-state capital-labor ratio.
e. the savings rate will increase because there are more people.
Answer: A. The growth rate of total (aggregate) output in steady state is equal to the population growth rate regardless of the savings rate or capital-labor ratio. Answers B and C would be correct if they were in the opposite direction (where the standard of living may be measured as output per worker). Although the growth rate of total output would increase with the higher population growth rate, the standard of living and output per worker would actually decline with a constant savings rate. The capital-labor ratio would be lower because a given amount of savings must be spread around a greater number of new entrants to the labor force.
A similar question would ask what happens when there is a change in the savings rate. An increase in the savings rate would increase the standard of living and output per worker because of an increase in the capital-labor ratio. The growth rate of total would temporarily increase as the economy moves from one steady state to a new steady state at the higher savings rate. Once at the new steady state the growth rate of aggregate output would return to the population growth rate.
To add a twist the question could ask what happens if the capital-labor ratio were above or below the steady state level, which implies the capital-labor ratio would change in the direction of the steady state. A capital-labor ratio below the steady state level implies that total savings exceeds investment. Investment and the capital-labor ratio would increase to the level of total savings.
1. According to the endogenous growth theory
a. the steady-state growth rate is affected only by the population growth rate.
b. the steady-state growth rate decreases as the savings rate increases.
c. the long-term growth rate of capital is not affected by the savings rate.
d. the steady-state growth rate is affected by the savings rate.
e. none of the above
Answer: D. Answers A and C are characteristic of the simple neoclassical growth model. The key difference between the neoclassical and endogenous growth models is the relationship between steady state rate of economic growth and the savings rate. In the neoclassical model the steady state growth rate of output is unaffected by the savings rate. A country with a higher savings rate will be wealthier but the growth rates of the economies will be the same. The population growth rate is the only factor that determines differences in economic growth rates between countries (this assumes the benefit of technological change is available to all countries).
The savings rate becomes an important variable in the endogenous growth model because the increase in labor productivity may be greater the higher the savings rate. High savings rates may lead to better education, more job training, and increased research and development, which contributes to higher rates of technological change. Answer B is the opposite of what we would expect.
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