Question

Consider the Solow model with the standard Cobb-Douglas production function y = ka, where y = Y/eL is output per effective worker and k = K/eL is capital per effective worker. Assume that the number of effective workers per actual worker, e, grows at rate ê and the number of actual workers, L, grows at rate n. Show how each of the following events will affect this economy. Illustrate your answer using a steady-state diagram and time plots for e, y, Y/L, and Y.

a. The rate of productivity growth (ê) decreases
b. The depreciation rate (δ) increases.
c. The saving rate (γ) increases.
d. A war destroys half the capital stock (K) in a country.
e. The rate of labor force growth (n) declines.
f. There is a one-time jump in the labor force (L), but the labor force growth rate (n) is unchanged.

Answer 1

In the Solow model, different events affect the economy in various ways. Decreased productivity growth and increased depreciation rate lead to decreases in output per effective worker.

Increased saving rate and a one-time jump in the labor force lead to increases in output per effective worker.

Step-by-step explanation:

In the Solow model with the Cobb-Douglas production function y = ka, there are several events that can affect the economy.

1. When the rate of productivity growth (ê) decreases, it means that the economy is becoming less efficient in using its resources.
2. This leads to a decrease in output per effective worker (y) and a decrease in total output (Y). The steady-state diagram and time plots will show a downward shift in the y, Y/L, and Y.a curves.
3. When the depreciation rate (δ) increases, it means that the capital stock (K) is being depleted at a faster rate. This leads to a decrease in capital per effective worker (k) and a decrease in output per effective worker (y).
4. The steady-state diagram and time plots will show a downward shift in the y curve.
5. When the saving rate (γ) increases, it means that a larger proportion of income is being saved and invested. This leads to an increase in capital per effective worker (k) and an increase in output per effective worker (y). The steady-state diagram and time plots will show an upward shift in the y curve.
6. When a war destroys half the capital stock (K), it means that the economy loses a significant portion of its productive capacity.
7. This leads to a decrease in capital per effective worker (k) and a decrease in output per effective worker (y). The steady-state diagram and time plots will show a downward shift in the y curve.
8. When the rate of labor force growth (n) declines, it means that the number of actual workers (L) is growing at a slower rate.
9. This leads to a decrease in output per effective worker (y) and a decrease in total output (Y). The steady-state diagram and time plots will show a downward shift in the y, Y/L, and Y.a curves.
10. When there is a one-time jump in the labor force (L), but the labor force growth rate (n) is unchanged, it means that there is a sudden increase in the number of actual workers.
11. This leads to an increase in output per effective worker (y) and an increase in total output (Y). The steady-state diagram and time plots will show an upward shift in the y, Y/L, and Y.a curves.