econ

Homework #3

Intermediate Macroeconomics

Question 1 (Taken from Mankiw, Chapter 8, Problem #1)

Country A and country B both have the production function

Y = F(K;L) = p K p L:

(i) Does the production function have constant returns to scale? Explain.

(ii) What is the per-worker production function, y = f(k)?

(iii) Assume that 5 percent of capital depreciates each year. Assume further

that country A saves 10 percent of output each year and country B saves 20

percent of output each year. Find the steady-state level of capital per worker

for each country. Then �nd the steady-state levels of income per worker and

consumption per worker.

(iv) Suppose that both countries start o¤with a capital stock per worker of

2. Show how the capital stock per worker will evolve over time in both countries.

For each year, calculate income per worker and consumption per worker. How

many years will it be before the consumption in country B is higher than the

consumption in country A?

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Questions from your textbook

1. Exercise #2, chapter 5: Technology transfer in the Solow model

2. Exercise #4, chapter 5: An increase in the labor force

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