Question

1. • Country A and country B both
have the production function
Y 5 F(K, L) 5 K1/3L2/3.
a. Does this production function have constant
returns to scale? Explain.
b. What is the per-worker production function,
y 5 f (k)?
c. Assume that neither country experiences
population growth or technological progress
and that 20 percent of capital depreciates each
year. Assume further that country A saves
10 percent of output each year and country
B saves 30 percent of output each year. Using
your answer from part (b) and the steady-state
condition that investment equals depreciation,
find the steady-state level of capital per worker
for each country. Then find the steady-state
levels of income per worker and consumption
per worker.
d. Suppose that both countries start off with a
capital stock per worker of 1. What are the
levels of income per worker and consumption
per worker?
e. Remembering that the change in the capital
stock is investment less depreciation, use a
calculator (or, better yet, a computer spreadsheet)
to 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?

Answer 1