Suppose two countries, A and B, with the same production function Y = KαL 1−α . The value of α is 0.30, the growth rate of population is 2% and the depreciation rate is 5%. a) Show that with price-taking firms the share of labor must be 1 − α. b) Compute the stock of capital, output and consumption per unit of labor in the steady state if the savings rates were 25% for country A and 35% for country B. c) Compare both economies to the Golden Rule. d) Explain what would happen to both countries if suddenly their savings rate became the Golden Rule savings rate.
Suppose two countries, A and B, with the same production function Y = KαL 1−α . The value of α is 0.30, the growth rate of population is 2% and the depreciation rate is 5%. a) Show that with price-taking firms the share of labor must be 1 − α. b) Compute the stock of capital, output and consumption per unit of labor in the steady state if the savings rates were 25% for country A and 35% for country B. c) Compare both economies to the Golden Rule. d) Explain what would happen to both countries if suddenly their savings rate became the Golden Rule savings rate.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Exercise 4: Growth and capital over-accumulation
Suppose two countries, A and B, with the same production function Y = KαL
1−α
. The
value of α is 0.30, the growth rate of population is 2% and the depreciation rate is 5%.
a) Show that with price-taking firms the share of labor must be 1 − α.
b) Compute the stock of capital, output and consumption per unit of labor in the steady
state if the savings rates were 25% for country A and 35% for country B.
c) Compare both economies to the Golden Rule.
d) Explain what would happen to both countries if suddenly their savings rate became
the Golden Rule savings rate.
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