In the economy of Phobos, there is a representative household with utility descr
ID: 1218106 • Letter: I
Question
In the economy of Phobos, there is a representative household with utility described by the following function: U = log(ct) + log(ct+1) + 2log(ct+2) + . . . Assume = 0.7
The houshold owns all the capital and supplies both labor and capital to the firm. The firm rents capital at rate rt and pays a wage of wt each period. The firm has the following production function: Yt = A¯ kt L 1 t Assume A¯ = 1 and = 1/3. Since the household does not receive utility from leisure, assume Lt = L¯ = 1. Capital depreciates every period at rate ¯d = 0.05. The household saves by investing in capital, It . Kt+1 = Kt ¯dKt + It
a. What fraction of output do the people of Phobos invest every period in steady state? Hint:This is It/ Yt and is the same as s is the Solow model.
b. The economy of Deimos is identical to Phobos, but people are more patient with = 0.95 What is the marginal product of steady state capital in Deimos?
c. What is the fraction of output that the people of Deimos save every period?
d. Which economy has higher GDP per capita, Phobos or Deimos?
Explanation / Answer
a. It is It/Yt
b. Marginal prodict will be higher in Deimos
c. 5%
d. Phobos will have higher GDP per capita as people are investing more in this country