Question

Suppose Canada’s aggregate production function is given by the following:
Y = K^1/3 *(AN)^2/3


Variables are defined as they were in class. Suppose the savings rate in Canada is 20% (s = 0.2), the depreciation rate is 5% (δ = 0.05), the population growth rate is 2% (gN = 0.02), and the growth rate of technology is 4% (gA = 0.04).
a) Solve for the equilibrium level of capital per effective worker ( K/AN ) and output per effective worker ( Y/AN ). Solve for the equilibrium growth rates of the following variables: A, N, K, Y , Y N , K N , Y/AN , and K/AN . Use a table to summarize your answers.

b) Suppose the savings rate increases to 25%. Solve for the new equilibrium level of capital per effective worker ( K/AN ) and output per effective worker ( Y/AN ). Solve for the new equilibrium growth rates of the following variables: A, N, K, Y , Y N , K N , Y/AN , and K/AN . Use a table to summarize your answers.

c) In this model does an increase in the savings rate lead to sustained long-run growth? Explain.

Answer 1

c)

an increase in the savings rate increases output and capital per effective worker. However, in the long run, a higher savings rate does not have any impact on the steady-state growth rates. Hence, it does not lead to sustained long-run growth.