Question

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

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.

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.

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