Question

Suppose that output (Y ) in an economy is given by the following aggregate production function:...

Suppose that output (Y ) in an economy is given by the following aggregate production function: Yt = Kt + Nt

where Kt is capital and Nt is the population. Furthermore, assume that capital depreciates at rate δ and that savings is a constant proportion s of income. You may assume that δ > s.

  1. Suppose that the population remains constant. Solve for the steady-state level of capital per worker.

  2. Now suppose that the population grows at rate n. Solve for the steady-state level of capital per worker.

  3. Based on your answer to part 2) above, solve for the steady-state growth rates (in terms of n) of the following:

(a) capital per worker

(b) output per worker

(c) capital

(d) output

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