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