Consider the production function F = K^0.5L^0.5 (technology is normalized at 1). Suppose that the savings rate
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Question:
Consider the production function F = K^0.5L^0.5 (technology is normalized at 1). Suppose that the savings rate is 0.4, the depreciation rate, , equals 0.05, and population growth, n, is 0.05.
- a)Show that the production function exhibits constant returns to scale.
- b)Derive the per-worker production function y = f(k)
- c)Solve for the steady-state level of capital per worker.
- d)Solve for the steady-state output per worker.
- e)Solve for the steady-state consumption and investment level.
Now assume that the savings rate is not fixed.
- f)Solve for the Golden-Rule level of capital per worker and the associated consumption level.
- g)Solve for the savings rate that allows for the golden rule level of capital in the steady state.
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