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.

1. a)Show that the production function exhibits constant returns to scale.
2. b)Derive the per-worker production function y = f(k)
3. c)Solve for the steady-state level of capital per worker.
4. d)Solve for the steady-state output per worker.
5. e)Solve for the steady-state consumption and investment level.

Now assume that the savings rate is not fixed.

1. f)Solve for the Golden-Rule level of capital per worker and the associated consumption level.
2. g)Solve for the savings rate that allows for the golden rule level of capital in the steady state.