Question 1 Solow-Swan Model (25 pts) Consider the production function F = 2K0.5L0.5. Technology is set at 2 and does not grow. Suppose that the savings rate is 0.2, the depreciation rate, 8, equals 0.05, and population growth, n, is 0.05. a) Show that the production function exhibits constant returns to scale. (2pts) b) Derive the per-worker production function y = f(k) (3pts) c) Solve for the steady-state level of capital per worker. (5pts) d) Solve for the steady-state output per worker. (5pts) e) Solve for the steady-state consumption and investment level. (2pts) 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. (3pts) g) Solve for the savings rate that allows for the golden rule level of capital in the steady state. (5pts)