1. Assume that production is a function of capital and labor, and that the rate of savings and depreciation are constant, as described in Chapter 8's version of the Solow Model. Further, assume that the production function can be described by the function: = ! " ! # where K is capital and L is labor. a. What is the per-worker production function y=f(k)? Show your work. (3 points) b. Solve for steady-state capital per worker, production per worker, and consumption per worker with s = 0.4, =0.1? (Note: you need to set k = 0, to get an equation in s, , and k, and then solve for k). (7 points) c. Assume initial value of k is 27, s = 0.4, =0.1 (12 points) Year k y c i k k 1 2 d. With population growth which is 5% per year. Calculate Golden Rule steady state. (3 points) e. In order to achieve the Golden Rule steady state, what happened to s? (2 points) f. What is the steady-state growth rate of (i) capital per worker (ii) output per worker (iii) total output? (6 points