Suppose the production function is Y =10(K)^1/4 (EL)^3/4 and the capital lasts an average of 10 years. Assume that the rate of growth of population is 4 percent and the rate of technological growth is 2 percent.
a) Derive the equation for the output per effective worker y = Y / EL = f (k) , where k equals the amount of capital per effective worker.
b) What is the marginal product of capital (MPK)?
c) find out the Golden Rule level of capital per effective worker and the saving rate associate with this steady state.
d) find out all of the following at their Golden Rule levels: Output per effective worker, saving and investment per effective worker, and the consumption per effective worker.