Suppose that the production function is Y = zK^1/2N^1/2 and that 7% of capital wears out every year. Assume that the rate of growth of the population is 3% and the saving rate is 15%. The productivity level is z = 2.

(d) What is the steady-state growth rate of the capital per worker, kss, and the steady-state growth rate of the output per worker, yss? \

(e) What is the steady-state growth rate of the capital stock, Kss, and the steady-state growth rate of the aggregate output, Yss? Show your work.

(f ) The government is benevolent (cares about the consumers) and wants to maximize the steady state consumption per worker. Write down the maximization problem that the golden rule capital per worker, k*gr, solves. Find k*gr.

(g) What is the savings rate associated with the golden rule level of capital, s*gr? Can the country increase the consumption per-capita by changing the saving rate?

(h) Now assume that there is no population growth, i.e. n = 0, and that the saving rate is given by some other value called s . Suppose that this economy is in a steady state where the marginal product of capital is less than the depreciation rate. By changing the saving rate is it possible to increase the steady state consumption per-capita? Explain how would you change the saving rate.