Suppose the closed economy Catbuktu has the following production function: Y = AKL(1 - ) , where 1 > > 0. a) Derive the marginal product of capital, and country's optimal capital demand curve as a function of (A, L, (R/P)). In your answer submitted show your objective function and some of the steps used to derive your answer. (6 points) b) Suppose in equilibrium that the real rental price of capital is equal to the real interest rate (r). Demonstrate that the capital demand function is a downward sloping function of the real interest rate. (4 points) c) Treat the demand for capital curve as the investment curve in the loanable funds market. Suppose the national saving curve is given by: SNAT = 2r Where r is written in percentage points, so that if r = 5.5 this would be interpreted as 5.5% If total factor productivity is equal to 2, capital's income share is 50%, and there are 16 workers in the economy. Find the long-run equilibrium real interest rate and levels of national saving and investment. (6 points)

d) Suppose the capital stock is currently equal to the long-run equilibrium level demanded as determined in part c above AND that the economy is presently in a steady state. We are also told that capital depreciates at a rate of 10% per year, the population and technology are both constant. Solve for the saving rate, the steady state level of income per worker and consumption per worker. Show some of the steps used to obtain/derive these figures. (6 points) e) Is the economy at its golden rule steady state? Explain why or why not. If not, explain what the agents within this economy would need to do with respect to its saving in order to move to the golden rule steady state. (3 points)