1. Investment Demand and Current Capital Stock (25 pts) Suppose that the rm has the following production function F( Kt, Nt) = At Kt^ * Nt^ Recall that our rm's optimality condition with respect to capital is the following: MPKt+1+ (1) = (1 + r)

(a) First derive the desired amount of capital stock next period, as a function of, labor, TFP, depreciation and the real interest rate r

(b) Now recall the law of motion of the capital stock is given as Kt+1 = (1)Kt+It Utilize it to derive Investment Demand as a function of today's capital stock, labor, TFP, depreciation and the real interest rate.

(c) Now suppose that a natural disaster hits the country such that the present capital stock is halved but nothing else changes. How is desired capital stock next period impacted? How is investment demand impacted? If there's a difference explain why. (d) Now suppose that we have our goods market as detailed in class. Suppose that Savings Demand is a standard upward sloping curve. Draw and explain what happens to investment demand after the naturaldisaster. What happens to the equilibrium interest rate and the equilbrium level of investment.

(e) In general, given an upward sloping savings demand function, will capital next period in equilibrium be more, less or the same as it would have been without the natural disaster