Consider a firm with the following production function Y = (1 )k where Y denotes output, k measures capital and 0 < < 1 is corporate taxes. Also, 0 < < 1.

(a) Show that the marginal productivity of capital (MPK) is decreasing in the amount of capital the firm has. Show graphically the MPK. Show graphically what happens to the MPK if corporate taxes are lowered.

(b) Suppose now the interest rate is 1 + r and the rate of capital depreciation is . Suppose further the price of capital is fixed at 1. Describe the equilibrium condition that determines the firms choice of capital.

(c) Suppose = 0.3, = 0.1, = 0.3 and r = 0.02. Calculate the amount of capital held by the firm.

(d) Suppose now that corporate taxes are lowered to 0.2. Calculate the impact of capital. What would be the increase in firms investment (use the capital accumulation equation). Show graphically what how the equilibrium changes in response to a lower corporate tax rate.