Assume that a firm has future marginal productivity of capital given by MPK = A(100-K). The price of capital (machine) is $20,000, the real interest rate is 10%, and capital depreciates at a 10% rate. Assume further that each unit of output sells for $50.

A) Calculate the user cost of the capital (in real term) that the firm faces.

B) Assume A=1, then calculate the desired capital stock. What is the firm’s gross investment if the firm currently has 10 machines? (Assume the machines depreciate at the same rate as the usual rate above.)

C) If the TFP increases to 2, i.e. A=2, then what is the gross investment (still assume the firm currently has 10 machines)?