3. Derive the equilibrium wage and rental rate, w,, from the firm's prob- lem. The production function has constant returns to scale property in land and labor: F(M, L) = Mall-2. (6 points) 4. Define a competitive equilibrium of this economy and the equations that are related to it. (6 points) 5. Derive a solution for q in the steady state. (6 points) Problem 2 (70 points) Consider the infinite horizon model of a firm facing adjustment costs to investment. The firm pays a corporate income tax, To and it also benefits from an investment tax credit, at the rate s on its investment expenditures. The investment tax credits apply to investment expenditures alone and not to the capital installation costs. Moreover, the installation cost is valued at the output price. The firm managers maximizes its present value of the firm, V. Vi = [ Loltrill - )F (K.) - PK, (1 - s,) 4 - C(InKI)) (1) where F(K, ), is the net output from using the capital stock K,, (F' > 0) and F. 0, and 0