申論題

4. Consider a two-period economy (/ = 0, 1). The operating profit of firm j can be expressed asis the exogenous profitability shock; A_t is a technology shook at time t; is private capital of fimm j. a ＞ 0 is assumed. The depreciation rate of capital k for firm / is δj. Thus, the investment of firm, firm j has a liquidation value of. The investment in private capital involves adjustment cost . The stochastic discount factor between time 0 and 1 is m, where log(m) = logβ + γ(x0 -x1), where 0 ＜β＜ 1, and γ＞ 0. Firm j then chooses i_j.0 to maximize its value, which is the sum of the discounted cash flows from the two periods: E[.] is an expectation operator. From standard asset pricing equation, -Cov₀(r₁,m). Specifically, the cash flows from t = 0 are equal to the operating profit minus the investment cost and the adjustment cost. The cash flows from ! = I are equal to the operating profit plus the liquidation value.

(2) (10 points) Note that the investment return, defined as the ratio of marginal benefit to marginal cost of investment, is equal to the firm's stock return (r_l) under equilibrium. Please show that