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.