2. The "Permanent Profitability Hypothesis" Consider a firm which solves the infinite horizon value maximization problem subject to uncertainty given by max{It+s}s=0Ets=0(1+r1)sDt+ss.t.Dt+s=(Kt+s;t+s)It+sKt+s+1=It+s+(1)Kt+s 1 Here, capital prices are normalized to be equal to the constant level PKt=1. The firm's profit function takes the Cobb-Douglas form (Kt+s;t+s)=t+sKt+s for all s0, where 1. The uncertainty that the firm faces involves potential fluctuations in , with log(t+s)=+t+s. Here, >0 is the constant permanent of mean level of log profitability for the firm in all periods, while t+s is a transitory shock to profitability which is independent across periods and normally distributed with t+sN(0,2). (a) Write the optimality condition for investment It. Explain the intuition behind this equation in words. (b) Assume that 0 is the constant permanent of mean level of log profitability for the firm in all periods, while t+s is a transitory shock to profitability which is independent across periods and normally distributed with t+sN(0,2). (a) Write the optimality condition for investment It. Explain the intuition behind this equation in words. (b) Assume that