3. The \"Permanent Profitability Hypothesis\" Consider a firm which solves the infinite horizon value maximization problem subject to uncertainty given by 'X' r: 1 , Ih' IE D N. nits. Elm) \" 5:0 57L DH\" : U(Kr+.~: 0f+,) 7 Ir+.~ 1\\'f+s+t : [Ii-Fa + (l 6)I\\',r+h. Here. capital prices are normalized to be equal to the constant level PM = l. The firm's profit function takes the Cobb-Douglas form II(fr'r+,,:fi,_,,) : ri,+,,1r','-,, for all s 2 ll. where q 5 1. The uncertainty that the firm laces involves potential fluctuations in f}, with log-(9H,) = r) + 5H,. Here. .9 > ii is the constant permanent of mean level of log profitability for the firm in all periods. while m, is a transitory shock to profitability which is independent across periods and normally distributed with a, ,._, ~ NU}, ail. 2 (a) Write the optimality condition for investment 1,. Explain the intuition behind this equa- tion in words. (b) Assume that q f). Dividends DH, can now be written as DH, : r1(rc,+,; 9H,) , I\