10' L1+e ((31 3 1+E ) Clor U = s 2 10' 10 where c1and agate consumption of the production good in each period and L is the household's labor supply in period 1. The budget constraints in both periods are: c1+K=3L+Hl, P1 ma; 2 TKK-I- K. Here, H1 stand for the prots of monopolistic behaving rms. Here households invest in capital K only to invest in it and rent it out later. Production in each period is produced by rms operating the following technologies: Y1 = L, Y2 = Kl-s. Different from model's we've seen before, now the household invests directly in capital, and then rents it to rms at time t = 2. (a) [5 points, easy] Demonstrate that the labor supply is given by 3 = BLE. P1 (b) [5 points, easy] Show that the households optimal investment in K is given by (the Euler equation): 1+6 _r (Cl _ 915+ 5) Z 18 (1 + TK) (C2)\"- (c) [2 points, easy] Show that if rms at t = 2 behave competitively, the maximization of their prots leads to the following equilibrium return on capital: rK = (1 a)K-s >K= [rKMTXQ. (d) [3 points, easy] Assume that rms ideally want to charge a markup relative to marginal costs given by: markup where the nominal marginal cost is simply the wage: quw