6. Consider an economy with two consumers, a and b. There are two periods, today and tomorrow, and two possible states of nature tomorrow. Today there is one commodity, time (labor/ leisure), denoted 4?. Each consumer is endowed with one unit of E today, and nothing tomorrow. Tomorrow there is a single consumption good (food) in each state. Each consumer's utility function has the form Ui(,,x,a,2) = %lnx,1 + ln 32,2 where E, denotes i's consumption of leisure today, and 231-3 denotes i's consumption of food tomorrow if state 3 occurs, for s = 1, 2. There are three rms. Consumer a owns rm 1, while consumer b owns rms 2 and 3. The production sets of the rms Y1 = {PM/1,312) = 3/1 S 313,92 S 0, where I? 2 0} are: Y2 = {(,y1,y2) : yl g 0,y2 3 39, where E Z 0} where 1? denotes the amount of labor input Y3 = {(-5791792) 2 3/1 S 5,112 S E. where E Z 0} used today, and ys denotes the amount of food produced tomorrow if state 3 occurs, for s = 1, 2. In particular, notice that rm 1 produces only in state 1, while rm 2 produces only in state 2. Normalize the price of labor / leisure to be 1. (a) Find the competitive equilibria in this economy. (b) Suppose rm 3's production set is instead 173 = {(,y1,y2) : yl g 313,112 g 31?, where E 2 0}. How does the answer to (a) change