Questions 1-5 are based on the following scenario. Consumers A and 3 [Alice and Bob) both live for two periods, t = 0 and t = 1. There is one physical consumption good. The consumers receive none of this good at 15 : O and at that date they are equally uncertain about the state of the economy att : 1. If it ends up in state 1 (the economyr is in recession). then Q4 2 9, Log 2 15. If it ends up in state 2 (the economy is booming), then WA 2 12 and Lab 2 24. Denote with 351' {and 1:?) the desired consumptions in states i = 1, 2 at date 1 for consumerA [and consumer B.) Neither consumer cares aboutt = 0 consumption.The utilih'es from t = 1consumption are as follows: 1 U31 (mfg) Elncisf1 + hung, 2 1 Us [sci-3.x?) = Elna? +1113? At date 0 the consumers mayr trade contingent claims for date t = 1 consumption. You need to presentthis description as a contingent claim economy and derive the equilibrium in this economy. Denote the price in state 1 bpr and normalize the price in state 2 so that 102 = 1. Question 1 What is consumer's A budget constraint? O picA + xA = 12p1 + 9 O PITA + 4 = 12p1 + 24 O PITA + xA = 9p1 + 15 O PITA + XA = 9p1 + 12\fQuestion 3 2 pts Formulate the optimization problem for consumer A and derive his demands (@A, 4 ) for contingent consumption in states 1 and 2 . These demands should depend on p1 and A's endowment. A's demand functions are: O x4 = 4+4/p1, 24 = 6p1 + 8 Or = 3 + 4/p1, 24 = 8p1 + 6p1 OrA = 3 + 4/p1, 24 = 6p1 + 8 OrA = 3p1 + 4, x4 = 6+ 8/p1Question 4 2 pts Formulate the optimization problem for consumer B and derive his demands (@ , 2 ) for contingent consumption in states 1 and 2 . These demands should depend on p1 and B's endowment. B's demand functions are: Or = 5p1 + 8, 12 = 10p1 + 16p] Or = 5p1 + 8, 12 = 16p1 + 10 Or =5+8/p1, x5 = 10p1 + 16 Or = 8+8/P1, 15 = 10p1 + 16 Question 5 2 pts Impose market clearing conditions and derive the equilibrium price p1 : The equilibrium price p1 is: O P1 = 3/4 O P1 = 1/2 O P1 = 3/2 O P1 = 4/3