Questions 1-5 are based on the following scenario. Consumers A and B (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 t = 0 and at that date they are equally uncertain about the state of the economy at t = 1. If it ends up in state 1 (the economy is in recession), then WA = 6, Wg = 18. If it ends up in state 2 (the economy is booming), then WA = 18 and WB = 30. Denote with a (and a?) the desired consumptions in states i = 1, 2 at date 1 for consumer A (and consumer B.) Neither consumer cares about t = 0 consumption. The utilities from t = 1 consumption are as follows: UA (24, 24) = -In24 + In24, UB (x], x2 ) = -Inap + Ina?. At date 0 the consumers may trade contingent claims for date t = 1 consumption. You need to present this description as a contingent claim economy and derive the equilibrium in this economy. Denote the price in state 1 by p1 and normalize the price in state 2 so that p2 = 1. Question 1 1 pts What is consumer A's budget constraint? Opici +xa = 6+18p1 O piaf + x4 = 18p1 + 6p1 O pixi + x2 = 18p1 + 30 O pixi + x2 = 6p1 + 18 Question 2 1 pts What is consumer B's budget constraint? O PIXP + x2 = 30p1 + 18 O PIXP + x2 = 18p1 + 30 O PixB + x = 18p1 + 18 O PIXP + x = 6p1 + 18p1 Question 3 2 pts Formulate the optimization problem for consumer A and derive his demands (21 , a2 ) for contingent consumption in states 1 and 2 . These demands should depend on p1 and A's endowment. A's demand functions are: O x1 = 2+6/P1, 24 = 4p1 + 12 O x1 = 2p1 + 6/P1, 24 = 12p1 + 4 O x4 = 2p1 + 6, x4 = 4 +12/p1 O x4 = 2p1 + 6, 24 = 4p1 + 12p1 Question 4 2 pts Formulate the optimization problem for consumer B and derive his demands (x] , a? ) for contingent consumption in states 1 and 2 . These demands should depend on p1 and B's endowment. B's demand functions are: O x = 6 +10/P1, a = 12p1 + 20 O XP = 6p1 + 10, 25 = 12p1 + 20 O XP = 6p1 + 10, x2 = 12p1 + 20p1 O xP = 6+6/P1, 25 = 20p1 + 12 Question 5 2 pts Impose market clearing conditions and derive the equilibrium price p1. The equilibrium price P1 is: O P1 = 1 O P1 = 1/3 O P1 = 3/2 O P1 = 1/2