Questions 1-5 are based on the following scenario. Consumers A and B (Alice and Bob) both...

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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 = 9, WB = 15. If it ends up in state 2 (the economy is booming), then WA = 12 and wB = 24. Denote with x (and x) 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 = 1consumption are as follows: UA (a, a2) = U (x, x) = 1 2 1 2 n x4 + Inz, n x + ln 2. 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 p and ormalize the price in state 2 so that P2 = 1. Question 1 What is consumer's A budget constraint? Px + x = 12p + 24 O Px + xA = 12p +9 Px + x =9p + 12 Px + x = 9p +15 Question 2 What is consumer's B budget constraint? Px + x = 24p +15 Px + x = 15p +24 O px + x = 15p + 12 px + x = 9p1 + 12 1 pts 1 pts Question 3 Formulate the optimization problem for consumer A and derive his demands (x,x) for contingent consumption in states 1 and 2. These demands should depend on p and A's endowment. A's demand functions are: x = 3p + 4, x = 6 +8/p x = 4+4/P, x 6p +8 O x = 3 +4/p, x2 = 8p1 + 6p1 O x = 3 + 4/p, x = 6p +8 Question 4 = 2 pts O x = 5p1 + 8, x2 = 10p + 16p x = 5 +8/p, x = 10p + 16 x = 5p + 8, x2 = 16p + 10 x = 8+8/p, x = 10p + 16 2 pts Formulate the optimization problem for consumer B and derive his demands (x,x) for contingent consumption in states 1 and 2. These demands should depend on p and B's endowment. B's demand functions are: Question 5 Impose market clearing conditions and derive the equilibrium price p: The equilibrium price p is: O P = 4/3 O P = 3/2 O P = 1/2 O P = 3/4 2 pts 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 = 9, WB = 15. If it ends up in state 2 (the economy is booming), then WA = 12 and wB = 24. Denote with x (and x) 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 = 1consumption are as follows: UA (a, a2) = U (x, x) = 1 2 1 2 n x4 + Inz, n x + ln 2. 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 p and ormalize the price in state 2 so that P2 = 1. Question 1 What is consumer's A budget constraint? Px + x = 12p + 24 O Px + xA = 12p +9 Px + x =9p + 12 Px + x = 9p +15 Question 2 What is consumer's B budget constraint? Px + x = 24p +15 Px + x = 15p +24 O px + x = 15p + 12 px + x = 9p1 + 12 1 pts 1 pts Question 3 Formulate the optimization problem for consumer A and derive his demands (x,x) for contingent consumption in states 1 and 2. These demands should depend on p and A's endowment. A's demand functions are: x = 3p + 4, x = 6 +8/p x = 4+4/P, x 6p +8 O x = 3 +4/p, x2 = 8p1 + 6p1 O x = 3 + 4/p, x = 6p +8 Question 4 = 2 pts O x = 5p1 + 8, x2 = 10p + 16p x = 5 +8/p, x = 10p + 16 x = 5p + 8, x2 = 16p + 10 x = 8+8/p, x = 10p + 16 2 pts Formulate the optimization problem for consumer B and derive his demands (x,x) for contingent consumption in states 1 and 2. These demands should depend on p and B's endowment. B's demand functions are: Question 5 Impose market clearing conditions and derive the equilibrium price p: The equilibrium price p is: O P = 4/3 O P = 3/2 O P = 1/2 O P = 3/4 2 pts

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Based on the scenario described lets solve each question step by step Question 1 What is consumer As budget constraint Consumer A Alice can spend her endowment on consumption in both states Her endowm... View the full answer