Question

Consider a pair of investors A and B who only care about one good - wealth at date t = 1. They both know that at date t = 1 the economy will be either in state 1 or in state 2. They both agree that state 1 is twice as likely as state 2. In state 1 A will have the wealth endowment of 3 and B will have the wealth endowment of 9. In state 2 A will have the wealth endowment of 6 and B will have the wealth endowment of 16. Neither investor has any wealth at date 0. At date 0 both investors have access to the financial markets with the following payoff matrix states egin{bmatrix} 1 & 3 \ 3 & 2 end{bmatrix} assets The prices of the assets are not specified at the moment, but assume that they are such that there is no arbitrage. Investor A is risk-averse, and values wealth y according to v^A(y) = 2sqrt{y}, investor B is risk-neutral and values wealth y according to v^B(y) = y. d. (3 marks) State the Mutuality Principle. According to that Principle how should be wealth allocated in this economy across the investors and across the states? e. (2 marks) Set alpha_1 = 1. By Mutuality Principle what price alpha_2 should result in equilibrium? Your answer, should, of course, respect the budget constraints and the preferences of the investors. Hint: you should already know the equilibrium allocation of wealth from d. You have to find the price alpha_2 such that that allocation is the result of the investors' optimization. You can choose which investor to deal with, since they face the same prices (alpha_1, alpha_2). f. (3 marks) Derive the equilibrium prices for the original assets (q_1, q_2) consistent with your answer in e.

          Consider a pair of investors A and B who only care about one good - wealth at date t = 1. They both know that at date t = 1 the economy will be either in state 1 or in state 2. They both agree that state 1 is twice as likely as state 2. In state 1 A will have the wealth endowment of 3 and B will have the wealth endowment of 9. In state 2 A will have the wealth endowment of 6 and B will have the wealth endowment of 16. Neither investor has any wealth at date 0. At date 0 both investors have access to the financial markets with the following payoff matrix states egin{bmatrix} 1 & 3 \ 3 & 2 end{bmatrix} assets The prices of the assets are not specified at the moment, but assume that they are such that there is no arbitrage. Investor A is risk-averse, and values wealth y according to v^A(y) = 2sqrt{y}, investor B is risk-neutral and values wealth y according to v^B(y) = y. d. (3 marks) State the Mutuality Principle. According to that Principle how should be wealth allocated in this economy across the investors and across the states? e. (2 marks) Set alpha_1 = 1. By Mutuality Principle what price alpha_2 should result in equilibrium? Your answer, should, of course, respect the budget constraints and the preferences of the investors. Hint: you should already know the equilibrium allocation of wealth from d. You have to find the price alpha_2 such that that allocation is the result of the investors' optimization. You can choose which investor to deal with, since they face the same prices (alpha_1, alpha_2). f. (3 marks) Derive the equilibrium prices for the original assets (q_1, q_2) consistent with your answer in e.

Consider a pair of investors A and B who only care about one good - wealth at date t = 1. They both know that at date t = 1 the economy will be either in state 1 or in state 2. They both agree that state 1 is twice as likely as state 2. In state 1 A will have the wealth endowment of 3 and B will have the wealth endowment of 9. In state 2 A will have the wealth endowment of 6 and B will have the wealth endowment of 16. Neither investor has any wealth at date 0. At date 0 both investors have access to the financial markets with the following payoff matrix states eginbmatrix 1 3 3 2 endbmatrix assets The prices of the assets are not specified at the moment, but assume that they are such that there is no arbitrage. Investor A is risk-averse, and values wealth y according to v^A(y) = 2sqrty, investor B is risk-neutral and values wealth y according to v^B(y) = y. d. (3 marks) State the Mutuality Principle. According to that Principle how should be wealth allocated in this economy across the investors and across the states? e. (2 marks) Set alpha1 = 1. By Mutuality Principle what price alpha2 should result in equilibrium? Your answer, should, of course, respect the budget constraints and the preferences of the investors. Hint: you should already know the equilibrium allocation of wealth from d. You have to find the price alpha2 such that that allocation is the result of the investors' optimization. You can choose which investor to deal with, since they face the same prices (alpha1, alpha2). f. (3 marks) Derive the equilibrium prices for the original assets (q1, q2) consistent with your answer in e.

Added by Eric W.

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