(a) What is the stochastic discount factor m++1? (hint: Recall m++1 = SU' (c+1)) U'(a) (b) What are the prices q and q² of complex securities s¹ and s² at t = 0? (hint: Recall that q = Et[mt+1X++1] and that the security payoff X++1 finances consumption.) (c) What weights create Arrow-Debreu securities? (hint: What are the weights of the complex securities that create payoffs (1,0)' and (0, 1)'?) (d) What are the state prices q₁ and 92? (hint: State prices are a function of prices from part b) and the weights from part c).) (e) What is the price of a risk free bond qb? (f) What are the risk neutral probabilities RN and TRN? (g) Using the risk neutral probabilities solve for q¹ and q². (hint: These are equal to the same values in part b).) RN (h) Is greater than or less than the true probability ₁? Why? There is one period. Assume a representative agent with utility function U(ct) = act - Be². In parts b) through h) assume the following: a =100, 31, and 8 = 0.97. Consumption at t = 0 is Co = 24. ⚫ At t = 1 one of two states 01 and 02 eventuate with probability ₁ = respectively. There are two complex securities s¹ and s². .5, and T2 = .5, s¹ has a payoff of 23 in 1 and 27 in 02. s² has a payoff of 20 in 01 and 32 in 02.

(a) What is the stochastic discount factor m++1? (hint: Recall m++1 = SU' (c+1)) U'(a) (b) What are the prices q and q² of complex securities s¹ and s² at t = 0? (hint: Recall that q = Et[mt+1X++1] and that the security payoff X++1 finances consumption.) (c) What weights create Arrow-Debreu securities? (hint: What are the weights of the complex securities that create payoffs (1,0)' and (0, 1)'?) (d) What are the state prices q₁ and 92? (hint: State prices are a function of prices from part b) and the weights from part c).) (e) What is the price of a risk free bond qb? (f) What are the risk neutral probabilities RN and TRN? (g) Using the risk neutral probabilities solve for q¹ and q². (hint: These are equal to the same values in part b).) RN (h) Is greater than or less than the true probability ₁? Why? There is one period. Assume a representative agent with utility function U(ct) = act - Be². In parts b) through h) assume the following: a =100, 31, and 8 = 0.97. Consumption at t = 0 is Co = 24. ⚫ At t = 1 one of two states 01 and 02 eventuate with probability ₁ = respectively. There are two complex securities s¹ and s². .5, and T2 = .5, s¹ has a payoff of 23 in 1 and 27 in 02. s² has a payoff of 20 in 01 and 32 in 02.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.1P

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