(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.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
a,b,c and d please
![(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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b2e65f2-c472-45bf-885c-00dffce84016%2F73d13be1-15e2-417f-8c20-cac4f1ce9745%2Ftra06gw_processed.png&w=3840&q=75)
Transcribed Image Text:(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?
Transcribed Image Text: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.
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