Question B.1 (Word Limit: 500 words) For this exercise t=1+the fourth digit of your student number. Consider a good consumed in two possible states of nature S = {a,b}. There are two types of contracts, each delivering one unit of the commodity in one state a or b, which can be traded in corresponding markets at prices p(a) and p(b). (i) Consider a consumer h with preferences and endowment • Un (xh(a), xh (b)) = 2log ₂ (a) + 3 log xn (b), (en(a), en (b)) = (3, 4 × t) who wishes to trade in contingent markets. Setup the optimization problem of this consumer and compute the optimal consumption plan as a function of the prices of the contingent contracts. (ii) Consider another consumer k with preferences and endowment • Uk (xk(a), xk (b)) = 3 log x₁(a) + 2log x₁(b), (ek(a), ek(b)) = (2, 4 × t) who also wishes to trade in contingent markets. Setup the optimization problem of this consumer and compute the optimal consumption plan as a function of the prices of contingent contracts. (iii) Consider another consumer m with preferences and endowment • Um (xm(a), xm(b)) = xm(a) + log xm(b), (em(a), em(b)) = (0, 2 × t) who also wishes to trade in contingent markets. Setup the optimization problem of this consumer and compute the optimal consumption plan as a function of the prices of the contingent contracts.
Question B.1 (Word Limit: 500 words) For this exercise t=1+the fourth digit of your student number. Consider a good consumed in two possible states of nature S = {a,b}. There are two types of contracts, each delivering one unit of the commodity in one state a or b, which can be traded in corresponding markets at prices p(a) and p(b). (i) Consider a consumer h with preferences and endowment • Un (xh(a), xh (b)) = 2log ₂ (a) + 3 log xn (b), (en(a), en (b)) = (3, 4 × t) who wishes to trade in contingent markets. Setup the optimization problem of this consumer and compute the optimal consumption plan as a function of the prices of the contingent contracts. (ii) Consider another consumer k with preferences and endowment • Uk (xk(a), xk (b)) = 3 log x₁(a) + 2log x₁(b), (ek(a), ek(b)) = (2, 4 × t) who also wishes to trade in contingent markets. Setup the optimization problem of this consumer and compute the optimal consumption plan as a function of the prices of contingent contracts. (iii) Consider another consumer m with preferences and endowment • Um (xm(a), xm(b)) = xm(a) + log xm(b), (em(a), em(b)) = (0, 2 × t) who also wishes to trade in contingent markets. Setup the optimization problem of this consumer and compute the optimal consumption plan as a function of the prices of the contingent contracts.
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.11P
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Transcribed Image Text:Question B.1 (Word Limit: 500 words) For this exercise t=1+the fourth
digit of your student number. Consider a good consumed in two possible states
of nature S= {a, b}. There are two types of contracts, each delivering one unit of
the commodity in one state a or b, which can be traded in corresponding markets at
prices p(a) and p(b).
(i) Consider a consumer h with preferences and endowment
• Un (xh(a), xh (b)) = 2log ₂ (a) + 3 log xn (b), (en(a), en (b)) = (3, 4 × t)
who wishes to trade in contingent markets. Setup the optimization problem of this
consumer and compute the optimal consumption plan as a function of the prices of
the contingent contracts.
(ii) Consider another consumer k with preferences and endowment
● Uk (xk(a), xk (b)) = 3 log x (a) + 2log xk (b), (ek(a), ek(b)) = (2,4 × t)
who also wishes to trade in contingent markets. Setup the optimization problem of
this consumer and compute the optimal consumption plan as a function of the prices
of contingent contracts.
(iii) Consider another consumer m with preferences and endowment
• Um (xm(a), xm (b)) = xm(a) + log xm(b), (em(a), em(b)) = (0,2 × t)
who also wishes to trade in contingent markets. Setup the optimization problem of
this consumer and compute the optimal consumption plan as a function of the prices
of the contingent contracts.
(iv) Consider now an economy consisting of (in millions): 3 individuals of type h, 9
individuals of type k and 5 individuals of type m. Compute the equilibrium prices
and allocation of contingent commodities of this economy.
(v) Comment on the equilibrium risk allocation for type m individuals. Comment
on the Pareto optimality of the equilibrium.
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