= Consider the following 2 person, 1 good economy with two possible states of nature. There are two states of nature j = {1,2} and two individuals, i = {A, B}. In state- of-nature j 1 the individual i receives income y₁,1 whereas in state-of-nature j = 2, individual i receives income y₁,2. Let cij denote the amount of the consumption good enjoyed by individual i if the state-of-nature is j. State-of-nature j occurs with probability T₁ and ₁ + 2 = = 1. Prior to learning the state-of-nature, individuals have the ability to purchase (or sell) contracts that specify delivery of the consumption good in each state-of-nature. Let aj denote the number of consumption goods that individual i contracts to deliver in the event that state-of-nature j is realized. The relative price of contracts that specify delivery of goods in state-of-nature 2 is denoted by p. Individuals cannot create wealth by making promises to deliver goods in the future so the total net expenditure on purchasing contracts must equal zero, that is, aį,1 + paį,2 = 0. The individual's problem is {T₁u(C₁,1) + T₂u(C₁,2)} subject to the budget constraints C₁,1 = Yi,1 + ai,1, C₁,2 = Yi,2+ ai,2 and max Ci,1,Ci,2,ai,1,ai,2 + pai, 2 ai,1 = 0.

= Consider the following 2 person, 1 good economy with two possible states of nature. There are two states of nature j = {1,2} and two individuals, i = {A, B}. In state- of-nature j 1 the individual i receives income y₁,1 whereas in state-of-nature j = 2, individual i receives income y₁,2. Let cij denote the amount of the consumption good enjoyed by individual i if the state-of-nature is j. State-of-nature j occurs with probability T₁ and ₁ + 2 = = 1. Prior to learning the state-of-nature, individuals have the ability to purchase (or sell) contracts that specify delivery of the consumption good in each state-of-nature. Let aj denote the number of consumption goods that individual i contracts to deliver in the event that state-of-nature j is realized. The relative price of contracts that specify delivery of goods in state-of-nature 2 is denoted by p. Individuals cannot create wealth by making promises to deliver goods in the future so the total net expenditure on purchasing contracts must equal zero, that is, aį,1 + paį,2 = 0. The individual's problem is {T₁u(C₁,1) + T₂u(C₁,2)} subject to the budget constraints C₁,1 = Yi,1 + ai,1, C₁,2 = Yi,2+ ai,2 and max Ci,1,Ci,2,ai,1,ai,2 + pai, 2 ai,1 = 0.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter2: Mathematics For Microeconomics

Section: Chapter Questions

Problem 2.15P

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