Exercise 4 Consider an economy with two consumers, Alexia and Bart, who live two periods, t = 0 and t = 1. In each period they can consume one type of good and their preferences for consumption are given by U (co, ci) = c(ci)² _i = A, B. Alexia and Bart have the following endowment of good in each period M=1, M₁ = 1, MB = 2, MB = 2. In t = 0, Alexia and Bart can exchange a financial contract for the delivery of one unit of consumption good in t = 1 (a bond). Name p the price of the bond and b² the amount bought by agent i = =A, B. (a) Write down each agent's utility maximization and budget constraints assuming that he/she can trade the bond without restrictions. (b) Find each agent's optimal quantity b² as a function of the bond net return r. (c) Find the equilibrium value of r and the equilibrium demand/supply of each agent.
Exercise 4 Consider an economy with two consumers, Alexia and Bart, who live two periods, t = 0 and t = 1. In each period they can consume one type of good and their preferences for consumption are given by U (co, ci) = c(ci)² _i = A, B. Alexia and Bart have the following endowment of good in each period M=1, M₁ = 1, MB = 2, MB = 2. In t = 0, Alexia and Bart can exchange a financial contract for the delivery of one unit of consumption good in t = 1 (a bond). Name p the price of the bond and b² the amount bought by agent i = =A, B. (a) Write down each agent's utility maximization and budget constraints assuming that he/she can trade the bond without restrictions. (b) Find each agent's optimal quantity b² as a function of the bond net return r. (c) Find the equilibrium value of r and the equilibrium demand/supply of each agent.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Exercise 4 Consider an economy with two consumers, Alexia and Bart, who live two periods, t = 0
and t = 1. In each period they can consume one type of good and their preferences for consumption are
given by
U (co, ci) = c(ci)² _i = A, B.
Alexia and Bart have the following endowment of good in each period
M=1, M₁ = 1, MB = 2, MB = 2.
In t = 0, Alexia and Bart can exchange a financial contract for the delivery of one unit of consumption
good in t = 1 (a bond). Name p the price of the bond and b² the amount bought by agent i = =A, B.
(a) Write down each agent's utility maximization and budget constraints assuming that he/she can trade
the bond without restrictions.
(b) Find each agent's optimal quantity b² as a function of the bond net return r.
(c) Find the equilibrium value of r and the equilibrium demand/supply of each agent.
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