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.
Principles of Economics 2e
2nd Edition
ISBN:9781947172364
Author:Steven A. Greenlaw; David Shapiro
Publisher:Steven A. Greenlaw; David Shapiro
Chapter6: Consumer Choices
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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd34c0034-2bd9-40e8-9c21-f29697294464%2Fc0f888d8-0ab5-437f-b331-b4facb876009%2Fzdiu4cr_processed.jpeg&w=3840&q=75)
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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