ECO206Y1 Lecture Notes - Lecture 1: Pareto Efficiency, Exchange Economy, Competitive Equilibrium

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Published on 6 Jul 2016
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Department
Course
Professor
Problem Set for Lecture 1 Exchange
ECO206: Microeconomic Theory
Summer 2015
1 Asymmetric Cobb Douglas Economy
Consider a pure exchange economy with two consumers 1 and 2. The two goods are consumption today
xand consumption tomorrow y. Consumer 1 is more patient and values the future consumption more
than the current consumption, and consumer 2 has the opposite preference. Let consumer i has preference
ui(x, y) = x
i
3y
1
i
3for i= 1,2. (Added assumption in tutorial: The economy has ¯xunits of goods today
and ¯yunits of goods tomorrow, initially evenly shared among the the consumers on each day.)
1. Find the expression for the set of Pareto optimal allocations.
2. Find the competitive equilibrium.
2 Double Quasi-linear Economy
Consider a pure exchange economy with one good xand money y. Both consumers A and B has utility
functions equal to the total dollar value of the good and the money, say ui(x, y) = y+ log (x). Consumer A
has 10 dollars but no goods, and consumer B has 10 goods but no money.
1. Find the expression for the set of Pareto optimal allocations.
2. Find the competitive equilibrium.
3 Economy with a Bad Good
Consider a pure exchange economy with two goods: work x and money y. Both consumers hate work and
love money, but consumer 2 hates work more than consumer 1. Let ui(x, y) = yi·x2. Initially, there are 10
dollars and 10 units of work in the economy, evenly shared among consumer 1 and 2. (Another endowment
that makes solving easier is ω1= (6,0) , ω2= (4,10))
1
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Document Summary

Consider a pure exchange economy with two consumers 1 and 2. The two goods are consumption today x and consumption tomorrow y. Consumer 1 is more patient and values the future consumption more than the current consumption, and consumer 2 has the opposite preference. Let consumer i has preference ui (x, y) = x i. Consider a pure exchange economy with one good x and money y. Both consumers a and b has utility functions equal to the total dollar value of the good and the money, say ui (x, y) = y + log (x). Consumer a has 10 dollars but no goods, and consumer b has 10 goods but no money: find the expression for the set of pareto optimal allocations, find the competitive equilibrium. Consider a pure exchange economy with two goods: work x and money y. Both consumers hate work and love money, but consumer 2 hates work more than consumer 1.

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