Alberto's utility function is u(xã, YA) = min{¤Ã, YA}, where ï and yд are his consumptions of goods and y. Bella's utility function is u(XB,YB) = XBYB, where x and yß are her consumptions of goods and y. Alberto's endowment s 5 units of ï and no y. Bella's endowment is 11 units of y and no x. If x is the numeraire and p is the price of y in units of x, then in a competitive equilibrium

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.11P
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A
and yд are his
= XBYB,
Alberto's utility function is u(xA, YA) = min{A, YA}, where
consumptions of goods and y. Bella's utility function is u(XB, YB)
where x³ and yß are her consumptions of goods and y. Alberto's endowment
is 5 units of x and no y. Bella's endowment is 11 units of y and no x. If x is the
numeraire and p is the price of y in units of x, then in a competitive equilibrium
○ 11/5 = p
11/(p+1) +2.5 = 11
O min{5, 11}+11/2p=11
O min{5, 11}+5/2p=11
○ 5/(p+1) +5.5 = 11
Transcribed Image Text:A and yд are his = XBYB, Alberto's utility function is u(xA, YA) = min{A, YA}, where consumptions of goods and y. Bella's utility function is u(XB, YB) where x³ and yß are her consumptions of goods and y. Alberto's endowment is 5 units of x and no y. Bella's endowment is 11 units of y and no x. If x is the numeraire and p is the price of y in units of x, then in a competitive equilibrium ○ 11/5 = p 11/(p+1) +2.5 = 11 O min{5, 11}+11/2p=11 O min{5, 11}+5/2p=11 ○ 5/(p+1) +5.5 = 11
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