Consider a pure exchange economy with two private goods, and two con- sumers denoted A,B whose respective utility functions and initial endowments are: uA(x1A, x2A) = x1A + x2A, uB(x1B,x2B)=1/3 lnx1B+2/3 lnx2B and WA=(2,0), WB= (0,2). Then, a competitive equilibrium allocation is:

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 23EQ: 23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes...
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Consider a pure exchange economy with two private goods, and two con-

sumers denoted A,B whose respective utility functions and initial endowments

are: uA(x1A, x2A) = x1A + x2A, uB(x1B,x2B)=1/3 lnx1B+2/3 lnx2B and WA=(2,0), WB= (0,2). Then, a competitive equilibrium allocation is:

(a) (x1A, x2A) = (2,2), (x1B, x2B) = (0,0)

(b) (x1A, x2A) = (1,1), (x1B, x2B)=(1,1)

(c) (x1A, x2A) = (2/3,4/3), (x1B, x2B)=(4/3,2/3)

(d) (x1A, x2A) = (4/3,2/3), (x1B, x2B) = (2/3,4/3)

(0) none of the previous answers is correct (NOPAC).

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