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Topic: Exercise 2.6
Conf: Chapter 2, Topics in Consumer Theory, Msg: 13502
From: Martin Caley (martin.caley@economics.treasury.gov.im)
Date: 10/15/2003 10:21 AM
Exercise 2.6 Martin Caley MCaley martin.caley@economics.treasury.gov.im
Re-arrange and substitute e=y to get
V=(1/p1+1/p2)y.
x1/x2 = (dV/dp1)/(dV/dp2)=(p2/p1)^2 using Roy's identity twice.
From the budget constraint y/p1=x1+(p2/p1)x2=x1+sqrt(x1x2). Similarly for y/p2. (You can just swop the 1's and 2's in questions like this!)
Next U=V=y/p1+y/p2 so U=x1+x2+2sqrt(x1x2)=(sqrt(x1)+sqrt(x2))^2.
This is a bit quicker than the suggested answer.