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Boadway's Paradox xxxxxxxx [Potential Pareto Improvement] 214 Boadway sets up his argument within the context of a simple exchange economy with two people and two goods. Let E1 and E2 be two points on the contract curve so that there will be no potential Pareto improvements from moving from one point to the other (since both of the points are already Pareto Optimal by definition). He then proceeds to calculate individual welfare measures in terms of CV and EV and shows that there is a net non-zero aggregate welfare change. This is a paradox because we would expect a zero net aggregate welfare change from such a move (between two Pareto Optimal points on the contract curve). HOW COULD THIS BE?  Since both E1 and E2 are on the contract curve by construction, they are equally efficient and there will not be any potential Pareto improvement in moving from one point to the other. ICB2 YA XB
Price Ratio E2 OB E1 ICA2
Price Ratio ICA1 ICB1 OA Y B XA  If we move from E1 to E2, consumer B will be worse off (with a lower indifference curve and a positive value CVB > 0). This means we have to give B an income supplement of the amount CVB in order to bring her back to the old indifference curve ICB1 at E1. 215 ICB2 YA XB OB
Price Ratio E2 E1 Price Ratio ICA2 ICA1 ICB1 CVB OA Y
B XA  On the other hand, if we move from E1 to E2, consumer A will be better off (on a higher indifference curve and having a negative value for CVA < 0). This means we have to take away an income amount CVA in order to bring him back to the old indifference curve ICA1 at E1. ICB2 YA XB ICB1
E1 Price Ratio OB
Price Ratio E2 ICA2 ICA1 CVA CVB OA Y
B XA  Since, by construction, the absolute value of the welfare change CVA < 0 of consumer A is greater than the absolute value of the welfare change CVB > 0 of consumer B, we have a net aggregate welfare change when moving from E1 to E2... 216 CVsum = CVA + CVB <0 We would presumably conclude that E2 is "better" than E1 since we get a net...
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.
- Spring '10