Rational Consumer Behavior and Social Efficiency

1. Rational Consumer Behavior and Social Efficiency ECO61 Microeconomic Analysis Udayan Roy Fall 2008

2. Economic efficiency • What does the tangency condition for rational consumer choice tell us about the overall efficiency of the economy? • Or, what can we say about the overall efficiency of the economy if the tangency condition is not satisfied?

3. Economic efficiency • As all consumers pay the same prices, PX/PY is the same for all • Therefore, the tangency condition for rational consumer behavior implies that MRSXY must be the same for all • Why is this significant? • To see why, imagine two consumers, Blue and Red, such that Red’s MRSXYexceeds Blue’s

4. Economic efficiency • Blue’s (Red’s) goods bundle is B (R) • The shaded areas denote superior bundles • The (negatives of the) slopes of the tangent lines at B and R denote MRSXY. • Blue’s MRS < Red’s MRS • Red’s MRS = 3 • Blue’s MRS = 0.5 Y R +3 -1 +0.5 -1 B X

5. Economic efficiency • Shift Blue’s indifference curve till B coincides with R • It is now possible to find a blue arrow and a red arrow, of equal length and pointing in diametrically opposed directions, from R such that the red arrow is pointing to an improved bundle for Red and the blue arrow, when moved to B, points to an improved bundle for Blue. • In this way, it can be shown that when MRSXY is not equal for two or more consumers, it is possible to make everybody better off by simply redistributing X and Y among the consumers—no additional X or Y is necessary! • This proves that an economy in which not all consumers have the same MRSXY is inefficient Y R B X

6. Economic efficiency • In this example, Blue and Red have the same MRSXY • Recall that this is what prevails under rational consumer behavior • Now it is impossible to redistribute goods among them in a way that would benefit both • This satisfies one condition of Pareto efficiency Y R B X

7. Economic efficiency • Under the tangency condition of rational consumer behavior, Blue and Red have the same MRSXY • As a result, it is impossible redistribute X and Y between Blue and Red so as to make both of them better off • This is one condition that an efficient—formally, Pareto efficient—economy must satisfy • A competitive, free-market economy does satisfy this requirement of Pareto efficiency

8. Economic efficiency • Here’s another way to look at the issue • Suppose • Red is willing to pay 3 units of Y for 1 unit of X. (That is, Red’s MRSXY = 3.) • Blue is willing to pay 0.5 units of Y for 1 unit of X • Then it is easy to make both Red and Blue better off by • taking 1 unit of X from Blue (who does not like X very much) and giving it to Red (who likes X a lot) • and compensating Blue by taking, say, 2 units of Y from Red and giving it to Blue 2Y Blue Red MRSXY = 0.5 MRSXY = 3 1X

9. Economic efficiency • Under rational consumer behavior both Blue and Red will have the same MRSXY • Suppose both individuals are willing to pay 2 units of Y for 1 unit of X • If you take 1 unit of X from Red to give to Blue, you will have to compensate Red by taking 2 units of Y from Blue and giving it to Red • But in that case neither Red nor Blue would be better off and the redistribution would be pointless • This shows that under rational consumer behavior, it is impossible to improve upon the market outcome • If the market outcome is unimprovable (in Pareto’s sense) it must be efficient to begin with