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

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?

Economic efficiency As all consumers pay the same prices, P X /P Y is the same for all Therefore, the tangency condition for rational consumer behavior implies that MRS XY must be the same for all Why is this significant? To see why, imagine two consumers, Blue and Red, such that Red’s MRS XY exceeds Blue’s

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 MRS XY. Blue’s MRS < Red’s MRS – Red’s MRS = 3 – Blue’s MRS = 0.5 X Y B R

R 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 MRS XY 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 MRS XY is inefficient X Y B

R Economic efficiency In this example, Blue and Red have the same MRS XY – 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 X Y B

Economic efficiency Under the tangency condition of rational consumer behavior, Blue and Red have the same MRS XY 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

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 MRS XY = 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 Red Blue MRS XY = 3 MRS XY = 0.5 1X1X 2Y2Y

Economic efficiency Under rational consumer behavior both Blue and Red will have the same MRS XY – 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