Indifference Curve Analysis 1. Develop indifference curves 2. Develop budget constraint 3. Some basic analysis: a. changes in prices; b. changes in income; c. the Engels Curve 4. The Food Stamps Problem

Indifference curve: A collection of points for which the consumer is indifference between each of them and some reference point. Typically shown in the context of a two good world on a two-dimensional graph.

The axiomatic approach to indifference curves is a search for a minimum set of assumptions regarding consumer behavior through which to generate indifference curves. Standard axioms: 1.More is preferred to less—nonsatiation 2.Completeness—all points in a relation 3.Transitivity– A  B; B  C;  A  C

The budget equation: B = p og OG + p f F  OG = B/p og – p f /p og F Meaning: The budget equation will depict a curve in OG-Food space that is downward sloping (note: its derivative –p f /p og is negative).

Applying calculus to find an expression for the slope of the other curve, the indifference curve:  OG/  F = - (  U/  F) /(  U/  OG) or, using an equivalent notation:  OG/  F = - MU f / MU og

At an equilibrium, tangency implies that the slope of the budget constraint equals the slope of the indifference curve: Hence,

Consumer equilibrium requires that p f /p og = MU f /MU og or MU f /p f = MU og /p og In words: The marginal utility per dollar of expenditure must be equal for each good.