January 14, 2003
Theory of the Consumer
The theory of the consumer nicely illustrates how economists analyze the factors internal to the agent (the utility function and associated indifference curves) and the factors external to the agent (the budget constraint and prices) to determine economic behavior.
Indifference curves are like a relief map of a mountain.
Indifference curves do not cross.
The next diagram show the effects of an increase in the price of X1, decomposing the overall change into income and substitution effects.
The specific utility function in the lower-left corner is here to challenge our assumptions. Question: How many econ majors can find X1 and X2 to maximize this utility function subject to the budget constraint? If econ majors cannot do the math, it might be important to consider how people in general actually succeed in maximizing their utility.
The change in the price of X1 causes a change in the quantity consumed. We reorganize this information to create the demand curve for X1.
The direction of the substitution effect is unambiguous. It is possible, however, for the income effect to be large enough to reverse the outcome from the substitution effect as shown below. Note that you have to construct this example without letting the indifference curves cross.
The income effect in unlikely to have such a large effect in reality because the fraction of their income people spend on X1 is not very large. The substitution effect may well make the demand for Subway sandwiches downward sloping when Chick Fil A is across the room, but the income effect of a sandwich sale is not large for most people.
We concluded with the labor-leisure tradeoff as an explanation for the supply of labor. This interesting application of the two goods - two prices mechanism is important in thinking about the effects of a tax cut. Will people work more if you cut the income tax rate?
Another variation is the welfare problem. If you add a point where people can have a positive consumption if they do not work, but will lose that consumption if they work at all, the budget constraint looks like this. The point marked "welfare" is on a higher indifference curve than the point marked "work".
