[Editor’s note: We’re bringing back price theory with our series on Price Theory problems with Professor Bryan Cutsinger. You can view the previous problem and Cutsinger’s solution here and here. Share your proposed solutions in the Comments. Professor Cutsinger will be present in the comments for the next two weeks, and we’ll again post his proposed solution shortly thereafter. May the graphs be ever in your favor, and long live price theory!]
question:
Consider a consumer who uses his monetary income to purchase only two goods, X and Y. Assume that the price of these goods is twice this consumer’s monetary income. Evaluation: There is no change in the quantities of X and Y that she purchases.
Solved:
This question is one I like to ask my students when introducing the concept of budget constraints. Although briefly explained, this highlights an important point in consumer theory. This means that what influences consumer behavior is the consumer’s real (i.e., inflation-adjusted) wage and the real price of the goods they consume.
The easiest way to answer this question is to establish a consumer budget constraint. In this case, a consumer uses all of his income to purchase two goods, X and Y. Let’s assume that the prices of X and Y are unaffected by how much of either item she buys. This is a reasonable approximation for many consumer products. .
The budget constraint can be expressed mathematically as:
where M denotes her monetary income, which is equal to the product of the number of hours she works and her hourly wage, Px and Py denote the prices of the two goods, and X and Y denote the quantities she consumes . [1]
This question shows that she uses her monetary income to purchase only two products, so this condition must be met no matter what combination of X and Y the consumer buys. You can see that it must be done.
Solving the budget constraint for Y is more beneficial for our purpose.
The ratio Px/Py is the price of X in terms of Y. This represents the amount of Y that the consumer must give up in exchange for an additional unit of X. This ratio is the actual price of the ratio Py/Px. Y’s
The ratio M/Py is the purchasing power of her income in Y units. Think of this ratio as her actual income (you could also express her actual income in units of X).
The question states that her monetary income will double depending on the prices of X and Y. This change can be explained as follows.
Viewed this way, doubling her monetary income and the dollar prices of the two goods she consumes has no effect on her budget constraint because the two cancel out to give her initial budget constraint. It is clear that it will not be given.
It is real prices and real incomes that influence people’s behavior, so doubling the dollar prices of X and Y and her monetary income has no effect on the quantity of these goods she buys (Assume that this doubling did not affect her preference for products X and Y).
You may also consider interesting extensions. For example, what if her income did not double even though prices doubled? Alternatively, consider the case where the prices of two goods increase at different rates. These enhancements involve changes in real prices and real incomes, which, of course, will result in changes in consumer behavior.
[1] Note that her monetary income can also be expressed in hours. In that case, M could simply be her wage, or it could be expressed in months or years. It is not very important which option she chooses, but it is important that the quantities of X and Y that she consumes are expressed in the same terms. For example, if M represents her annual income, then X and Y should represent the quantities of these goods she consumes per year.
Brian Cutsinger is an assistant professor of economics at Florida Atlantic University’s School of Business and a Phil Smith Fellow at the Phil Smith Center for Free Enterprise. He is also a Fellow of the National Bureau of Economic Research’s Sound Money Project and a member of the editorial board of the journal Public Choice.
