[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!]
Ask:
Consider a consumer who uses her money income to purchase only two goods: X and Y. Suppose the prices of these goods double, as does this consumer’s money income. Evaluate: There will be no change in the quantities of X and Y she buys.
Solution:
I like to ask my students this question when I introduce the concept of budget constraint. As I will explain shortly, it highlights an important point in consumer theory, namely that what influences consumers’ behavior are their real (that is, inflation-adjusted) wages and the real prices of the goods they consume.
The easiest way to answer this question is to set the budget constraints for the consumer. In this case, we have a consumer who uses all her monetary income to buy two goods, X and Y. Let’s assume that the prices of for many consumer goods. .
We can express the budget constraint mathematically as:
Here, M indicates her monetary income, which is equal to the number of hours she works times her hourly wage, PX and Pj indicate the prices of the two goods, and X And Y indicate the quantities she consumes. [1]
Since the question tells us that she uses her money income to buy only two goods, we know that any combination X And Y our consumer purchases must meet this condition.
Solving the budget constraint for Y will be more useful for our purpose:
The ratio PX/Pj is the price of X in terms of Y. It represents the amount of Y our consumer must give up in exchange for an additional unit of X. This ratio is the actual price of X. By the same logic, the ratio Pj/PX is the actual price of Y.
The relationship M/Pj is the purchasing power of her income in units of Y. Consider this ratio as her real income (we can also express her real income in units of X).
The question states that her money income doubles along with the prices of X And Y. We can illustrate this change as follows:
Viewed this way, it is clear that doubling her money income and the dollar prices of the two goods she consumes has no effect on her budget constraint, since the two will cancel each other out, creating the original budget constraint.
Because real prices and real incomes influence people’s behavior, the dollar price doubles X And Y and her money income will not affect the quantities of these goods she purchases (assuming this doubling does not affect her preferences for goods X And Y).
We could consider interesting extensions. For example, what happens if prices double, but her money income does not. Or we can consider a case where the prices of the two goods increase by different proportions. These expansions will bring changes in real prices and real incomes, and it will be no surprise that our consumers will change their behavior.
[1] Note that we can express her money income in hourly terms, in which case M would be just her wages, or in monthly or annual terms. While it doesn’t matter much which option we choose, it is crucial that we express the amounts of X and Y she consumes in the same terms. For example, if M declares her annual income, then X and Y must indicate the quantities of these goods that she consumes per year.
Bryan Cutsinger is an assistant professor of economics at Florida Atlantic University’s College of Business and a Phil Smith Fellow at the Phil Smith Center for Free Enterprise. He is also a fellow at the American Institute for Economic Research’s Sound Money Project and a member of the editorial board of Public Choice magazine.