[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!]
Query:
Think about a shopper who makes use of her cash earnings to buy solely two items: X and Y. Suppose the costs of those items double as does this shopper’s cash earnings. Consider: There can be no change within the portions of X and Y she purchases.
Answer:
This query is one I prefer to ask my college students after I introduce the notion of a funds constraint. As I’ll clarify shortly, it highlights an necessary level in shopper principle–particularly, that what influences shopper conduct is their actual (i.e., inflation-adjusted) wages and the true costs of the products they eat.
The best method to reply this query is to arrange the buyer’s funds constraint. On this case, we have now a shopper who makes use of all her cash earnings to buy two items, X and Y. Let’s assume that the costs of X and Y are unaffected by how a lot of both good she purchases–an inexpensive approximation for a lot of shopper items.
We will categorical the funds constraint mathematically as:
Right here, M denotes her cash earnings, which equals the variety of hours she works instances her hourly wage, Px and Py denote the costs of the 2 items, and X and Y denote the portions she consumes. [1]
For the reason that query tells us that she makes use of her cash earnings to buy solely two items, we all know that no matter mixture of X and Y our shopper purchases should fulfill this situation.
Fixing the funds constraint for Y can be extra helpful for our goal:
The ratio Px/Py is the worth of X by way of Y. It represents the quantity of Y our shopper should hand over in alternate for an extra unit of X. This ratio is the true worth of X. By the identical logic, the ratio Py/Px is the true worth of Y.
The ratio M/Py is the buying energy of her earnings in models of Y. Consider this ratio as her actual earnings (we might additionally categorical her actual earnings in models of X).
The query states that her cash earnings doubles together with the costs of X and Y. We will illustrate this alteration as follows:
Seen this fashion, it’s clear that doubling her cash earnings and the greenback costs of the 2 items she consumes has no impact on her funds constraint, because the twos will cancel out, yielding the preliminary funds constraint.
Since actual costs and actual earnings are what affect individuals’s conduct, doubling the greenback costs of X and Y and her cash earnings won’t have an effect on the portions of those items she purchases (assuming this doubling didn’t have an effect on her preferences for items X and Y).
We might think about attention-grabbing extensions. For instance, what occurs if costs double however her cash earnings doesn’t. Or, we might think about a case the place the costs of the 2 items rise by completely different proportions. These extensions contain adjustments in actual costs and actual earnings, and, unsurprisingly, would lead to our shopper altering her conduct.
[1] Word that we might categorical her cash earnings in hourly phrases, during which case, M would simply be her wage, or in month-to-month or annual phrases. Whereas it doesn’t matter a lot which choice we choose, it’s essential that we categorical the portions of X and Y she consumes in the identical phrases. For instance, if M denotes her annual earnings, then X and Y ought to denote the portions of those items she consumes per 12 months.
Bryan Cutsinger is an assistant professor of economics within the Faculty of Business at Florida Atlantic College and a Phil Smith Fellow on the Phil Smith Middle for Free Enterprise. He’s additionally a fellow with the Sound Cash Undertaking on the American Institute for Financial Analysis, and a member of the editorial board for the journal Public Selection.
