[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:
Take into account a shopper who makes use of her cash revenue to buy solely two items: X and Y. Suppose the costs of those items double as does this shopper’s cash revenue. Consider: There will likely be no change within the portions of X and Y she purchases.
Answer:
This query is one I wish to ask my college students after I introduce the notion of a price range constraint. As I’ll clarify shortly, it highlights an essential level in shopper principle–particularly, that what influences shopper habits is their actual (i.e., inflation-adjusted) wages and the true costs of the products they eat.
The only technique to reply this query is to arrange the patron’s price range constraint. On this case, we have now a shopper who makes use of all her cash revenue 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 price range constraint mathematically as:
Right here, M denotes her cash revenue, 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 revenue 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 price range constraint for Y will likely be extra helpful for our goal:
The ratio Px/Py is the value of X by way of Y. It represents the quantity of Y our shopper should quit in trade 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 revenue in items of Y. Consider this ratio as her actual revenue (we might additionally categorical her actual revenue in items of X).
The query states that her cash revenue doubles together with the costs of X and Y. We will illustrate this modification as follows:
Considered this manner, it’s clear that doubling her cash revenue and the greenback costs of the 2 items she consumes has no impact on her price range constraint, because the twos will cancel out, yielding the preliminary price range constraint.
Since actual costs and actual revenue are what affect individuals’s habits, doubling the greenback costs of X and Y and her cash revenue is not going to 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 take into account attention-grabbing extensions. For instance, what occurs if costs double however her cash revenue doesn’t. Or, we might take into account a case the place the costs of the 2 items rise by totally different proportions. These extensions contain modifications in actual costs and actual revenue, and, unsurprisingly, would lead to our shopper altering her habits.
[1] Observe that we might categorical her cash revenue in hourly phrases, through 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 revenue, 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 Enterprise 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 Venture on the American Institute for Financial Analysis, and a member of the editorial board for the journal Public Alternative.
