Client Buying Value Principle: Cutsinger’s Resolution

[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!]

Resolution:

This query is one I wish to ask my college students after I introduce the notion of a finances constraint. As I’ll clarify shortly, it highlights an vital level in shopper idea–particularly, that what influences shopper conduct is their actual (i.e., inflation-adjusted) wages and the true costs of the products they devour.

The best strategy to reply this query is to arrange the buyer’s finances constraint. On this case, we now have 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 are able to specific the finances constraint mathematically as:

Right here, M denotes her cash earnings, which equals the variety of hours she works instances her hourly wage, P_x  and P_y 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 finances constraint for Y will probably be extra helpful for our objective:

The ratio P_x/P_y  is the worth of X by way of Y. It represents the quantity of Y our shopper should hand over in change for a further unit of X. This ratio is the true value of X. By the identical logic, the ratio P_y/P_x is the true value of Y.

The ratio M/P_y is the buying energy of her earnings in items of Y. Consider this ratio as her actual earnings (we might additionally specific her actual earnings in items of X).

The query states that her cash earnings doubles together with the costs of X and Y. We are able to illustrate this transformation as follows:

Considered 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 finances constraint, because the twos will cancel out, yielding the preliminary finances 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 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 fascinating extensions. For instance, what occurs if costs double however her cash earnings 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 adjustments in actual costs and actual earnings, and, unsurprisingly, would end in our shopper altering her conduct.

[1] Observe that we might specific 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 decide, it’s essential that we specific 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 yr.

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 Selection.