Alchian and Allen, opportunity cost, and the kid in the candy store

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The new Alchian and Allen book Universal Economics is out. The publisher reports the authors have collaborated to produce a ”fresh, final presentation of the analytical tools” contained in their famous (among a certain kind of economics nerd) textbooks University Economics and Exchange and Production.

In introducing the idea of opportunity cost in the new book, Alchian and Allen give us a “kid in the candy store example.” Alchian and Allen get their explanation wrong.

From the new Alchian and Allen:

A candy-store owner told Annie: “I want to give you some candy for free. Select whichever one you want.” She responded, “Thank you. But it’s not free!” Annie’s smart! She recognized that choosing her favorite, Snickers, is costly. She would have to give up here next best-liked candy, a bag of M&Ms—her alternate personal highest-worth good. Costs can occur in several forms, and some things that are not costs are often called costs.

Definition of cost of a chosen action

The cost of an action is the best alternative you otherwise would have chosen. Cost is what you forgo. When Annie chose the Snickers, she gave up one of the several other kinds of candy she could have had. The best—the highest valued—alternative in her opinion was the M&Ms. So for Annie, the cost of the Snickers was the M&Ms. “Opportunity” is sometimes used with “cost”—“opportunity cost”—to emphasize that the cost of an act is the best of the forgone opportunities.

Annie did get the right to choose some candy. Getting that right didn’t cost her anything. The cost occurred when she had to choose to have this rather than that. We must recognize the difference between (a) the gift of the right to choose among the specified items and (b) the act of choosing among them. Though the right to choose some candy was obtained without payment, the choice itself was not free.

The example reminded me of the famous (again, among a certain kind of economics nerd) joke about opportunity cost by “the stand-up economist” Yorum Bauman. It also features Snickers and M&Ms:

[S]omebody offers you a choice between a Snickers bar and a package of M&Ms. Suppose, for the sake of argument, that you take the M&Ms. According to Mankiw, the cost of those M&Ms is the Snickers bar that you had to give up to get the M&Ms. Your gain from this situation—what economists call “economic profit”—is therefore the difference between the value you gain from getting the M&Ms (say, $.75) and the value you lose from giving up the Snickers bar (say, $.40). In other words, your economic profit is only $.35. Although you value the M&Ms at $.75, having the choice of the Snickers bar reduces your gain by $.40….

Indeed, the more choices you have, the worse off you are. The worst situation of all would be somebody coming up to you and offering you a choice between two identical packages of M&Ms. Since choosing one package (which you value at $.75) means giving up the other package (which you also value at $.75), your economic profit is exactly zero! So being offered a choice between two identical packages of M&Ms is in fact equivalent to being offered nothing.

The version here is taken from Bauman (2003) in the Annals of Improbable Research; you can also find Bauman joking on Youtube.

Alchian and Allen are not joking, but they make a mistake that gets them into Bauman’s trap. They continue:

When Annie was asked if she would rather have the Snickers over two bags of M&Ms, she replied, “No, I’d still choose the Snickers. But I would have a hard time deciding whether one Snickers was worth three bags of M&Ms. I’d let you choose whether I obtained a Snickers or three bags of M&Ms.”

As we improve the alternative from one to two to three bags of M&Ms, the economic profit (Annie’s net value from choosing Snickers and giving up the M&Ms) gets smaller. If offered three bags of M&Ms, Annie’s economic profit becomes zero. Equivalent, as Bauman said, to being offered nothing.

This is the problem: Annie’s costs rise as her alternatives improve, reducing the net gain from the choice and seemingly making her worse off. We do not even need to offer Annie three bags of M&Ms. If the store has two identical Snickers bars, the choice between them appears to be as valuable as no choice at all.

We need an explanation of Annie’s choice that makes more sense.

Alchian and Allen helpfully separate (a) the gift of the right to choose from the candy store, from (b) the act of choosing among the alternatives. The value of the right given Annie is equal to the value of her best choice from the candy story, in this case the value of a Snickers bar. This value does not depend on the alternatives, which are irrelevant once Annie spots a Snicker’s bar.

When Annie exercises her right to choose, when she picks the Snickers bar and foregoes other alternatives, is it correct to say that value of the M&Ms foregone are the opportunity cost of the choice of the Snickers bar? Alchian and Allen said yes. I say no.

What happens when Annie chooses the Snickers bar? She gives up the right to choose that, to her, was worth a Snickers bar, and in return gets a Snickers bar.

If Annie simultaneously gets and gives up an equivalent value, then she is no better off that before. Isn’t this, in fact, equivalent to being offered nothing? Have I fallen into Bauman’s trap?

Of course not.

Annie became better off with (a) the gift of the right to choose from the candy store. Her wealth increased with the gift  valued by her at exactly one Snickers bar. In (b) exercising that right Annie does not further add to her wealth, but rather trade one form of wealth for another. To be precise, presumably she exercises the right because it makes her at least a little better off, otherwise she would hold onto the right.

Alchian and Allen’s primary difficulty comes from the lack of a standardized way of opportunity cost accounting in economics. The issue has been examined in the literature of the most recent opportunity cost controversy – see Ferraro and Taylor (2005), Potter and Sanders (2012), and the symposium in the Journal of Economic Education beginning with Parkin (2016). In my view the best proposed approach is Stone (2015).

A second difficulty comes from the framing of Annie’s choice. Working in an obvious but overlooked point from Coase (1938) can help.

The first point that needs to be made and strongly emphasized is that attention must be concentrated on the variations which will result if a particular decision is taken, and the variations that are relevant to business decisions are those in costs and/or receipts.

Coase is writing for accountants about business decisions, which explains the focus on expenses and revenues. In Annie’s case we are working in more subjective terms of gained or lost satisfaction.

In deciding between two identical Snickers bars, there are no “variations which will result.” It would be, literally, a decision about nothing: nothing to be gained and nothing to be sacrificed. If all options are identical in every respect, there is no scarcity, no choice, and no cost.

Here is the refinement: In choosing between the right to take any candy bar (which is worth one Snickers bar to Annie) and a physical Snickers bar, there are some slight variations which will result. The differences are between Annie having a generalized right to choose a candy bar or having a ready-to-eat Snickers bar. Annie’s choice is about this slight variation.

I agree with Alchian and Allen: “Though the right to choose some candy was obtained without payment, the choice itself was not free.”

What they get wrong is in identifying the cost of the choice, which has nothing to do with irrelevant alternatives.

 

ADDENDUM: By no means do I intend any general criticism of the new Alchian and Allen book, which I have only begun to read. The difficulty they have here with opportunity cost is endemic within economics. I did have higher hopes for them on this issue because Alchian has contributed fresh thinking on costs, still mostly neglected. See Alchian (1968) for his survey and work from there.

REFERENCES

Alchian, Armen. “Costs.” International Encyclopedia of the Social Sciences (1968). Republished at Encyclopedia.com: http://www.encyclopedia.com/social-sciences/applied-and-social-sciences-magazines/cost

Alchian, Armen, and William Allen. Universal Economics. Liberty Fund (2018).

Bauman, Yoram. “Mankiw’s Ten Principles of Economics, Translated for the Uninitiated.” Annals of Improbable Research (2003).

Coase, Ronald H. “Business Organization and the Accountant.” The Accountant (1938). Reprinted in LSE Essays on Cost (1973).

Ferraro, Paul J., and Laura O. Taylor. “Do economists recognize an opportunity cost when they see one? A dismal performance from the dismal science.” Contributions in Economic Analysis & Policy (2005).

Parkin, Michael. “Opportunity cost: A reexamination.” The Journal of Economic Education (2016).

Potter, Joel, and Shane Sanders. “Do economists recognize an opportunity cost when they see one? A dismal performance or an arbitrary concept?” Southern Economic Journal (2012).

Stone, Daniel F. “Clarifying (opportunity) costs.” The American Economist (2015).