With the indulgence of the blog mediator, I am posting a comment on the opportunity cost debate referenced below and on Marginal Revolution. I do this as a favor to Chris, but promise not do this on a regular basis. I am only the messenger.

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This is in response to a recent article by Professor Robert H. Frank that appeared in the Friday, September 2nd, 2005 issue of the New York Times titled "The Opportunity Cost of Economics Education." The article concerned the economic concept of opportunity cost, citing work by Ferraro and Taylor of Georgia State University showing that most professional and
academic economists fail to understand this most basic of concepts. The question asked a group of economists the following question:

You won a free ticket to see an Eric Clapton concert (which has no resale value). Bob Dylan is performing on the same night and is your next-best alternative activity. Tickets to see Dylan cost $40. On any given day, you would be willing to pay up to $50 to see Dylan. Assume there are no other costs of seeing either performer. Based on this information, what is the opportunity cost of seeing Eric Clapton?

(a) 0, (b) $10, (c) $40, or (d) $50.

The answer given as the correct answer was b) $10. The article went on to say that only about 21% or so of respondents got this answer correct.

Moreover, the article goes to say that $10 is the "unambiguously" correct answer. I don't know this for sure since the article did not provide information on the percentage of responds to selected d) $50, but I strongly suspect that the most popular answer was indeed d) $50.

In what follows I would like to offer an argument for $50 as an answer to the above question - one that is as equally correct as $10, and perhaps offer a rationale for why $50 may in fact be a superior answer to the above question.

Basically there are at least two approaches to answering the above question that can lead to two different "opportunity cost" answers. While this might be a troubling result, I also suggest that so long as the decision maker is consistent in his calculation, both procedures will result in the correct decision being made. Hence, the study the Times' article cites may be "much ado about nothing" rather than an indictment of the economics profession.

Let me start with a couple of basic definitions of opportunity cost. Taken from their Economics and Strategy, 2nd ed. text, Besanko, Dranove (both of Northwestern University) and Shanley (of Perdue University) define opportunity cost as "a concept which states that the economic cost of deploying resources in a particular activity is the value of the best foregone alternative use of those resources." In his Principles of Microeconomics text, 3rd ed., Mankiw defines the opportunity cost of an item as "what you give up to get that item." The basic elements of these definitions appear to be shared by at least a half a dozen Principles of Microeconomics texts that I happen to have in my office. While I'm sure that there is likely universal acceptance of the content of these definitions, from the perspective of the question and answer given in the Times' piece, it is telling to highlight what these definitions do not say opportunity cost is. Indeed, the answer given in the Times' article is based on a calculation suggesting that opportunity cost is, strictly speaking, not the foregone benefit from making a decision but rather the forgone net benefit of making a decision. Again, as I show below, this may be a reasonable way to go, but it is not the only way to go and, indeed, it may be, at best, a rather "exotic" way to proceed.

Let me demonstrate what I believe is going on here.

Two Methods for Calculating Opportunity Cost from the Times' example.

From the above question, whether someone arrives at an answer of $10 or $50 for opportunity cost rests completely on how exactly the $40 cost of a Dylan ticket is treated. Does it act to reduce opportunity cost as the Times article asserts, or is it in fact a "cost savings" benefit that one realizes if the decision is made to go to the Clapton concert? I contend that treating this $40 explicitly as a benefit is 1) more logical and 2) more consistent with the basic definitions of opportunity cost. True, some may disagree and in the end this may be a matter of taste. At any rate, however, to see the ramifications of this question, consider the following.

Let's define some key variables first:
Bd = benefit of seeing Dylan (set at $50 by the Times’ article)
Cd = cost of seeing Dylan (set at $40)
Bc = benefit of seeing Clapton (not given in the article)
Cc = cost of seeing Clapton. (set at $0 because the ticket is free
and has no resale value)

Now, the decision to see Clapton over Dylan depends on the payoff from seeing Clapton instead of Dylan. Let's call this PAYOFFc. If this payoff is greater than zero then the decision should be to go to see Clapton. If it's negative, the decision is to go see Dylan. Let's consider two different representation of PAYOFFc.

Method 1.

This method compares the net payoff from seeing Clapton with the net payoff of seeing Dylan, mathematically represented as

(1) PAYOFFc = (Bc-Cc) - (Bd-Cd).

Now with Cc=0, the Times’ article claims that the pportunity cost of seeing Clapton is the term in the second set of parentheses in (1); that is, the net benefit of seeing Dylan that is forgone when the decision maker goes to see Clapton: (50-40 = 10).

Method 2.

While the above procedure seems logical, an alternative approach would be to reconsider (1) by grouping the total benefits of seeing Clapton over Dylan against the total cost of seeing Clapton over Dylan. Doing so we have

(2) PAYOFFc = (Bc+Cd) - (Cc+Bd).

The first two terms in the first set of parentheses in (2) are in fact the total benefits of seeing Clapton over Dylan. Bc is the benefit of seeing Clapton and Cd is a cost savings benefit the decision maker realizes if he chooses not to see Dylan. Indeed, Cd can logically be thought of as a benefit since the ticket cost savings represents resources the decision maker can now divert towards the purchase of other items. The second two terms in the second set of parentheses of (2) are the total costs of seeing Clapton. Cc is the explicit cost of the Clapton ticket and Bd is the foregone benefit of not seeing Dylan.

In the example given in the paper then, when we employ this second method of directly comparing all benefits against all costs, we have

PAYOFFc = Bc +40 - (50+0).

Hence, total opportunity costs are $50 (not $10) as $50 is the foregone benefit of not seeing Dylan. This to me seems much more consistent with the basic definitions of opportunity cost given above.

The Important Lesson of Opportunity Cost (and why method may not matter so much).

Let us remember that the most important lesson we learn from an analysis of opportunity cost is that failure to consider the foregone benefits will generally lead to a non-ultility or non-profit maximizing decision. As it turns out, whether or not one uses Method 1 or Method 2, the correct decision will still be made. To see this, consider the following. Let's assume that the benefit one realizes from seeing Clapton (which was not given in the Times article) is $5. The decidedly incorrect decision would be to go see Clapton simply because the ticket is free (i.e. PAYOFFc = $5-$0 = $5 is the wrong measure of PAYOFFc). Clearly a measure of the foregone benefit of seeing Dylan needs to be considered.

Now, using Method 1, we calculate the payoff from seeing Clapton over Dylan as

PAYOFFc = $5-($50-$40) = -$5.

Since the benefit from seeing Clapton $5 is less than the net opportunity cost of seeing Dylan ($50-$40 = $10), the decision is clear: Don't use the free ticket to see Clapton.

Now, using method 2, we can calculate the payoff from seeing Clapton over Dylan as

PAYOFFc = ($5+$40)-($0+$50) = -$5.

Since the Total benefit from seeing Clapton (the $5 benefit of the Clapton show and the $40 cost savings from not having purchased the Dylan ticket) is less than the opportunity cost form seeing Claption over Dylan (i.e., the foregone benefit form seeing Dylan, $50). The decision is clear, however: Don't use the free ticket to see Clapton.

Irrespective of method, the correct decision is made.

A Consideration favoring Method 2.

While I believe that $10 is a reasonable answer to the question posed in the Times' article (so long as it is recognized that the $10 is the net benefit forgone), it does strike me that this is a more exotic representation of opportunity cost than the $50 measure given by method 2.

I truly think, however, that method 2 would be a better way to proceed, not only as a matter of professional practice but also from a pedagogical perspective. Suppose, for instance that the benefit one realizes from seeing Dylan is not $50 but rather $40. Should we then conclude that there is NO opportunity cost of seeing Clapton? This can't be correct since the problem states clearly that there is a value to seeing Dylan (and if one goes to Clapton one must forgo this benefit).

Furthermore, suppose that the benefit one realizes from seeing Dylan is not $50 but rather $30. Should we then conclude that the opportunity cost of seeing Clapton is negative $10? This strikes me as not only conceptually clumsy but upon additional thought highlights, in my judgment, the merits of treating the $40 cost savings benefit realized from not purchasing the Dylan ticket rather than as a direct determinant in calculating opportunity cost.

Some Concluding Considerations.

I wish to state that I was in no way involved with the Ferraro and Taylor study at any time, I was only privy to their study via the Times' article. I must admit however, that while my first answer to the above question was $50 (one in which I stand by), upon further reflection I can see how some would say the correct answer is $10. The only point I wish to make here is that, as the question is framed, $50 is as good, and may even be a slightly better, answer than $10.

Economists often get a bad rap in the popular press, and often with some reason. However, I strongly believe this Times article, by asserting that most economists don't understand the basics of opportunity costs, is, at least as presented, an unfair criticism. I must admit that it would be troubling if a significant percentage of economists surveyed said that the correct answer of question posed in the article was $40. However, no such data was given and I do suspect that the majority said the correct answer was $50.

Moreover, I have to say I feel pretty strongly about this issue and the criticism the Times article levies against the economics profession. Indeed, this must be the case since I've spent my time writing this response rather than spending my time on some other task (which itself may indicate my personal limitations in understanding the concept of opportunity cost!). There are two things, however, that are eminently clear to me. First, whether one said the opportunity cost was $10 or $50, the correct economic decision would have been made so long as the forgone benefits entered into the decision-making calculus. Second, the statement made in Times article that "the unambiguously the correct answer to the question is $10" may be, in light of the standard definitions typically given for opportunity cost, a bit too strong of a statement.

Christopher S. Decker
Associate Professor
Dept. of Economics
College of Business Administration
University of Nebraska at Omaha
email: christopherdecker@mail.unomaha.edu