The Sunk Cost Fallacy

In both of these cases, the consumers base their decisions about current and future activities on the amount that had been paid in unrecoverable costs. Clearly, if being given a ticket would not result in attending a game in a snowstorm, then it cannot be worth it to attend the game if one has paid for the tickets. Further, after an injury one would likely not want to play tennis and will not recover the value of a yearly membership by undergoing pain and difficulty to play. Nonetheless, there is some ring of truth to the reasoning offered in each of the hypothetical stories. We probably have known people who made such arguments, and we can most likely recall making similar arguments ourselves. Why would such an argument be convincing on occasion if there is no merit to it? Do people really behave in this way? More importantly, if people do behave this way, would they necessarily be better off by avoiding the behavior? What implications might there be for manufacturers and retailers of goods?

For example, people attending an amusement park and purchasing an all-day pass may be influenced by the purchase price. Someone who purchases an all-day pass to an amusement park for $10 might get tired and uncomfortable and want to go home by 1 P.M. The same person paying $30 for the pass might feel just as tired at 1 P.M. but might also feel that she has not sufficiently realized the value of her purchase. Thus, she might stay for several more hours trying to have fun despite her desire to go home. Detecting such an effect may be difficult. For example, those who are likely to go home at 1 P.M. may be less willing to purchase a pass in the first place and thus more likely to show up when the pass price is only $10. In this case, simply finding that people stay later when the prices are higher might not be very good evidence of the sunk cost fallacy; it might simply be evidence that higher prices drive lower-value customers away. The sunk cost fallacy is generally related to the notion that a fixed access fee influences the extent of an activity. Thus, even if the return on the project does not necessarily turn negative, the people paying a larger fixed fee may be expected to consume more. This observation has led to several experiments examining the impact of fixed fees on use.

EXAMPLE 2.1 Theater Tickets and Pricing Programs

Theater ticket subscriptions are designed so that the subscriber pays a fixed fee for a package of tickets to several plays or productions. Theatergoers receive their tickets in a bundle before the first show. The subscriber may subsequently decide to attend a show, to give away the tickets to that show, or to simply discard the tickets.

Hal Arkes and Catherine Blumer worked with the Ohio University Theater to randomly offer different prices to the first 60 people to order tickets. Some paid full price, $15, some received a $2 (roughly 13%) discount, and some received a $7 (roughly 47%) discount. Over the first five plays of the 10-play season, the full-price group attended significantly more of the plays than either of the discount groups. Thus, it appears that at least some of the theatergoers were led to attend more plays because they had paid too much for the tickets to miss the plays. Their results are very suggestive of sunk cost fallacy–style reasoning. They also observed that over the last five plays of the season there were no real differences in attendance. They suggest that their results show that the effects of sunk cost persist over a substantial period of time, though not indefinitely. Following their reasoning, eventually people forget the pain they associate with the cost of the tickets and begin to decide attendance based on the enjoyment the play would offer.

EXAMPLE 2.2 The Concorde Paradox and Public Policy

The sunk cost fallacy is also sometimes called the Concorde paradox in honor of the late supersonic jet. The Concorde, the supersonic plane that was once used for cross-Atlantic traffic, was originally a joint venture between the British and French governments. The governments drew wide publicity in 1962 for their plans to develop a commercially viable passenger plane that could travel faster than the speed of sound. Each government had agreed to contribute $224 million to the project for a total of $448 million. Early into the design phase of the project, expenses began to run over budget. By 1964 the projected cost was more than $900 million. By completion, the plane had cost more than six times the original projected cost to develop. In the later stages of development, around 1973, both governments began to realize that the plane would not generate enough money to cover future costs of development and production.

Because there were only 100 passengers per plane and a substantially increased cost of operation with respect to conventional aircraft, few airlines were willing to take the chance of purchasing a Concorde. Despite the dismal prospects, the project continued to completion at considerable cost. Only 14 of the planes were ever used commercially, with most purchased with a substantial subsidy from either the British or French governments to induce operation. The planes were in service from 1976 until 2003. A crash in 2000, caused by a small piece of debris, killing all 100 passengers, led to a brief grounding of the planes. Later, with rising oil prices and decreased interest in flight following the 2001 terror attacks in the United States, the planes were permanently decommissioned. Other governments with similar projects (notably the Soviet Union and the United States) abandoned similar programs owing to concerns over costs and viability.

Of course, political decisions are made by politicians who might have very different motives than profit maximization. It may be that politicians believed that public opinion would turn on them if they abandoned the project when it was known to be a money loser. In this case, it may be perfectly rational for the politicians to continue a project, using constituent money for projects that will help ensure their own political gain. It may truly be the constituents who fall for the sunk cost fallacy.

Sunk cost reasoning is commonplace in politics. For example, when asked about the need for a NASA mission to Mars and Florida’s role in this mission, presidential candidate John McCain said “There’s too much invested there. There’s infrastructure that’s very expensive and very extensive.” Regarding the possibility of the United States withdrawing from the lengthy engagement in Iraq, Cal Thomas, a conservative columnist, argued in USA Today that “We have too much invested to quit now,” echoing earlier sentiments expressed by President George W. Bush. Similar arguments have been heard when discussing the termination of a missile shield defense or other defense projects. Arkes and Blumer cite two senators from the early 1980s lamenting the termination of a waterway project given the level of prior investment. Although it must be acknowledged that these are not the only reasons given for continuing these projects, the fact that sunk cost rhetoric is used by those whose profession is primarily to argue is a de facto statement on how effective this (il)logic is perceived to be.

Theory and Reactions to Sunk Cost

When making decisions on extent of consumption given a fixed price for access, or after some unrecoverable sunk cost, the consumer should have a demand for the activity, x1*y, that depends entirely on her remaining budget, or on her ability to purchase other goods that may be a complement or substitute for good 1. If all other goods can be considered independent of consumption of good 1, then the optimal consumption level is independent of even wealth, x1*. A behavioral model of reacting to fixed or sunk costs could simply insert the level of costs as an argument in the function x1*y, p0, or x1*p0, with the assumption that the consumer will increase consumption when the fixed cost is increased, dx1*dp0 > 0. Such a model could then be used by a retailer to determine the profit-maximizing price for access based on the quantity their customers would consume as a result of price.

On the other hand, if we were interested in why consumers may be influenced by fixed costs, we would need to employ and test a procedurally rational model. There are two primary explanations for why one might display the sunk cost fallacy or more generally adjust quantity decisions to fixed costs. The first supposes that consumers derive some value from believing they have gotten a good deal, called transaction utility as opposed to just utility derived from consumption, as is modeled in the rational model of consumption (Thaler refers to this utility of consumption as acquisition utility). Paying $10 for four hours at an amusement park might sound like an extremely good deal, whereas paying $30 for the same experience might not. Thus, someone who paid $30 for entry into the amusement park might consider going home and receiving some utility from not being in the park anymore, but also receiving some disutility for knowing she paid a lot for the experience at the park. If this feeling of disutility is strong enough, she might consider lengthening her stay to increase her transaction utility. For example, $30 for six hours at the park might sound like a much better deal than $30 for four hours.

In this case, the consumer problem may be more generally written as

where z represents the consumer’s perception of how good a deal she has received as a function of the level of consumption and the fixed price paid for the good. Really, this is just a generalization of the previous model where the bliss point for good 1 now depends upon the fixed price charged for consumption of good 1. Thaler further supposes that transaction utility is additively separable from consumption utility. In this case, we could write the utility function as Ux1, x2, zx1, p0 = ux1, x2 + zx1, p0. The bliss point for x1 occurs where the sum of marginal consumption utility and marginal transaction utility is zero, ux1, x2x1 +zx1, p0x1 = 0. If this utility function accurately describes preferences, then the bliss point would potentially increase as p0 increases. This would happen if marginal transaction utility increases as p0 increases, requiring marginal consumption utility to become more negative in order to reach a bliss point.