Market forces meet behavioral biases: cost misallocation and irrational pricing.

Psychological and experimental evidence, as well as a wealth of anecdotal examples, suggests that firms may confound fixed, sunk, and variable costs, leading to distorted pricing decisions. This article investigates the extent to which market forces and learning eventually eliminate these distortions. We envision firms that experiment with cost methodologies that are consistent with real-world accounting practices, including ones that confuse the relevance of variable, fixed, and sunk costs to pricing decisions. Firms follow "naive" adaptive learning to adjust prices and reinforcement learning to modify their costing methodologies. Costing and pricing practices that increase profits are reinforced. In some market structures, but not in others, this process of reinforcement causes pricing practices of all firms to systematically depart from standard equilibrium predictions.

1. Introduction

* Economic theory offers the unambiguous prescription that only marginal cost is relevant for profit-maximizing pricing decisions. Ongoing fixed costs or previously incurred sunk costs, although relevant for entry and exit decisions, are irrelevant for pricing. This theoretical prescription stands in stark contrast to evidence about real-world pricing practices. In surveys of pricing practices of U.S. companies, Govindarajan and Anthony (1995), Shim (1993), and Shim and Sudit (1995) find that most firms price their products based on costing methodologies that treat fixed and sunk costs as relevant for pricing decisions. Leading textbooks on managerial and cost accounting paint a similar picture. Maher, Stickney and Weil (2004) assert that, when it comes to pricing practices, "[o]verwhelmingly, companies around the globe use full costs rather than variable costs." They cite surveys of U.S. industries "showing that full-cost pricing dominated pricing practices (69.5 percent), while only 12.1 percent of the respondents used a variable-cost based approach." (Horngren, Foster, and Datar (2000), another leading accounting textbook, report other surveys in which a majority of managers in the United States, the United Kingdom, and Australia take fixed and sunk costs into account in pricing.

Although suggestive, surveys indicating that firms use full-cost pricing (i.e., confounding the roles of variable, fixed, and sunk costs; see Section 2) do not imply that this has a material effect on observed prices. Full-cost pricing may well be a convenient general rule managers use to find the rational pricing point. For instance, managers may be influenced by a combination of biases that "cancel out," leading them to price "as if" they understood the economic reasoning of marginal revenue and marginal cost. Moreover, behavioral biases in critical decisions such as cost allocation and pricing may eventually disappear in response to learning and competition. Pursuit of profit is a powerful incentive for firms to learn to price optimally. Also, competition among managers for promotion and advancement within a firm should favor those who price optimally. Alchian's (1950) classic argument that learning and imitation would propagate good practices suggests that interfirm competition would only reinforce the case for optimal pricing: "[W]henever successful enterprises are observed, the elements common to these observable successes will also be associated with success and copied by others in their pursuit of profits or success. 'Nothing succeeds like success.'"

Yet, important mechanisms for propagating best accounting practices lend little if any support for the use of economics-based pricing principles. For example, textbooks in managerial accounting often list marginal-cost-based pricing as just one of several acceptable methodologies, alongside others that incorporate fixed and sunk costs into pricing. Some managerial accounting texts even argue against basing prices on marginal costs. (1)

One way to resolve this issue is through controlled experiments where decision makers face environments that differ only in the presence of irrelevant costs. Offerman and Potters (2006) conduct such an experiment in a Bertrand duopoly context. In their baseline treatment with no fixed or sunk cost, Offerman and Potters find that prices converge to the Bertrand equilibrium. In the sunk cost treatment, subjects face the same demands and marginal costs as in the baseline treatment, but they must pay a sunk entry fee to play the game. In this treatment, Offerman and Potters find that prices are significantly higher: once the sunk entry fee is paid, the average markup over marginal cost is 30% higher than the markup in the baseline treatment.

The goal of this article is explain why cost misallocation, in the form of full-cost pricing, persists, and indeed thrives, despite the forces of learning and competition. Two key ideas underlie our model. First, the presence of irrelevant costs (e.g., sunk cost) triggers a predisposition among firms to use full-cost pricing. Psychological and experimental evidence, as well as a wealth of anecdotal examples, suggests that this confusion is, at least, plausible. (2) Second, when subjected to competitive market pressures, firms adjust their prices and, much less frequently, their "costing methodologies" by reinforcing the practices that yielded the best past results.

Thus, we do not assume optimal pricing rules or market equilibrium at the outset. Rather, we ask whether learning and competitive pressures force firms to overcome their initial biases, leading them to behave as though they played equilibrium strategies with optimal pricing rules. Long-run equilibrium behavior is derived, rather than assumed.

We show that market, forces eradicate irrational pricing in monopoly, perfectly competitive markets, and undifferentiated Bertrand oligopoly (see Section 4). Things are quite different in the case of Bertrand oligopoly with product differentiation. Theorem 1 shows that adaptive learning eventually leads to higher profits for any firm that unilaterally incorporates part of its irrelevant costs in its pricing decisions. We also provide a dynamic model in which firms experiment with new costing practices and reinforce successful ones. We assume that firms' choice of costing methodologies is subject to inertia (they adjust prices more frequently than they experiment with new costing methodologies). (3) Two conceptual problems arise: first, it is implausible that firms know their rivals' distorted costing practices. Second, even if these practices are known, computing payoff functions requires calculating the limit of the adaptive adjustment in prices. Firms that are naive enough to confuse cost concepts are unlikely to have the requisite sophistication and understanding of the game to carry out such computations. Thus, our firms face a learning problem where neither opponents' strategies nor the payoff functions are known. (4) Despite this, Theorem 2 shows that a simple process of experimentation and reinforcement leads all firms to eventually distort their relevant costs by incorporating fixed and sunk costs in their pricing decisions. This explains why full-cost pricing has been so hard to eradicate.

In our model, cost misallocation acts as though it is a commitment to raise prices. But it is a spurious commitment in the sense that it can be easily eliminated through learning. Firms can learn to price "correctly" in our model, and this indeed is what happens under some market structures. This is to be contrasted with the classical analysis of strategic commitment, where sophisticated players make binding decisions to limit their flexibility and foresee the impact of these decisions on their rivals' future behavior. Here, we envision real-world managers whose behavior is shaped by myopic incentives and refined by naive adaptive learning. The driving force in our model is confusion about which costs are relevant for pricing decisions. Because such confusion is unlikely to be observable, it is quite different from the familiar foundation of commitment, namely credible, transparent public actions designed to shape equilibrium outcomes in subsequent stages of the game. See Section 6 for further discussion.

The confusion of relevant and irrelevant costs in human decision making manifests itself in a myriad of ways. This is often referred to as the sunk cost bias or the sunk cost fallacy. See Thaler (1980) for a pioneering study of its role in economic decision making. One pattern, extensively supported by experimental evidence (see Arkes and Ayton, 1999), is for individuals to persist in an activity "to get their money's worth." (5) Under this pattern, individuals deflate the true cost of the activity. In this article, we focus on how the sunk cost bias manifests itself in pricing decisions. We allow firms to be rational, inflate, or deflate relevant cost. Our analysis identifies circumstances under which a systematic bias toward inflating cost appears.

To sum up, our concern is not with the origins of the predisposition to confound relevant and irrelevant costs, or to explain why this or other behavioral biases appear in one-off situations (like the anecdotal examples mentioned earlier). Rather, we examine the claim that the forces of learning and competition will eventually eliminate these biases. Because there is no reason to suspect that managers' innate predispositions to behavioral biases is correlated with industry structure, our model leads to testable predictions about how biases in pricing practices vary across market structures. In fact, our prediction that monopolists would eventually rid themselves of the sunk cost bias is consistent with the experimental findings of Offerman and Potters (2006).