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

The article proceeds as follows. In Section 2, we provide an interpretation of cost accounting practices as they relate to pricing decisions. Sections 3-5 introduce the model and our main results. In Section 5, we specialize our general model to the canonical case of symmetric linear demand. We obtain a closed-form solution that shows how the distortion of relevant cost depends on the degree of product differentiation and the number of firms. Finally, Section 6 compares the implications of our model with available experimental evidence and discusses related literature.

2. Price setting and costing methodologies in practice

* An economist reading managerial accounting textbooks may be surprised to discover that they mainly consist of a compilation of common company practices. In contrast to the traditional economic treatment of optimal pricing, managerial accounting offers no rigid guidelines as to how various costs should factor into firms' pricing practices.

In this section, we present our understanding and an interpretation of the accounting principles used as a guide in day-to-day costing practices.

[] Full-cost pricing. The most common set of real-world pricing practices falls under the rubrics cost-basedpricing, cost-plus pricing, or full-cost pricing. Although they come in a wide range of variations, they all base price on a calculation of an average or unit cost that includes variable, fixed, and sunk costs. (6)

Firms justify full costing using a variety of arguments with typically little or no foundation in economic theory:

* Simplicity. Full-cost formulas are thought to be relatively straightforward to implement because they do not require detailed analysis of cost behavior in order to separate the fixed and variable components of various cost items. A related argument is that estimates of marginal cost are often imprecise and indeed even misleading in large, multiproduct firms (Kaplan and Atkinson, 1989).

* Promote full recovery of all costs of the product. Pricing based on a full-cost formula is sometimes justified because it provides a clear indicator of the minimum price needed to ensure the long-run survival of the business (Horngren, Foster, and Datar, 2000, henceforth HFD). The idea is that without full-cost pricing, a firm's managers would not be as aware of the "pricing hurdle" that the firm would need to clear in order to generate economic profits for the firm. (7)

* Competitive discipline. Some managers believe that full-costing methodologies promote pricing stability by limiting "the ability of salespersons to cut prices" and reducing the "temptation to engage in excessive long-run price cutting." (HFD). Further, full costing may allow firms to better coordinate on price increases: "At a time when all firms in the industry face similar cost increases due to industry-wide labor contracts or material price increases, firms will implement similar price increases even with no communication or collusion among individual firms" (Kaplan and Atkinson, 1989).

[] Absence of common standards and the importance of flexibility. An underlying message of the accounting literature is that firms should adapt their costing methodologies to fit their particular competitive environment and product line idiosyncrasies. That is, an emphasis is placed on flexibility. The typical theme is that the appropriate methodology depends on the industry environment. For example, full-cost pricing is considered to be well suited for firms that operate in differentiated product industries (HFD), whereas companies that operate in highly competitive commodity industries are encouraged to set prices based on competitors' prices. (8)

Managerial practice mirrors the textbook emphasis on flexibility. For example, the cost of shared assets is often allocated to individual product lines according to fixed, and more or less arbitrary, percentages. In computing unit costs, there is no universally accepted benchmark for what quantity should go in the "denominator": some firms calculate unit cost at full capacity (in one of its various forms), whereas others use historical output levels, and still others base unit costs on forecasts of future sales. Some companies compute prices by applying a single markup to a chosen cost base, whereas others apply different markup percentages to different cost categories.

[] Representational faithfulness. Given the arbitrariness and flexibility in pricing methodologies, there is no presumption that a firm includes all of its fixed and sunk costs in its computation of unit costs for price-setting purposes. Still, it is reasonable to believe that 'firms do not create costs out of thin air." In fact, we shall assume that firms' distortions display a minimal degree of coherence, requiring that they only allocate existing fixed and sunk costs.

This can be justified by the accounting principle of representational faithfulness, which is one of the two major principles (the other being verifiability) that defines the standard to which external financial statements are expected to adhere (Financial Accounting Standards Board, 1980). This principle requires the "correspondence or agreement between a measure or description and the phenomenon it purports to represent." Although internal financial information is not required to meet external standards of reliability, external reporting systems often have an important impact on accounting information that is used for internal purposes. It therefore seems plausible that a principle designed to keep external accounting information grounded in the economic fundamentals of transactions would also keep internal accounting information similarly grounded.

Another justification may be based on psychological evidence that the sunk cost bias results from decision makers' taste for taking actions that rationalize past choices. Clearly, if no sunk or fixed costs are committed, there is nothing to rationalize and, under this theory, the sunk cost bias should not appear.

[] Budgets and variances. For pricing and other operating decisions, firms typically utilize a budget of forecasts of costs and quantities for a given accounting period. Budgets aid in decision making and also serve as a benchmark against which decisions can be evaluated ex post. Budgeted amounts may be based on historical performance, engineering studies of how various cost items might behave, and hypotheses about competitors' actions. (9) For example, a budget might specify a firm's per-unit cost based on the quantity of output produced in the most recent time period.

The budget process is subject to inertia. A firm may change its price and other operating decisions many times before changing the methodology used to determine its budget.

At the end of each accounting period, firms typically compute a variance, the difference between the budget amount and the actual result. (10) Variances provide a mechanism by which anticipated and actual performance can be reconciled. For example, suppose a firm has computed its unit costs based on a target output, and the actual output in the accounting period differs from this target output. A variance would then reconcile the unit cost the firm assumed would prevail and the unit cost that actually prevailed. Variance analysis ensures that managers ultimately are held accountable for the actual performance of the firm.

[] Summary. The discussion above highlights key features of managerial practice which we will incorporate in our formal model:

(i) Firms choose "costing methodologies" that might confound sunk, fixed, and variable costs. Firms do not necessarily allocate all of fixed and sunk costs to the cost base, but this allocation cannot exceed actual fixed and sunk costs.

(ii) Firms compute the per-unit fixed and sunk cost based on a budgeted output level that remains constant during an accounting period.

(iii) Day-to-day management of the firm's pricing strategy is guided by the firm's budget and costing methodology. Although firms can adjust prices quickly, budgets and costing methodologies are less flexible and change less often than prices.

(iv) Firms periodically reconcile actual and budgeted profits by adding back variances ensuring that, at the end of each accounting period, firms observe their actual economic profit.

3. The model

* We focus on the most challenging case for us, namely that of Bertrand competition with product differentiation. Analysis of other market structures is more straightforward, and is dealt with in Section 4.

We consider a Bertrand oligopoly in which boundedly rational firms may adopt costing methodologies which cause their pricing decisions to depart from those prescribed by textbook economic theory. This section sets up the basic model.

[] Demand and cost fundamentals. The industry consists of N single-product firms engaged in (Bertrand) price competition with differentiated products. (By a slight abuse of notation, N also denotes the set of firms.) Firm n's quantity, denoted [q.sub.n], is determined by a demand function [q.sub.n] = [D.sub.n](p), where p = ([p.sub.1], ... [p.sub.N]) denotes the industry's vector of prices. (11) We assume that firm n knows its own demand function, [D.sub.n], but not the demand functions of the other firms.