Reconciling Full-Cost and Marginal-Cost Pricing
Finance and Economics Discussion Series
Despite the clear prescription from economic theory that a firm should set price based only on variable costs, firms routinely factor fixed costs into pricing decisions. We show that full-cost pricing (FCP) can help firms uncover their optimal price from economic theory. FCP marks up variable cost with the contribution margin per unit, which in equilibrium includes the fixed cost. This requires some knowledge of the firm's equilibrium return, though this is arguably easier a lower informational
... lower informational burden than knowing one's demand curve, which is required for optimal economic pricing. We characterize when FCP can implement the optimal price in a static game, a dynamic game, with multiple products, and under a satisficing objective. Economic theory provides an unambiguous prediction on how a profit maximizing firm should set its price for a product: the firm includes only marginal (or variable) costs. It should not factor fixed costs into the pricing decision. Yet a wealth of survey evidence (Shim and Sudit  ; Noreen and Burgstahler ; Shim  ; Govindarajan and Anthony ) indicates that more than 60 percent of American manufacturing companies do include fixed costs in prices, a practice called full-cost pricing (FCP). We seek to resolve this puzzle between economic theory and real accounting practices with the following observation: optimal pricing by a firm requires accurate knowledge of their residual demand curve, even though firms rarely have such knowledge, and certainly not to the extent and precision needed for ascertaining the optimal price. FCP, on the other hand, may be based on a less stringent informational requirement, such as some knowledge of equilibrium income, and still lead to the optimal price. This lessens the apparent paradox, and full-cost pricing may simply be a concrete way to implement optimal pricing. We provide a specific algorithm by which the firm can formulate its full-cost price and achieve the optimal price. This may be achieved even when knowledge of equilibrium income is imperfect, such as for a multiproduct firm with complementarities between products, as well as in a firm that chooses to satisfice rather than optimize. In the classical economic textbook solution, the firm maximizes profits by equalizing marginal revenue and marginal cost, thereby marking up variable cost in a manner related to the elasticity of demand. Fixed costs vanish from the firm's optimization problem and therefore do not factor into the optimal price. Instead, they only affect the firm's decision on whether to enter the market. For the firm to pick the price correctly, it must know its demand curve, since the optimal price (via marginal revenue) is a function of the demand curve's shape and parameters. But even a slight bit of uncertainty regarding demand parameters can lead the firm to misprice its product. The economic model of the profit-maximizing firm works if the firm does, in fact, have all the necessary information on its market environment, including the demand coefficients. However, if these strong informational requirements are not met, pricing resulting from erroneous estimates of demand will be suboptimal, which may explain why firms don't actually price according to economic theory. 1 1 The classic defense of the economic model comes from Milton Friedman, who argued that firms behave "as if" they are solving an explicit optimization problem (Friedman  ). We are explicitly concerned with the actual pricing practice of firms, i.e. a "what exactly" explanation, rather than an "as if" explanation. Indeed, one can interpret our results as supporting Friedman's argument: full-cost pricing may be the practical method by which firms achieve optimal pricing. Friedman's "as if" argument begs the question of what the actual method is, and full-cost pricing may provide the answer.