Third-degree price discrimination under economies of scale.

• Author: Layson, Stephen K.

1. Introduction

   There has long been a controversy in economics about whether or not a firm with monopoly power should be allowed to exploit its monopoly power by engaging in third-degree price discrimination.(1) The effect of third-degree price discrimination on welfare is two-fold: (1) output under price discrimination is misallocated because different groups are charged different prices but (2) if total output is different under price discrimination than under uniform pricing, this will also affect welfare.(2) Schmalensee [8], Varian [11; 12] and Schwartz [9] have shown that price discrimination must decrease welfare if output under price discrimination is the same or less than output under uniform pricing. This fundamental result is quite robust and holds regardless of the number of sub-markets or the behavior of marginal cost (rising, constant or falling); it also holds even if the sub-market demands are interdependent.

   A necessary, but not sufficient, condition for price discrimination to be beneficial is that it increase total output. Perhaps the most common situation in which price discrimination will be beneficial is the case where only one sub-market is served under uniform pricing but two or more sub-markets are served under price discrimination. In this case Hausman and Mackie-Mason [3] have pointed out that price discrimination will result in a Pareto welfare improvement if marginal cost is constant or falling. Even when price discrimination does not open up new markets. Hausman and Mackie-Mason [3] and Nahata, Ostaszewski, and Sahoo [5] have shown that price discrimination can result in a Pareto improvement by lowering prices in all sub-markets.

   Hausman and Mackie-Mason [3,257] argue that price discrimination is most likely to be beneficial when economies of scale are present:(3)

   Scale and learning economies are important for three reasons. First, when discrimination leads to an output increase and Marshallian welfare gain, scale economies are achieved, which then increase the magnitude of the welfare gain. Second, when scale economies are possible, price discrimination can yield a Pareto improvement even if no new markets open. . . . Third, scale economies may lead to new markets' opening under discriminatory pricing when new markets would not open without such economies.

   This paper does not dispute Hausman and Mackie-Mason's [3] ingenious analysis but it does show that economies of scale and learning are very much a doubled edged sword as far as the welfare effects of price discrimination are concerned. As a consequence, the presence of scale economies does not justify a more lenient regulatory attitude toward price discrimination. There are three reasons for this. First, note that if output falls instead of rising, a result that is by no means inconsistent with economies of scale, declining marginal costs will exacerbate the welfare loss from discriminatory pricing. Secondly, this paper shows that when price discrimination occurs and the firm's output is subject to scale economies, all prices can just as easily rise as fall. Thirdly, this paper demonstrates a new and surprising possibility that can occur under declining, constant or rising marginal cost: price discrimination can result in some markets not being served that would have been served under uniform pricing.

2. Price Discrimination Under Economies of Scale

   Two important theoretical results derived by Hausman and Mackie-Mason [3] are: (1) the demonstration (in the two sub-market case) that price discrimination can lower prices in both sub-markets and (2) a proof that declining marginal cost is a necessary condition for price discrimination to lower prices in all sub-markets when the price profit function is concave(4) and the sub-market demands...