Third-degree price discrimination in oligopoly with endogenous input costs

Highlights

• This paper analyzes the output effect of third-degree price discrimination in oligopoly.

• The sign of the output effect can change when input costs are chosen endogenously by an upstream supplier with market power, rather than fixed exogenously.

• When input costs are endogenous, more intense competition in the strong market than in the weak market can make it less likely that discrimination raises aggregate output.

Abstract

This paper examines the output effect of third-degree price discrimination in symmetrically differentiated oligopoly. We find that when the sellers’ input costs are chosen endogenously by an upstream supplier with market power, as opposed to being fixed exogenously, long-standing qualitative conclusions about the effect of price discrimination on aggregate output can be reversed. In contrast to previous findings (e.g., by Holmes, 1989), more intense competition in the strong market than in the weak market can make it less likely that price discrimination raises aggregate output. For linear demand functions, we establish necessary and sufficient conditions under which the output effect changes sign when input costs are endogenized.

Introduction

Whether third-degree price discrimination raises or harms social welfare is a question of long-standing interest in economics. A critical ingredient to answering this question is the impact of price discrimination on aggregate output. This is because for a given level of aggregate output, price discrimination implies a misallocation of consumption relative to uniform pricing, by shifting output from high-value to low-value uses. An increase in aggregate output can offset this negative consumption allocation effect and make price discrimination welfare-improving.¹ Not surprisingly, therefore, much of the literature’s attention since Pigou (1920) and Robinson’s (1933) seminal works has focused on deriving conditions under which price discrimination raises or lowers aggregate output.

Pigou (1920) and Robinson (1933) found that price discrimination by a monopolistic seller keeps aggregate output unchanged when demand curves are linear and all markets are served at the uniform price. Subsequent work has shown that the sign of the output effect depends on the relative curvatures of the demand curves and, in the case of competing sellers, the relative intensities of competition in the different markets. Aguirre et al. (2010), for example, have shown that third-degree price discrimination by a monopolistic seller tends to raise aggregate output if demand is more convex in the weak market (where price falls) than in the strong market (where price rises).² In the context of symmetric oligopoly, Holmes (1989), Aguirre (2019), and others, have shown that, all else equal, aggregate output is more likely to increase under third-degree price discrimination if competition is more intense in the strong market than in the weak market.³

Nearly all of this literature treats the input costs and other input supply terms faced by the firms that engage in price discrimination as fixed.⁴ In many cases, however, firms that practice price discrimination in final-goods markets procure inputs from upstream firms that possess some market power. These upstream firms will typically find it optimal to adjust their supply terms, including the marginal input prices charged to downstream firms, depending on the downstream pricing regime (price discrimination versus uniform pricing). This matters for the effects of price discrimination, because if marginal input prices are adjusted upward under price discrimination relative to uniform pricing, downstream prices will adjust upward as well and any aggregate output gain from price discrimination will be lessened, or turn into an output loss. The opposite holds if marginal input prices are adjusted downward.

This paper takes a first step toward understanding how aggregate output is affected when the input costs of the firms that practice price discrimination are determined endogenously by an upstream supplier with market power. We find that endogenizing input costs can affect both the magnitude and the sign of the output effect of price discrimination. Taking these changes into account can even lead to a reversal of some of the literature’s long-standing qualitative conclusions. Instead of output being more likely to increase under third-degree price discrimination if competition is more intense in the strong market than in the weak market, as in Holmes (1989), for example, we find that the opposite may hold: output may be less likely to increase if competition is more intense in the strong market than in the weak market.

Assuming linear demands, and focusing on the case of a monopolistic supplier offering two-part tariffs to symmetrically differentiated downstream firms that compete in prices (essentially the set-up in Holmes (1989), but with an upstream firm that sells an essential input), we derive necessary and sufficient conditions that determine whether the output effect changes sign when supply tariffs are endogenized. These conditions involve the diversion ratios across competing goods and the monopoly prices (i.e., the prices that maximize the joint profits of the supplier and downstream firms) in the strong and the weak market.

Specifically, we find that the output effect changes sign if and only if either (i) the diversion ratio is higher (competition is fiercer) in the strong market than in the weak market, and the monopoly price in the weak market does not exceed the monopoly price in the strong market by too much,⁵ or (ii) the diversion ratio is lower (competition is less fierce) in the strong market than in the weak market, and the monopoly price in the weak market is sufficiently less than the monopoly price in the strong market. In the first instance, aggregate output increases with discrimination under a fixed wholesale price, but it decreases when the supply tariff is determined endogeneously. In the second instance, aggregate output decreases with discrimination under a fixed wholesale price, but it increases when the supply tariff is determined endogenously.

Our paper is related to three strands of the literature on price discrimination. First, as discussed, our paper extends the vast literature on the effects of third-degree price discrimination in final-goods markets by incorporating a strategic upstream supplier.

Second, our paper relates to the literature on price discrimination in intermediate-goods markets (see, e.g., Katz, 1987, DeGraba, 1990, Yoshida, 2000, Inderst, Valletti, 2009, and O’Brien, 2014), which analyzes the effects of allowing a supplier to discriminate across different downstream firms.⁶ What distinguishes our paper from this literature is that, although we also consider a vertical industry structure, we focus on the effects of price discrimination in the final-goods market. Discrimination by the supplier across downstream firms plays no role in our model.

Third, the analysis in this paper is related to our work on input price discrimination by resale market in Miklós-Thal and Shaffer (2019). In that paper, we consider a setting in which a supplier sells to competing multi-market downstream firms that practice third-degree price discrimination, and we analyze the effects of allowing the supplier to set different wholesale prices for the same input depending on where it is resold by the downstream firms (e.g., online versus off-line, or in different geographic locations). In contrast, in the present paper, the supplier cannot discriminate by resale market, and we analyze the output effect of allowing the multi-market downstream firms to move from uniform pricing to third-degree price discrimination.