Third-Degree Price Discrimination in Input Markets: Output and Welfare

Abstract

If price discrimination is realized, the economy shifts from one equilibrium to another. It clearly involves welfare effects: The price-discriminator clearly gains, some consumers may also gain from the price cut, but others may lose faced with higher prices, etc. Traditionally the change in social welfare is known to be closely related to the change in total output. In the case of third-degree price discrimination, it is well known that an increase in total output is a necessary condition for welfare improvement. Richard Schmalensee (1981) proves this fact in a model in which the monopolist with constant marginal cost can perfectly separate markets. Further, Hal R. Varian (1985) extends this result to the case of interdependent markets, permnitting increasing marginal cost of the monopolist. And finally, the assumption of nondecreasing marginal cost is eliminated by Marius Schwartz (1990). Roughly speaking, this proposition says that if there is a welfare gain from price discrimination, there has to be some gain to offset the distortion involved. On the other hand, the vast majority of legal and other policy disputes over the price discrimination concern input markets, not final good markets. Thus, it seems important to investigate the situation in which a discriminating monopolist is not a final good supplier but an input supplier, and the buyers of the input are downstream producers of a final good, as is assumed in this paper. If the downstream firms have different technologies, their input demand functions will be different, and thus the monopolist has an incentive to price-discriminate. In this scenario, Michael L. Katz (1987) and Patrick DeGraba (1990) study the effect of inputmarket price discrimination, and show that price discrimination always lowers welfare because it involves the distortion that a lower-cost downstream firm is assigned a higher price. Unfortunately, in their simple settings on the technology of downstream industry, price discrimination can never change total output (of the input or of the final good).1 Thus we must say that welfare effect of input-market price discrimination remains open to question if it has some effect on total output. In particular, we are curious as to whether we can obtain some close relationship between the changes in welfare and total output as we have obtained in the final good market settings. With this motivation, we will construct a model which involves change in total output (of the final good). In the next section, the model and assumptions are provided. In Section II, after we extend the result of Katz (1987) and DeGraba (1990), we find a relationship between the changes in welfare and total output. Strikingly, it states that an increase in the total output of the final good is a sufficient condition for welfare deterioration. This result contrasts with that obtained by Schmalensee (1981), Varian (1985), and Schwartz (1990) from usual models of price discrimination in a final good market. Section III concludes the analysis.