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Article Excerpt
We analyze the short- and long-run implications of third-degree price discrimination in input markets. In contrast to the extant literature, which typically assumes that the supplier is an unconstrained monopolist, in our model input prices are constrained by the threat of demand-side substitution. In our model, the more efficient buyer receives a discount. A ban on price discrimination thus benefits smaller but hurts more efficient, larger firms. It also stifles incentives to invest and innovate. With linear demand, a ban on price discrimination benefits consumers in the short run but reduces consumer surplus in the long run, which is once again the opposite of what is found without the threat of demand-side substitution.
1. Introduction
* According to the extant theory on price discrimination in input markets, more efficient firms should pay a higher price. Consequently, more efficient firms and not their less efficient, smaller competitors should lobby for a ban on price discrimination. This implication follows from the common assumption of a monopolistic supplier, which optimally charges more efficient, larger firms a higher wholesale price. (1)
More efficient firms should, however, also have more attractive alternative options. We show that the presence of a viable threat of demand-side substitution reverses the results from the existing literature. More efficient firms now receive a discount compared to their less efficient rivals. A ban on price discrimination would thus only be welcomed by less efficient, smaller firms.
We also show that a ban on price discrimination may benefit consumers in the short run, although in the long run it tends to reduce consumer surplus and welfare through stifling firms' incentives to invest and innovate. Intuitively, although this represents only one of the identified mechanisms, under price discrimination a firm that grows through becoming more efficient will additionally benefit from the subsequently obtained larger discount. For the case of linear demand and without demand-side substitution, the extant literature has obtained instead that a ban on price discrimination increases investment incentives, as it then becomes harder for the supplier to hold up downstream firms.
Our model and results accord well with the objectives that are typically pursued when passing bans on price discrimination, such as the famous Robinson-Patman Amendments to Section 2 of the Clayton Act, namely to protect smaller or otherwise weaker competitors. (2) Our findings also support the common belief that by protecting weak competitors, the imposition of uniform pricing tends to reduce efficiency in the long run.
The case where a monopolistic supplier faces no threat of substitution may be relevant in industries where, given their choice of technology, intermediate firms become highly locked into a relationship with a particular supplier. Likewise, it may be applicable to natural monopolies. Note, however, that an unconstrained monopoly position is not a necessary prerequisite for a firm to fall under the relevant antitrust provisions that prohibit or restrict price discrimination. All that is needed is that the respective supplier is to a sufficient extent shielded from effective competition. Furthermore, mandatory provisions in regulated industries, in particular in network industries, also apply to firms that do not enjoy (or no longer enjoy) a monopolistic position. (3)
Our analysis proceeds as follows. In Section 2, we introduce the basic model. (4) Section 3 analyzes the case where intermediate firms operate in separate markets. The case of geographic market segmentation is particularly relevant for Europe. European law tightly restricts the scope for price discrimination along the boundaries of the European Union's member states. (5)
In Section 4, we introduce competition between intermediate firms, which creates the possibility for secondary line injury. (6) Secondary line injury occurs when price discrimination practices put some of a dominant firm's customers at a competitive disadvantage vis-a-vis other customers. One example, to which we will return later in more detail, is that of retailing. The rise of powerful, cross-border "big box" retailers such as Wal-Mart, Carrefour, and Tesco has led to concerns that their purchasing power distorts competition and unduly harms smaller rivals. Moreover, as shown by Dukes et al. (2006), while public prosecution under the Robinson-Patman Act has become rare in the United States, each year there are still approximately 14 private-party suits pursued. Although we show that restrictions on price discrimination in wholesale markets could indeed benefit consumers in the short run, in the long run the reverse picture emerges as it dampens downstream firms' incentives to invest. The article closes in Section 5 with some concluding remarks. All proofs can be found in the Appendix.
2. The model
* The basic setup follows much of the literature on price discrimination in an intermediate goods industry. We consider a single supplier that provides an input to the intermediate industry. Firms in the intermediate industry use the input to produce a homogeneous final good. Firms transform one unit of the input into one unit of the output. (7) The supplier produces at constant marginal cost, which we take to be zero to simplify our expressions. Also, without much loss in generality, we restrict attention to two downstream firms, i = 1, 2. We denote firm i's own constant marginal cost of production by [k.sub.i] [greater than or equal to] 0.
Our analysis distinguishes between the following two cases. In the first case, the two downstream firms serve independent markets. For most of our analysis, we assume that both markets are symmetric and thus characterized by the same inverse demand function P(q). In the second case that we analyze, both firms are active in the same market, offer homogeneous goods, and compete in quantities. In both cases, we assume that P(q) is strictly decreasing and twice continuously differentiable where P(q) > 0. Moreover, we employ the standard assumption that P' 0. (8)
In specifying next the contractual game, we follow again closely the extant literature. The supplier can make take-it-or-leave-it offers to downstream firms. (9) Under price discrimination, the supplier thus offers each firm a possibly different wholesale price [w.sub.i], whereas under uniform pricing the same price [w.sub.i] = w applies to both firms. Consequently, upon accepting the supplier's offer, a firm's total marginal cost equals [c.sub.i] := [w.sub.i] + [k.sub.i]. Our restriction to linear contracts, which we discuss in detail after presenting our first results, is shared with much of the literature on third-degree price discrimination.
Our main deviation from most of the literature is that despite having the ability to make take-it-or-leave-it offers, the supplier is no longer an unconstrained monopolist. Here we follow Katz (1987) and suppose that instead of ceasing operations when rejecting the supplier's offer, a downstream firm can turn to an alternative source of supply. As in Katz (1987), this comes at costs F > and allows the respective firm to obtain the input at constant marginal costs [??] [greater than or equal to] 0. (10) Below we also discuss the possibility that the alternative input is only an imperfect substitute.
In Katz (1987), the buyers' alternative is that of backward integration, which is viable only for the largest buyer. In contrast, we focus our analysis on the case where the threat of demand-side substitution is credible for all firms. An alternative interpretation could be that the costs F are incurred to adopt another technology, which then allows purchasing a different input at the (competitive) price of [??]. Below we will also discuss the possibility that after rejecting the supplier's offer, a buyer can reduce [??] by expending more resources, for example by searching more intensively for a low-price alternative or, in the case of backward integration, by making higher investments. (11) There we will also discuss the applicability of our model to different industries.
The final part of our model is an initial investment stage. Following DeGraba (1990), each downstream firm can reduce its own marginal cost [k.sub.i]. (12) Precisely, a firm reduces its initial cost [[bar.k].sub.i] > by [[DELTA].sub.k] after incurring the expenditure e([[DELTA].sub.k]). We suppose that e is strictly increasing and continuously differentiable with e' (0) = and e' ([[DELTA].sub.k]) [right arrow] [infinity] as [[DELTA].sub.k] [right arrow] [[bar.k].sub.i], which allows us to focus on interior solutions. The chosen investment levels and, consequently, the respective values of [k.sub.i] are common knowledge. Our equilibrium concept is that of subgame perfection. We restrict attention to equilibria in pure strategies.
3. Separate markets
* The short run. In this section, we stipulate that two monopolists serve two segmented markets. In the short run, we take firms' own marginal costs [k.sub.i] as given. The long run, where [k.sub.i] is endogenous, is analyzed subsequently.
Firm i optimally chooses the unique quantity q ([c.sub.i]) := arg maxq {q [P(q) - [c.sub.i]]} and realizes the profits [pi] ([c.sub.i]) := q([c.sub.i])[P(q([c.sub.i])) - [c.sub.i]], where both q and [pi] are strictly decreasing in [c.sub.i] as long as P(0) > [c.sub.i]. In case the supplier's profits q([c.sub.i])[w.sub.i] are strictly quasiconcave where q > 0, an unconstrained monopolist would optimally choose the discriminatory prices
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
Turning to the case of a constrained supplier, note first that for firm i the value of the alternative supply option equals
[[pi].sup.A.sub.i] := [pi]([??].sub.i] - F, (2)
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] denotes the respective marginal cost. Consequently, the supplier's offer to firm i must satisfy the respective participation constraint
[pi]([c.sub.i])[greater than or equal to] [[pi].sup.A.sub.i]. (3)
In what follows, we first focus on the case where [[pi].sup.A.sub.i] is sufficiently attractive such that for each firm i the respective
condition (3) constrains the supplier's optimal choice of [w.sub.i]. This is in turn the case if the monopolistic input price [w.sup.UC.sub.i] is high enough, that is, if [pi] ([c.sub.i]) < [[pi].sup.A.sub.i] holds for [c.sub.i] = [k.sub.i] + [w.sup.UC.sub.i]. As is straightforward to show, this is in turn always the case if both F and [??] are not too large. In what follows, we assume that this is the case. We obtain the following result (all proofs not found in the text are presented in the Appendix).
Proposition 1. In the case with separate markets and price discrimination, wholesale prices [w.sub.i] are strictly increasing in own marginal costs [k.sub.i].
To see why in our model a supplier that is constrained by the threat of demand-side substitution grants the more efficient firm a discount, note first that a reduction of [k.sub.i] increases both the firm's profits under the supplier's offer, [pi] ([c.sub.i]), and the value under its alternative supply option, [[pi].sup.A.sub.i] = [pi]([[??].sub.i]) - F. As we argue next, however, the effect on [[pi].sup.A.sub.i] is strictly larger, implying that a reduction in [k.sub.i] tightens the participation constraint (3). This in turn makes it necessary to reduce [w.sub.i].
It thus remains to argue why a reduction in [k.sub.i] has a larger effect on the "off-equilibrium" profits [[pi].sup.A.sub.i] than on the "on-equilibrium" profits [[pi]([c.sub.i]). This results from the following two observations. First, note that a firm's profits [pi](c) are strictly convex in c. Intuitively, if c is already low and the firm thus produces a higher quantity, then it benefits more from a further reduction. The second observation is that for given [k.sub.i], the firm's total marginal costs are indeed lower under the outside option, that is, [c.sub.i] > [[??]sub.i]. Recall that this follows from the fact that from F > the supplier can charge an additional margin above [??] such that [w.sub.i] > [??]. (13)
It should also be noted that the argument for why there is a size discount in our model is different from that in Katz (1987). As discussed previously, in Katz (1987) only the large retail chain, which operates in several independent markets, has a credible option of backward integration. Expressed with our notation, the participation constraint of a (monopolistic) retailer operating in, say, two independent markets would in analogy to (3) become 2[pi] ([c.sub.i]) [greater than or equal to] 2[pi]([??])...
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