Forward contracts and competition - Springer Link

Span. Econ. Rev. 4, 281–300 (2002)

c Springer-Verlag 2002

Forward contracts and competition Manel Antelo1 , Llu´ıs Bru2 1 2

Departamento de Fundamentos da Análise Económica, Universidade de Santiago de Compostela, Campus Norte, 15782 Santiago de Compostela, Spain (e-mail: [email protected]) Departamento de Teor´ıa e Historia Económica, Universidad de Málaga, Plaza El Ejido, 29071 Málaga, Spain (e-mail: [email protected])

Abstract. This paper examines the strategic use of forward contracts in an industry where downstream firms must buy an essential input from imperfectly competitive upstream suppliers. When a single large firm and a fringe of firms exist downstream, the large firm buys forward contracts from the fringe, i.e. there is horizontal subcontracting from the large firm to the firms on the fringe, in order to make the spot market less competitive. Hence our paper argues that horizontal subcontracting becomes an anti-competitive device. We also compare the strategies of buying forward contracts and purchasing productive capacity and we find that both are equivalent tools. When the downstream industry has instead several large firms, they have a “horizontal” incentive to sell forward contracts in order to gain market share, but the former “vertical” incentive to buy them persists. In this case, forward contracting may then lead to less competition in the spot market. JEL classification: L13, L22, L23 Key words: Intermediate markets, buyer power, forward contracts, horizontal subcontracting 1 Introduction Forward contracting is a common practice in many industries with an oligopoly structure. In some of them, forward contracts sometimes adopt the form of horizonWe are indebted to Ramon Faul´ı-Oller, José Manuel Ordón˜ ez and Juan Carlos Reboredo for their helpful comments and suggestions on an earlier draft. We also gratefully acknowledge the valuable observations made by two anonymous referees and a Co-Editor that led to substantial improvements. Of course, the usual disclaimer applies. Antelo acknowledges financial support from the Xunta de Galicia (Grant PGIDIT02PXIA20101PR) and Bru that from the Spanish Ministerio de Ciencia y Tecnolog´ıa (Grant PB98-1402).

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tal subcontracting, namely rival firms that operate in the same stage of the industry agree to produce some output for the others. In the telecommunications sector, for instance, the so-called ‘Original Equipment Manufacturers’ usually subcontract a great proportion of their production to firms named as ‘Electronics Manufacturers Services’ (see The Financial Times 15.07.2001 and El Pa´ıs Negocios 15.07.2001). In other industries, forward contracts take place in a more or less organized futures market. As an example, the deregulation process in the power industry, with its general trend to the vertical break-up of formerly regulated firms, has led to the appearance of forward contracts for reserves, energy and transmission facilities (see Wilson 2002). Moreover, market power holds in many steps of this industry due to several reasons: gas is a basic input for power generators and is provided by a few number of firms, transmission constraints gives rise to local power market at many stages of such an industry, and so on. But, how does the presence of forward contracting affect the possibility of market manipulation by dominant or market power firms? This is the issue we want to address in this paper. For that, we consider a vertical structure in which both the upstream and downstream segments of the industry are composed by either one dominant firm or several dominant firms and a fringe of price-taking firms. We add, moreover, the existence of a forward market for the final good. In our set-up, a horizontal subcontracting agreement that leads fringe downstream firms to produce for the dominant downstream firm, rather than directly for consumers, unambiguously yields more collusion in the final market. If a dominant downstream firm buys forwardly one part of the production of price-taking rivals, it obviously reduces its own production. Hence, the market performance will be less competitive. We show below that the existence of imperfect competition in the intermediate market makes the purchase of forward contracts a profitable strategy for such a dominant or large downstream firm. In fact, with imperfect competition in the upstream side of the industry, the superior buyer power of the dominant downstream firm against input suppliers allows such a firm to appropriate one part of the additional rents created by the horizontal subcontracting agreement. As a consequence, our analysis suggests that a large downstream firm may use horizontal subcontracting as an anti-competitive device. In other words, a “vertical” strategic incentive to buy forward contracts arises in this context. Interestingly, we also show that, for a large downstream firm, to buy contracts in a forward market (or subcontracting to price-taking firms) is strategically equivalent –and hence may be used as an alternative tool– to the acquisition of productive capacity from the fringe. The existence of an imperfect intermediate market for basic inputs, therefore, may lead to a consolidation process in the marketing sphere of the industry, without an accompanying process of consolidation in the production phase of the good. However, its negative impact on market performance will be the same. Until now we have exclusively mentioned the strategic use of forward contracts in a “vertical” way. But imperfectly competitive firms may also strategically use forward contracting in a “horizontal” way, in order to modify the behavior of noncompetitive rivals in the spot market. The literature on forward contracting when the strategic use of futures contracts is entirely “horizontal” is rather optimistic in

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its conclusions (see Spiegel 1993 and Allaz and Vila 1993). However, this literature does not consider the effects of forward contracts in the presence of imperfect competition upstream, but it concentrates on the strategic interaction between two or more rival firms of a vertically integrated industry. In particular, Spiegel (1993) points out that horizontal subcontracting agreements only take place when firms have asymmetric costs. In such a case, subcontracting promotes productive efficiency to the point that may enhance welfare even when sometimes it leads to a more collusive outcome. Likewise, Allaz and Vila (1993) show that each firm in an oligopoly has an incentive to sell forward its production (to final consumers and/or firms on the fringe) in order to behave more aggressively in the spot market and increase its market share at the expense of rivals. In this framework, forward contracting is clearly pro-competitive. Contrariwise to Spiegel (1993), we assume in our model that downstream firms are all equally efficient, and hence the rationale for forward contracting of production placed in cost asymmetries is ignored. Moreover, we show that in a vertical structure, when there is imperfect competition in the upstream segment and several dominant or large firms downstream, the impact of forward competition on market performance is not unambiguously pro-competitive. Forward contracting may lead indeed to anti-competitive effects. The reason is due to the fact that the strategic use of forward contracts is not only governed by a “horizontal” strategic effect, but also by a “vertical” strategic effect. As a consequence, the latter may outweigh the former, and in any case, in the presence of imperfectly competitive intermediate markets, one should not expect from the use of forward contracts the increase in competitiveness suggested by Allaz and Vila (1993). The rest of the paper proceeds as follows. Section 2 contains the basic model. In Sect. 3, we derive results for a setting where the downstream side of the industry is composed of a single large firm together with a competitive fringe. In Sect. 4, we find that subcontracting of production and acquisition of productive capacity are equivalent tools for a non-competitive firm. In Sect. 5, we show how things work when two large firms and a competitive fringe operate in the downstream segment of the industry. Finally, Sect. 6 concludes. Formal proofs of the results are collected in the Appendix. 2 The model We consider an industry with input suppliers (upstream firms) and manufacturers and retailers (downstream firms). Upstream, there is one super-competitive supplier able to produce an essential input for the downstream industry at marginal cost c, c ≥ 0. There is also a competitive supply of the input at marginal cost c¯, c¯ > c. The input is transformed with no additional production costs into a final product in a one-to-one basis by downstream firms, which also sell the product to final consumers. Downstream, there is a single dominant firm together with competitive firms. These fringe firms use the same technology as the non-competitive firm and also have access to the final market. For saving on notation, we refer from now on to the super-competitive upstream firm as the efficient supplier and to the dominant downstream firm as the large firm.

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Upstream and downstream firms of the industry set vertical contracts that establish the terms under which the input is transferred. Specifically, the efficient supplier offers a two-part tariff to the large firm, which may accept or reject the deal. In the case of refusal, the large firm buys the input from the competitive suppliers at price w = c¯ per unit of input, which is the unit price that downstream fringe firms always pay. The final product is homogeneous and the market demand is given by P (Q), with P (Q) < 0. To this quite standard model of vertical relationships we incorporate the possibility of undertaking forward contracts in the downstream segment of the industry. Such forward contracts may consist of horizontal subcontracting agreements among downstream firms, by which some of them produce for others, rather than directly for consumers, in return for a transfer payment. Forward contracting may also arise in an organized futures market for the output, in which firms commit themselves through futures contracts to sell or buy a given amount of output at a pre-specified price (the so-called futures price) when the spot market opens.1 Finally, while in some industries the main role of forward contracts seems to be hedging against risk (see Newbery 1984 and 1987), we will ignore uncertainty in order to concentrate on the strategic use of forward contracts by firms with market power. After all, this is a common modeling strategy in the literature (see, for instance, Allaz and Vila 1993). Throughout the paper, kL denotes the capacity of production of the large firm, m stands for the capacity of production of the competitive fringe as a whole, q is the production of the large firm, pf stands for the futures price and f denotes the amount of forward contracts undertaken by the large firm. In particular, f > 0 means that the large firm sells a positive amount of output in the futures market (it is selling forward contracts), i.e. it sells one part of its production to other firms instead of selling it directly in the spot market. Contrariwise, f < 0 means that the large firm purchases output in the futures market, i.e. it is buying forward contracts or, equivalently, it is partially or entirely subcontracting its production to fringe firms. In this case, the large firm sells in the spot market its own production and the “subcontracted” one as well. Thus, in general, the level of sales of the large firm in the spot market will be given by q − f and total production of the industry by Q = q + m. We finally assume that contracting stage for the output comes before downstream firms buy the basic input, and that quantities forwardly contracted are publicly observable. More specifically, the sequence of actions we assume for the full game may be described as follows: Stage 1. Forward contracts for the output are signed. Stage 2. The efficient supplier offers an input contract to the large firm. Production costs of the large firm are given by wq + F if it accepts the offer, where F is a lump sum payment, and by c¯q in the case of refusal. 1 If there is a futures market, such forward contracts may be established not only among firms, but agents such as final consumers, speculators, market makers, and so on, may also intervene.


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Stage 3. Downstream firms compete among them by setting quantities in the final market for the good. This timing of the game is aimed at reflecting the fact that forward contracting for the output is the more long-term action. Later on, we discuss the role played by this timing in the results obtained. As usual, we look for a subgame-perfect Nash equilibrium of this three-stage game.

3 Solving the game The following restrictions on demand and cost are assumed throughout Sections 3 and 4 of the paper: Assumption 1. P (kL + m) ≥ c¯. Assumption 2. P (q + m)q + 2P (q + m) < 0, ∀q ∈ (0, Q]. Assumption 3. P (m)m + P (m) − c¯ > 0 and P (kL )kL + P (kL ) − c < 0. Assumption 1 guarantees that the final price of the good is always above c¯, and hence implies that fringe firms always produce at full capacity. Likewise, Assumptions 2 and 3 guarantee that the problem of the large firm in the third stage of the game is concave and that it has an interior solution. The subgame-perfect equilibrium of this three-stage game is calculated backwards. Once the amount of forward contracts, f , the price of futures contracts, pf , and the terms of the input contract are all set, the objective function of the large firm in the third stage of the game is given by profits (gross of any fixed fee) π (w, f, q) = P (q + m)(q − f ) − wq + pf f . So, this firm solves the problem M ax π(w, f, q), s.t: f ≤ q ≤ kL . q

(1)

In this stage of the game, the level of forward contracting has already been decided, so the objective function of the large firm includes the term P (q+m)(−f ), i.e. the revenues to be obtained from selling −f in the spot market (if f < 0) or the reduction of revenues in the spot market (if f > 0). Of course, the large firm takes into account the profits to be obtained through −f when it decides the optimal level of production, q(w, f ). The first-order condition of the problem (1) is given by 0 = P (q + m)(q − f ) + P (q + m) − w,

(2)

and Assumption 2 implies that the optimal production arisen from (2) is decreasing in w and increasing in f .2 In other words, the large firm reduces its production level as its marginal cost of production increases. The large firm also reduces its production when it buys output from the competitive fringe in the futures market (i.e. when f < 0), since the increase in sales from q to q − f leads to a larger For a linear demand specification as P (Q) = A − Q, where A > 0, which meets the conditions previously imposed in Assumptions 1–3, the optimal level of production of the large firm is given by q(w, f ) = 21 (A − m + f − w). 2

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profitability for the large firm of any increase in the spot price. Both effects will be crucial in the behavior of the large firm during the first stage of the game. Define the indirect gross profit function of the large firm as Π(w, f ) ≡ π (w, f, q(w, f )). In the second stage of the game, the efficient supplier offers a two-part tariff contract for the input, T (q) = F + wq, to the large firm. In such a contract, by setting the marginal wholesale price w = c, the large firm has the same marginal cost than the efficient supplier, and hence chooses the optimal level of production, given f . Therefore its profits are Π(c, f ) − F . On the other hand, the large firm has the alternative option of buying the input from competitive suppliers at wholesale price w = c¯, in which case its profits amount to Π(¯ c, f ). Finally, the efficient supplier can appropriate the increase in the large firm’s profits by imposing in the input contract a fixed fee F equal to Π(c, f )–Π(¯ c, f ), by which net profits of the large firm are in fact Π(¯ c, f ).3 Given that we model fringe firms as a total level of capacity, m, and that Assumption 1 implies that fringe firms always produce at full capacity, we need not be very specific about how fringe firms buy the input. In any case, for the efficient supplier it is optimal to sell them the input at a wholesale price slightly below c¯. If it turns out to be the case that the efficient supplier serves all downstream firms, then internal production is efficient. In the first stage of the game, the large firm’s profit function is c, f ) + m)] f, Π (¯ c, f ) = [P (q(¯ c, f ) + m) − c¯] q(¯ c, f ) + [pf − P (q(¯

(3)

and such a firm decides upon its optimal level of forward contracts, which is the one that solves the problem c, f ), s.t: − m ≤ f ≤ kL . M ax Π(¯ f

(4)

Under rational expectations, fringe firms correctly infer the final spot price. In fact, they observe the level of forward contracts, f , and may evaluate the impact caused by f on final or spot prices (through the effect of f on the expected level of production of the large firm). We also impose a no-arbitrage condition in the sense that if fringe firms sell their product in both the futures and the spot markets, then prices must not leave any arbitrage opportunity. Formally, pf = P (q(c, f ) + m).

(5)

Thus, the price given in (5) is the price to be paid for production contracted in the futures market. The large firm may be interested in buying output from the competitive fringe in order to reduce total production, and hence to increase the price in the spot or final market. When it chooses the level of futures contracts f , however, it must take into account how f affects the price of forwards. Fringe firms 3 We assume that the efficient supplier obtains all the rents only for the sake of simplicity. We could allow some sharing of such rents between the efficient supplier and the large downstream firm, by assuming, for instance, that profits of the large firm are given by βΠ(c, f ) + (1 − β)Π(¯ c, f ), with 0 < β < 1.


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will ask for higher futures prices if they expect an increase in final prices. From the envelope theorem, the first-order condition of the problem (4) is 0=

∂Π ∂Π ∂q + ∂f ∂q ∂f

= pf − P (q(¯ c, f ) + m) +

∂pf f, ∂f

(6)

and once the no-arbitrage condition (5) is plugged into (6), the first-order condition (6) may be rewritten as 0 = P (q(c, f ) + m) − P (q(¯ c, f ) + m) + P (q(c, f ) + m)

∂q (c, f ) f. ∂f

(7)

c, f ) + m), The first term on the right-hand side of (7), P (q(c, f ) + m)−P (q(¯ reflects the difference in buyer power (in the intermediate market) between the large firm and any firm on the competitive fringe. This is the strategic effect of the futures market vis-à-vis the efficient input supplier (the so-called “vertical” strategic effect of forward contracting). Fringe firms sell each unit of product at price P (q(c, f ) + m), while the large firm has the possibility of rejecting the offer from the efficient supplier, in which case it sells a smaller amount, q(¯ c, f ) − f , at price P (q(¯ c, f ) + m), which is strictly above the equilibrium price.4 Although this is an off-the-equilibrium price, this is the relevant one for the large firm to compute its net profits, Π (¯ c, f ). Thus, if it buys the amount of product –f in the futures c, f ) + m)]. Such an market, it gets an extra margin of − [P (q(c, f ) + m) − P (q(¯ extra margin reflects the fact that the large firm has more buyer power against the efficient supplier than any fringe firm, since it is the only one that can affect the level of spot prices. It is clear that if c¯ − c = 0, the strategic effect of forward contracting vis-à-vis the efficient upstream supplier vanishes and all downstream firms pay the same wholesale price for the input. So the only remaining effect on the right-hand side ) of (7) is the one reflected in the term P (q(c, f ) + m) ∂q(c,f ∂f f , which is the direct effect of forward contracts. It measures the impact of forward contracting in final prices mediated by the change in the production level of the large firm. In this framework, the strategy f > 0 is not optimal for such a firm because it would lead to higher production and hence lower prices. Likewise, to set f < 0 is also unprofitable for the large firm because any increase in final prices induced by the purchase of forward contracts would go freely to the competitive fringe through an increase in futures prices. The large firm is then induced to choose f ∗ = 0 when c¯ − c = 0, i.e. it neither wants to sell nor to buy futures contracts.5 Summing up, the introduction of an efficient input supplier in the upstream side of the industry and the difference in buyer power between the large firm and the competitive fringe of the downstream segment of the industry lead to the following proposition. Recall from the first-order condition (2) that q(w, f ) is a decreasing function of w. Newbery (1984) already pointed this out. He also shows that the large firm will act strategically in the futures market if fringe firms are risk-averse. 4 5

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Proposition 1. Under Assumptions 1, 2 and 3, if a single large firm exists in the downstream segment of the industry, then: (a) In equilibrium, the large firm buys forward contracts, namely f ∗ < 0. (b) In the case of a linear demand as P (Q) = A − Q, where A > 0, it holds that −f ∗ = min {¯ c − c, m}. Proof. See the Appendix. This proposition shows that the large firm subcontracts to the competitive fringe the amount −f ∗ of output. Although competitive firms have direct access to the final market and the large firm does not have any marketing advantage in terms of costs, fringe firms sell part of their production forward to the large firm, rather than directly to consumers, and sometimes they do not even enter into marketing activities at all and only produce for the large firm. Hence we obtain a rationale for horizontal subcontracting closely related to the difference in buyer power (in the intermediate market) among firms of the downstream segment of the industry. From Proposition 1, unambiguous results are obtained with respect to the effects on market performance and on consumer surplus coming from the existence of a futures market. These are contained in the following corollary. Corollary 1. When there is a single large firm in the downstream industry, the existence of a futures market leads to: (a) A reduction in total production, (b) an increase in final prices, (c) an increase in profits of all downstream firms, and (d) a reduction in profits of the efficient upstream supplier. Proof. See the Appendix. The possibility of subcontracting by the large firm, f ∗ < 0, is harmful for consumers as this allows such a firm to profitably exert a higher market power downstream by means of a reduction in total sales. Thus, the industry becomes less competitive. In the same way, it follows from Corollary 1 that aggregate welfare, defined by the sum of consumer surplus and profits of the industry, decreases when the large firm subcontracts one part of its production to firms on the fringe. Subcontracting is just a device for the large firm to exercise additional market power downstream. Interestingly, and as the next section below makes clear, the large firm may replicate by subcontracting the same results that it could obtain by purchasing productive capacity from the fringe. It is worth noticing that imperfect competition upstream, perfect observability of forward contracts, and the specific timing on the signature of contracts between upstream and downstream firms assumed above, are all crucial conditions for Proposition 1 to hold. With respect to the first assumption, it follows that the large firm buys a lower amount of forward contracts and the final market tends to be more competitive as the difference in costs between the efficient supplier and suppliers on the fringe, c¯ − c, decreases. Thus, an increase in competition upstream, in the sense of input suppliers more symmetric in costs, is welfare enhancing because it drives to an increase in competition downstream. As we have already discussed above, in the


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case of c¯ = c the large firm does not use the futures market at all, since there is not any strategic gain to be obtained against input suppliers. On the other hand, forward contracts become a commitment device against the efficient supplier only if the level of contracts, f , is publicly observable. The intuition is as follows: The buyer power of the large firm depends on the alternative option to buy the input from competitive suppliers at wholesale price w = c¯, in which case its profits amount to Π(¯ c, f ). When the efficient supplier observes the large firm position in the futures market, it imposes the fixed fee F = Π(c, f ) − Π(¯ c, f ) in the input contract and the large firm has net profits Π(¯ c, f ). Hence the large firm may modify the fee through the strategic choice of f . However, when the efficient supplier does not observe f , the two-part tariff offered contains a fixed fee that can only depend on the conjectured level of futures contracts, not on the actual level, f . The efficient supplier anticipates that the large firm sets a given level of contracts f c (where superscript c indicates the conjectured or anticipated value of f ). In stage one, the large firm knows that its choice of f is not going to influence the anticipated value of f c . In other words, the large firm cannot modify its buyer power in the intermediate market through its level of futures contracts. But as its choice of f will distort its output decision in stage three, such firm has an obvious incentive to set f = 0 at time one (and this is true regardless of the particular value taken by f c ). Therefore, the game with unobservable forward contracts is characterized by a unique (Perfect Bayesian) Nash equilibrium in which f ∗ = f c = 0. Notice that in our model the large firm benefits from making its level of forward contracts public, since this increases its buyer power. In more general terms, one can argue that transparency in contracts market may not only have a pro-competitive effect (as Allaz and Vila 1993 point out and we discuss further on in Sect. 5), but may also be a necessary condition for the good functioning of any industry as has been widely discussed in electricity markets (see, for instance, Powell 1993). This author indeed suggests that observability has two social benefits: It is easier for entrants to evaluate the profitability of entry, and it becomes more difficult to practice any price discrimination against final consumers. However, Proposition 1 shows that transparency may be anti-competitive when there is imperfect competition in the provision of basic inputs, since large downstream firms will tend to use the futures market in a “vertical” strategic way, i.e. to obtain more bargaining power against the input supplier. Finally, we may consider what would happen if the order of first and second stages of the game were reversed, namely if the contract for the input was signed before the futures market opens. In such a case, the large firm is already committed to operate at wholesale price w (the optimal two-part tariff would have w = c), by which any increase in final prices induced from buying futures contracts would go to the fringe through the increase in the price of the futures market. Formally, for any input contract T (q) = F + wq, gross profits of the large firm would be given by Π(w, f ) = [P (q(w, f ) + m) − w] q(w, f ) + [pf − P (q(w, f ) + m)] f. (8)

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From (8), the effect of futures contracts on gross profits of the large firm would be measured by the derivative ∂Π(w, f ) ∂pf = pf − P (q(w, f ) + m) + f ∂f ∂f ∂q(w, f ) f, = P (q(w, f ) + m) ∂f

(9)

where we set pf = P (q(w, f ) + m). In this case, it is clear that the large firm could not retain any of the additional rents created in the downstream industry from an increase in final prices. Thus, the optimal level of forward contracts for the large firm would be f ∗ = 0 and the existence of a futures market becomes innocuous. In the timing of the game we have analyzed, the efficient supplier and the large firm agree on the contract for the input only once the futures market is opened. This is, we believe, a sensible assumption for industries where fast technical progress makes it difficult to set long-term contracts for inputs provision. It is clear, however, that in other industries, upstream and downstream firms have the possibility to agree on input contracts both before (long-term input contracts) and after the futures markets are opened. Or they could even vertically integrate. A good example of this is the case of the two Spanish firms Gas Natural SA –a gas supplier– and Endesa SA –an electricity generator– that signed in the year 2000 a multi-year contract for gas supply (see Cabral 2000). We can more generally discuss what happens if firms can contract both before and after the futures market opens. As long as the input contract is established before the futures market opens, the optimal level of forward contracts we arrive at is f ∗ = 0, as there is no strategic incentive to use forward contracts. This does not mean that the existence of a futures market becomes innocuous in this context, but that the only change is in the buyer power of the large firm. When the efficient supplier offers a long-term contract for the input (before the futures market opens), and if there is still the possibility –in case of disagreement– to set a short-term contract (i.e. after the futures market opens as is the case all along the paper), the outside option for the large firm provides it the profits Π(¯ c, f ∗ ). Hence the efficient supplier must offer a contract with a fixed fee F satisfying the condition Π(c, 0) − F ≥ Π(¯ c, f ∗ ).

(10)

Condition (10) means that although in equilibrium the large firm subcontracts no part of its production to the fringe, the mere possibility of such a “threat” gives it more buyer power because its outside option increases the profits from Π(¯ c, 0) to Π(¯ c, f ∗ ), with f ∗ < 0. Hence a long-term contract for the input increases the level of profits of the “efficient supplier-large firm” structure as there are no strategic distortions. Interestingly, it also benefits consumers, as we have seen that the effect of forward contracting is to reduce total production.6 6 The contract between Gas Natural SA and Endesa SA raised the European Commission concern about its potential anti-competitive effect on the input market as a barrier to entry to new suppliers of gas in the Spanish market. In our model, we have assumed that there is a competitive supply of the input at a given higher marginal cost, and that Assumption 1 guarantees competitive downstream firms


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4 Capacity purchasing and subcontracting: Are they equivalent? It is well known that restructuring of firms usually involves both changes in their levels of subcontracting and productive capacity.7 Until now, we have only considered the strategy by which a large firm, maintaining its capacity fixed, asked other firms in the fringe (interpreted as subcontractors) to produce for it. A natural extension of the model is then to consider the possibility that the large firm can acquire productive capacity from the competitive fringe simultaneously with the use of forward contracts. Assume that in the first stage of the game, the large firm may simultaneously set forward contracts and buy capacity of production. Second and third stages are just as in Sect. 2. Clearly, if the large firm buys a level of productive capacity k from the competitive fringe, the size of the latter becomes m − k. Thus, in the third stage of the game, the large firm has the objective function π(w, k, f, q) = P (q + m − k)(q − f ) − wq + pf f.

(11)

Let us denote the optimal level of production of the large firm, coming from the resolution of the problem M ax π(w, k, f, q), by q(w, k, f ), and short-run profits, q

gross of costs of capacity acquisition, by Π(w, k, f ) ≡ π (w, k, f, q(w, k, f )). From here, it is worth noticing that the optimal level of sales of the large firm, s(w, k, f ) ≡ q(w, k, f ) − f , is in fact a function both of the level of marginal costs of production, w, and of the difference k − f . If the large firm acquires the amount of capacity k = ∆, then fringe sales in the spot market are reduced from m to m − ∆, and the large firm chooses the level of sales s that solves the problem M ax [P (s + m − ∆) − w] s. s

(12)

Consider now what happens if instead the large firm contracts in the futures market the amount of output f = −∆. Clearly, fringe sales in the spot market are as before reduced from m to m − ∆, and the large firm chooses the level of sales that solves the problem M ax [P (s + m − ∆) − w] s + w∆, s

(13)

where the term w∆ is the saving in costs from reducing production level from s to s − ∆. In view of problems (12) and (13), it is immediate to see that in both of work at full capacity even at that cost. Hence, the efficient supplier and the large firm cannot use the long-term contract to raise barriers to entry in the input or in the output market. The efficient supplier wants to serve firms on the fringe and, as a consequence, the large firm has nothing to gain through an exclusive contract. Without Assumption 1, or if we had two large firms rather than only one in the downstream segment of the industry, a long-term contract between the efficient supplier and one of the two downstream large firms could lead to the vertical foreclosure of the industry (see Rey and Tirole 1999). 7 A nice example of this practice is the restructuring of Alcatel, announced in June 2001 (see, for instance, The Financial Times 15.07.2001 and El Pa´ıs Negocios 15.07.2001).

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them the large firm faces the same residual demand in the spot market. Hence it will choose the same amount of sales.8 More generally, in terms of the impact on sales and final prices, one marginal unit of acquired capacity by the large firm is tantamount to one additional unit of output contracted by it in the forward market. In other words, how much market power the large firm exercises depends exclusively on the difference k − f . This will be an important fact for Proposition 2 later on to be obtained. In equilibrium, the large firm and the efficient supplier sign the input contract T (q) = F + wq, in which w = c and F = Π(c, k, f ) − Π(¯ c, k, f ). Hence net profits of the large firm are given by Π(¯ c, k, f ). When such a firm buys a certain level of capacity from the fringe, it must pay for each unit of capacity the expected per unit profits for the remaining firms on the fringe, pe − c¯, where pe = P (q(c, k, f ) + m − k). In other words, we continue to assume that competitive firms have rational expectations and forecast correctly the final or spot price. Therefore, in the first stage of the game, the large firm has net profits given by Π N (¯ c, k, f ) ≡ Π(¯ c, k, f ) − [P (q(c, k, f ) + m − k) − c¯] k,

(14)

that is, the market profits, Π(¯ c, k, f ), net of the costs of acquiring the level of capacity k from the fringe, [P (q(c, k, f ) + m − k) − c¯] k, and such a firm solves the problem M ax Π N (¯ c, k, f ). Proposition 2 below shows that the purchase of k,f

forward contracts (or subcontracting) and the acquisition of capacity are similar anti-competitive devices for the large firm, in the sense that both can lead to an increase in final prices and in profits of the large firm. Proposition 2. Under Assumptions 1, 2 and 3, if there is a single large firm in the downstream industry, then any pair (k, f ) satisfying k − f = −f ∗ maximizes its profits. Proof. See the Appendix. We have already noted above that, when the large firm acquires the amount of capacity k = ∆ from the fringe, the impact on sales (and therefore in final prices) is the same that when it buys the amount of forward contracts f = −∆. Moreover, the underlying idea of proposition is that net profits for the large firm are the same under any combination of (capacity-forward contracts)-strategies that satisfies the condition k − f = ∆. To show the intuition behind this proposition, consider first the purchase of capacity. When the large firm buys capacity, fringe firms ask for a payment (per unit of capacity) equal to their unit expected profits, which are the expected spot price minus their cost of production multiplied by the amount of capacity, i.e. pe −¯ c. On the other hand, if the large firm buys output in the futures market, then fringe firms will ask for a payment (per unit of output) equal to the expected spot price, pe . The difference between the price for capacity and the price for forward contracts is then given by the marginal cost of production c¯, which is equal to the saved cost Provided that ∆ < m and w ∈ [c, c¯], Assumption 3 guarantees an interior solution in both problems (12) and (13), i.e. guarantees that the optimal level of sales, s∗ , is the same in both of them and satisfies s∗ > ∆. 8


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by the large firm when it buys the output from firms on the fringe. Hence, in both cases, a reduction ∆ of fringe sales in the spot market costs (pe − c¯)∆ to the large firm. In more general terms, what this proposition shows is that the large firm has several ways for optimally combining capacity acquisition and forward contracts. As noted above, in equilibrium, the benefit for such a firm to exercise more market power downstream by buying one additional unit of output through a forward contract is the same as that of acquiring one additional unit of productive capacity from the fringe. The gap in buyer power between the large firm and the fringe when dealing with the efficient supplier outweighs the free riding of competitive firms from any effort made by the large firm to reduce the level of production of the industry as a whole. Thus, in the presence of an efficient supplier, it is profitable for the large firm to acquire productive capacity from the fringe, just like it is profitable to buy output in the futures market. In other words, the large firm has an incentive to “bribe” other competitive downstream firms to leave some of their capacity idle. Incidentally, Proposition 2 gives an interesting insight to the incentives of the large firm to acquire capacity. As the efficiency gap c¯ − c decreases, it buys less capacity, and finally has no incentive to acquire capacity at all when the efficiency gap disappears. Just as it has no incentive to intervene in the futures market when the efficiency gap disappears. This result rationalizes observed firms’ policies based on changes in both levels of subcontracting and productive capacity. Likewise, Proposition 2 reinforces our claims in previous section that antitrust authorities should regard subcontracting activities by market power firms with a similar status to capacity acquisition strategies. Finally, notice that for the equivalence result of Proposition 2 to hold it is crucial the fact that, costs of the input away, both the large firm and firms on fringe have the same marginal costs of production.9 Although this point is beyond the scope of the paper, if the large firm would have different marginal costs of production than fringe firms, the result no longer holds. 5 Several large firms in the downstream segment of the industry In this section we extend the analysis to an industry whose downstream segment is composed of several large firms. The aim is to examine the strategic use of forward contracts by such firms not only vis-à-vis the dominant input supplier, i.e. in a “vertical” way as until now, but also regarding other dominant downstream firms, i.e. in a “horizontal” way. In what follows, we assume that downstream there are two large firms, a and b, that have levels of capacity ka and kb , respectively, and a competitive fringe of size m. The upstream side of the industry is the same as in Sect. 2. Finally, and in order to make the problem tractable, we restrict our attention to the linear demand case P (Q) = A − Q, where A > 0 and Q = i=a,b qi + m. For the analysis below, we assume the following two conditions hold: Assumption 1’. A − m − ka − kb ≥ c¯. 9 They have indeed zero marginal costs of production given the assumed condition that the input is transformed with no additional costs.

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Assumption 2’. min {ka , kb } > max

1

3 (A

− m − c) , 25 (A − m − c¯) .

Assumption 1’ guarantees that fringe firms always obtain non-negative profits, and hence they always fully use their respective capacities of production. In his turn, Assumption 2’ ensures an interior solution in the problem of each large firm.10 The game runs similarly to that of Sect. 2. That is, in the first stage, duopolists a and b decide upon their levels of forward contracting, fa and fb , respectively. In the second stage, the downstream industry buys the input. Finally, in the third stage, downstream large firms can just choose their levels of output. In stages one and three of the game, firms choose their strategies simultaneously. In the input contracting step, and with several large firms in the downstream segment as is the case, we must clarify how they and the efficient supplier set the vertical contracts by which the input is transferred. Following Rey and Tirole (1999), we ignore any strategic use of the input contracts by the efficient supplier. (This allows us to concentrate solely on the interaction among downstream firms.) What we assume is that the efficient supplier can neither establish an exclusive contract with any of the large firms, nor can it enter into publicly verifiable contracts with them. The efficient supplier offers two-part supply contracts that are secret, and downstream duopolists have passive conjectures. Secrecy of contracts implies that, in equilibrium, the efficient supplier serves both large firms and sets two-part tariffs with a marginal wholesale price w = c, as this is the tariff that maximizes bilateral profits. Likewise, passive conjectures of large firms a and b mean that fringe firms and large firm a (respectively, fringe firms and large firm b) expect that the efficient supplier and the large firm b (the efficient supplier and the large firm a) will reach an agreement. Hence it is expected that large firms produce at marginal cost c. In the last stage of the game, and given fa and fb , each large firm i, i = a,b, has (short-run) profits πi (fi , fj , w, qi , qj ) = [P (qi + qj + m) − w] qi + [pf − P (qi + qj + m)] fi , i, j = a, b; i = j, (15) and solves the problem M ax πi (fi , fj , w, qi , qj ), s.t: fi ≤ qi ≤ ki , i, j = a, b; i = j. qi

(16)

In the linear demand case, the system of first-order conditions of the program given in (16) yield the best reply functions of large firms in the production stage qi = R(qj ) =

1 (A − m − w + fi − qj ), i, j = a, b; i = j. 2

(17)

In this stage, if both large firms have reached an agreement with the efficient supplier of the input to produce at marginal cost w = c, then they produce the amount of output given by 10 Corner solutions do not give further insights, and would imply cumbersome calculations that we omit for the sake of simplicity.


qi (fi , fj , c) =

295

1 (A − m + 2fi − fj − c), i, j = a, b; i = j, 3

(18)

which holds from (17). In the second stage of the game, both large firms always have the option to use the input provided by the inefficient supplier, and then produce at marginal cost c¯. In such a case, their profits would be πi (fi , fj , c¯, qi , qj (fi , fj , c)) = [P (qi + qj (fi , fj , c) + m) − c¯] qi + [pf − P (qi + qj (fi , fj , c) + m)] fi , i, j = a, b; i = j. (19) Given the passive conjectures of large firms, notice in (19) that each one believes the rival would not change its level of production. Let us denote the level of production of each large firm i in the off-the-equilibrium path, i.e. the one that solves the problem M ax πi (fi , fj , c¯, qi , qj (fi , fj , c)), as qioff (fi , fj , c¯),11 and the resulting qi

profits as Πi (fi , fj , c¯). Then, competition among upstream suppliers drives down payments for the input until the level for which large firms are indifferent between producing at high or at low marginal cost. More specifically, the efficient upstream firm supplies the input to each large downstream firm at the wholesale price w = c and the fixed payment Fi = Πi (fi , fj , c) − Πi (fi , fj , c¯), i = a, b. Thus, net profits of each large firm i are those it would obtain in the off-the-equilibrium path with the second source of the input at marginal cost c¯, namely Πi (fi , fj , c¯). With the linear market demand assumed above, each large firm i would produce in the off-the-equilibrium path the quantity of output given by qioff (fi , fj , c¯) =

1 [A − m − c¯ + fi − qj (fi , fj , c)], i, j = a, b; i = j. 2

(20)

From (18) and (20) we arrive at 1 [2(A − m − c¯) − (¯ c − c) + 4fi − 2fj ], i, j = a, b; i = j, 6 (21) as the off-the-equilibrium quantity of each large firm. Hence, each one of them would obtain the profits given by Πi (fi , fj , c¯) = P qioff (fi , fj , c¯) + qj (fi , fj , c) + m − c¯ qioff (fi , fj , c¯) + pf − P qioff (fi , fj , c¯) + qj (fi , fj , c) + m fi , qioff (fi , fj , c¯) =

i, j = a, b; i = j. (22) Finally, in the first stage of the game, when large firms choose their levels of forward contracts, fi , each one takes into account its profits net of the fixed fee of the tariff, i.e. the profits given in (22). In addition, the condition of no-arbitrage in This is the quantity that each large firm i would produce if it is buying the input from the competitive supply instead of the efficient supplier while the rival j does the opposite, and expects that its rival j produces at low marginal cost. 11

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the forward market, reflected in (5), implies that forward price must equal the price in the spot market, i.e. pf = P (qi (fi , fj , c) + qj (fi , fj , c) + m).

(23)

Thus, each large firm i has at this stage the objective function given by Πi (fi , fj , c¯) = P qioff (fi , fj , c¯) + qj (fi , fj , c) + m − c¯ qioff (fi , fj , c¯) + P (qi (fi , fj , c) + qj (fi , fj , c) + m) −P qioff (fi , fj , c¯) + qj (fi , fj , c) + m fi , i, j = a, b; i = j, (24) and solves the problem M ax Πi (fi , fj , c¯), by which its optimal level of forward fi

contracts, fi , is the one satisfying the first-order condition ∂Πi ∂Πi ∂qi ∂Πi ∂qj + + ∂fi ∂qi ∂fi ∂qj ∂fi ∂q off (f , f , c¯) i j = − qi (fi , fj , c) − qioff (fi , fj , c¯) − i fi ∂fi

0=

−

∂qjoff (fi , fj , c) off qi (fi , fj , c¯), ∂fi

i, j = a, b; i = j, (25)

where we evaluate it for the linear demand case. Recall that in the case of a single large firm in the downstream side of the industry, there were two effects coming from the use of the futures market. With two large firms in the downstream industry, both effects persist. On the one hand, there is the effect mediated by the difference in buyer power vis-à-vis the efficient input supplier (the “vertical” strategic effect of forward contracting). Particularly, if a large firm i buys the amount −fi of output in the futures market, then it will get an extra margin of − P (qi (fi , fj , c) + qj (fi , fj , c) + m) − P qioff (fi , fj , c¯) + qj (fi , fj , c) + m per unit, which is qi (fi , fj , c) − qioff (fi , fj , c¯) in the case of a linear demand.12 This is the term in square brackets on the right-hand side of (25). On the other hand, there is the impact of forward contracts in final prices (the so-called direct effect of forward contracting) through the change in the production of large firms. This is reflected in the second term on the right-hand side of (25). But with two large downstream firms there is one more effect given by the third term on the right-hand side of (25), namely the incentive of each large firm i, i = a, b, to influence the level of production of the rival j, j = i, through its level 12

Recall Condition (7) in Sect. 3.


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of contracts, fi . This is the pioneering effect observed by Allaz and Vila (1993) and that we name in our setting the “horizontal” strategic effect. Summing up, the direct effect coming from the use of the futures market would lead any large firm to choose f ∗ = 0. At the same time, the two strategic effects, against the efficient supplier (“vertical” strategic effect) and against the rival large firm (“horizontal” strategic effect), work in the opposite sense. Although in general one may dominate the other as a function of the parameters of the model, for the linear demand case, however, we are able to characterize values of parameters that unambiguously ensure the sign of the net strategic effect of forward contracting. This is the content of the following proposition. Proposition 3. If a linear demand holds and there are two large firms in the downstream side of the industry, then: (a) There is a unique subgame-perfect equilibrium, given by fi∗ = qi∗ =

1 5 1 3

[A − m − c¯ − 5(¯ c − c)] and 1 c − c)) , i = a, b. A − m − c + 5 (A − m − c¯ − 5(¯

(b) In such an equilibrium, both firms buy forward contracts from the fringe, fi∗ < 0 (i.e. they subcontract), if, and only if, c¯ − c > 51 (A − m − c¯) and sell forward contracts,fi∗ > 0, otherwise. Proof. See the Appendix. From this proposition it can be seen that comparative statics for the parameters of the model are intuitive. Both large firms ask fringe firms (the subcontractors) to produce for them, rather than directly for consumers, when the efficiency gap between the efficient input supplier and suppliers on the fringe is high enough as part (b) of proposition states. In this case, one should expect that the existence of a futures market leads to a decrease in the level of competition in the spot market. Contrariwise, when the upstream industry is sufficiently competitive, in the sense that it is composed of input suppliers symmetric enough in costs, large downstream firms sell part of their productions through the competitive segment of retailers. In this case, the existence of a futures market increases competition in the final market, as Allaz and Vila (1993) suggest. Concerning the market size for the final good, a decrease in it (a lower demand intercept A) makes it more likely that the “horizontal” incentive of large firms to become the “leader” in the spot market will be dominated by the “vertical” incentive to gain buyer power. In such a case, it is more likely that the strategic effect vis-à-vis the efficient supplier outweighs the strategic effect vis-à-vis the rival large firm, and large firms buy forward contracts. The same is true when the size of downstream fringe, m, increases. Finally, it is straightforward from Proposition 3 to evaluate the impact of forward contracts on social welfare. This is summarized in the next corollary. Corollary 2. The existence of a futures market is welfare decreasing (respectively, enhancing) if, and only if, fi∗ < 0 (fi∗ > 0), i = a, b.

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The explanation of this result follows the same argument as in the aforementioned case of a single large firm in the downstream industry. In fact, when large firms buy forward contracts, total production decreases and the price in the spot market increases. Consumers are then worse-off from the possibility of forward contracting if large firms subcontract one part of their productions to fringe firms. Moreover, this outweighs the increase in firms’ profits, and hence social welfare decreases. The contrary holds when large downstream firms sell contracts in the futures market, in which case the result of Allaz and Vila (1993) survives.

6 Concluding remarks

We have studied the strategic use by market power firms of a futures market for a final good in a vertical industry with an efficient input supplier. We have shown how the presence of an efficient upstream firm in the industry dramatically alters the use of forward contracts with respect to the case of a vertically integrated industry (or even a vertical industry with equally efficient upstream firms). With risk-neutral consumers, a large downstream firm is induced to buy output in the futures market from other (fringe) downstream firms in order to make the spot market less competitive. The superior buyer power of the large downstream firm against the efficient input supplier, compared with that of fringe firms, is what makes this practice profitable to such a large firm. Similarly, when the downstream side of the industry has several large firms, each one of them has a “horizontal” incentive to sell forward contracts in order to increase its market share at the expense of the rival. This obviously leads to a more competitive spot market. However, the former “vertical” incentive to strategically use the forward market against the efficient input supplier persists, and it countervails the “horizontal” incentive each large firm has. As a whole, the trade-off between both effects does not lead to clear-cut results. The net impact of forward contracting on market performance of the industry may in fact be pro-competitive, but also anti-competitive. One can only forecast exactly the effect of forward contracts on competition by examining the details of the industry. Finally, the result stating that large downstream firms buy forward contracts from firms on a competitive fringe may be interpreted as horizontal subcontracting. In this way, the paper rationalizes the observed pattern in many industries, by which the level of subcontracting made by firms is growing in recent times. In our model, to subcontract one part of the production to competitive firms is strategically equivalent, for market power firms, to the acquisition of capacity from such competitive firms, a device widely seen as anti-competitive by antitrust authorities. More generally, our results may explain why the marketing stage of many industries tends to be more “consolidated”, i.e. with (some or even all) fringe firms specialized as subcontractors of large firms, rather than producing and selling by themselves to consumers, even if one does not observe significant economies of scale in marketing activities.


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Appendix Proof of Proposition 1 Part (a): The first term on the right-hand side of (7) is negative for any value of ) f . On the other hand, the fact that ∂q(c,f > 0 implies that the second term on ∂f the right-hand side of (7) is negative (respectively, positive) (zero) when f > 0 (respectively, < 0) (= 0). Thus, the optimal level of forward contracts is negative. Part (b): Straighforward. Proof of Corollary 1 ) Part (a): From the fact that ∂q(c,f > 0 and f ∗ < 0, it immediately holds that ∂f q (c, f ∗ ) < q (c, 0). Part (b): The final price increases as total production is reduced. Part (c): From part (b), fringe firms have higher mark-ups. The large downstream firm is also better off with the possibility of subcontracting one part of its production (in fact, it chooses to do it when it might set f = 0). Part (d): The efficient upstream supplier’s profits Π U are given by

c, f ). Π U = Π(c, f ) − Π(¯ Then

∂Π U ∂Π(c, f ) ∂Π(¯ c, f ) = − . ∂f ∂f ∂f

From

∂Π(c, f ) = −P (q(c, f ) + m) ∂f

and

∂q(c, f ) 0. ∂f Hence, such profits are reduced when the large downstream firm chooses f < 0. Proof of Proposition 2. Given net profits of the large downstream firm in (14), N (¯ c,k,f ) first-order conditions of the problem M ax Π N (¯ c, k, f ) are ∂Π ∂k = 0 and ∂Π N (¯ c,k,f ) ∂f

k,f

= 0, i.e.

P (q(¯ c, k, f ) + m − k) − P (q(c, k, f ) + m − k) (26)

k, f ) ∂q(c, + P (q(c, k, f )+m−k) −1 (f −k) =0 ∂k

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and − [P (q(¯ c, k, f ) + m − k) − P (q(c, k, f ) + m − k)] ∂q(c, k, f ) + P (q(c, k, f ) + m − k) (f − k) = 0, ∂f

(27)

respectively. In the third stage of the game, the large firm solves the problem of M ax π(c, k, f, q), where π(c, k, f, q) is defined as in (11), by which its optimal q

level of production q(c, k, f ) is the one that solves the first-order condition 0=

∂π(c, k, f, q) = P (q(c, k, f ) + m − k) (q(c, k, f ) − f ) ∂q +P (q(c, k, f ) + m − k) − c,

(28)

) ) and from (28) it is straightforward to see that ∂q(c,k,f = 1 − ∂q(c,k,f . Hence, ∂f ∂k first-order conditions (26) and (27) hold for any pair (k, f ) satisfying the condition f − k = f ∗.

Proof of Proposition 3. By solving the first-order conditions given in (25), i.e. − 21 (¯ c − c) − 32 fi + 31 qioff (fi , fj , c¯) = 0, i, j = a, b; i=j, we arrive at the system of linear best replies fi = R(fj ) = 41 (A − m − c¯ − 5(¯ c − c) − fj ). Straightforward computation then leads to the result claimed in the proposition. References Allaz, B., Vila, J.L. (1993) Cournot Competition, Forward Markets and Efficiency. Journal of Economic Theory 59: 1–16 Cabral, L. (2000) Introduction to Industrial Organization. The MIT Press, Cambridge, Mass. (see also http://luiscabral.org/iio/ch15/) Newbery, D. M. G. (1984) Manipulation of Futures Markets by a Dominant Producer. In: Anderson, R. (ed.) The Industrial Organization of Futures Markets. Lexington Books, Lexington Mass. Newbery, D. M. G. (1987) Futures Markets, Hedging and Speculation. In: Eatwell et al. (eds.) The New Palgrave: a Dictionary in Economics. The MacMillan Press Limited, London Powell, A. (1993) Trading Forward in an Imperfect Market: The Case of Electricity in Britain. The Economic Journal 103: 444–453 Rey, P., Tirole, J. (1999) A Theory of Foreclosure. In: The Handbook of Industrial Organization, vol. 3. North-Holland, Amsterdam (in preparation) Spiegel, Y. (1993) Horizontal Subcontracting. Rand Journal of Economics 24: 570–590 Wilson, R. (2002) Architecture of Power Markets. (Available at http://faculty-gsb.stanford.edu/wilson/)