To this point, we have focussed on contracts as coordinating the incen-tives of agents along a supply chain. Contracts can be designed to serve a completely different kind of role: contracts can have strategic value in competition against other manufacturers or other supply chains. While this role has not been featured in the literature on supply chain coordi-nation, it is prominent in the contract theory foundations of antitrust policy. In this section, we offer an overview of one particular strategic role: the use of contracts to deter entry into a market.
The theory begins with the classic article by Aghion and Bolton [3].
An incumbent, in a market with a single downstream firm, faces the threat of entry by another firm. The downstream firm requires one unit of the input, which it values at a known value v. The incumbent’s cost of producing this unit is cI. Entry is uncertain because the entrant’s cost, c, is random. Let G(c) represent the distribution of the entrant’s cost. The incumbent is assumed to have a first-mover advantage in contracting in the sense that it can contract with the downstream firm before the entrant’s cost is realized. A contract can be expressed as a pair (p, d) consisting of a price that the buyer (the downstream firm) agrees to pay if it buys in the future as well as a stipulated damages, d, that the buyer pays if the decision is made not to purchase (i.e., too purchase from the entrant instead). Equivalently, the buyer pays d up front and an additional (p− d) if the decision is made to purchase. In other words, the contract is a call option with an option price po= d and an exercise price, x = p− d.
If a contract is not struck in the Aghion–Bolton model, the incumbent and the entrant compete in prices ex post. In the Bertrand equilibrium of this no-contract subgame, if c < cI then the entrant sup-plies ex post at a price equal to cI; if c > cIthen the incumbent supplies at a price min(c, v).
A contract yields a superior combined payoff to the buyer and incumbent than no contract, because if a contract is in place, then the entrant must meet the exercise price x of the contract option if it is to supply the buyer.3 By lowering x below cI, which is the price that a low-cost entrant would have to charge to attract the buyer in the absence of a contract, the incumbent and buyer as a pair are thus able to extract a lower price from the entrant (conditional upon the states of successful entry) than in the absence of a contract. The optimal choice of x satisfies
cI − x
x = 1
ε (8.6)
where ε≡ dlnG(c)/dc is the elasticity of the distribution function [96].
Since G(p) is the probability that the entrant would be willing to supply at a price p, G can be interpreted as a supply curve of the entrant, and ε as the elasticity of supply. Equation (8.6) is the Lerner equation for a monopsonist (rather than the more familiar monopolist Lerner equation): the value that the incumbent–buyer pair obtain with the purchase from the incumbent is cI, the incumbent’s cost of production, because this is the opportunity cost avoided when the purchase is made.
The incumbent and buyer, as a pair, sign a contract that extracts the optimal monopsony rents from the entrant.
A contract can thus be designed to extract a transfer from a party outside the contract — in the Aghion–Bolton model, a transfer from the entrant. Jing and Winter [96] suggest a variation on this theory.
The variation involves actions by four parties: the incumbent, the buy-ers downstream from the incumbent, a set of entrants, and an input supplier further upstream from the incumbent. Suppose that entrant’s costs are common but random. Instead of market power resting with
3If buyers have an option to buy at x, then an entrant can attract them only with a price offer less than x.
an entrant, the supplier of an input further upstream is a monopo-list (with known cost). The incumbent anticipates future negotiations with the upstream supplier over its input price. The incumbent strikes a long term contract (with a relatively low exercise price) with the down-stream buyer. The downdown-stream contract makes the market less prof-itable for the entrants because they have to meet a low exercise price.
This reduces the willingness-to-pay of the entrants for the upstream input (since it is now harder for them to cover costs upon entry). Since selling to an entrant is the upstream monopolist’s best alternative to selling to the incumbent, the incumbent is therefore able to bargain for a lower input price. Thus, long-term contracts at one stage of the supply chain may be used by a firm to extract rents from a firm with market power at another stage of the supply chain. Jing and Winter apply this theory to an antitrust case in the supply of marketing information.
Let us return to the framework of a single potential entrant into a market with one incumbent. Consider now the possibility of many buy-ers. If the buyers (downstream firms) are all local monopolists, and the entrant has constant returns to scale, then the story is unchanged from Aghion–Bolton. If a potential entrant has a fixed cost, so that it needs to capture a substantial share of the market to cover the fixed cost and justify entry, then the theory of exclusionary contracts is strengthened.
To enter the market with a given cost realization, an entrant needs to capture an adequate share of free buyers, those who are not committed to a contract or who would choose not to exercise an option contract.
The incumbent can profitably sign up substantial numbers of buyers to long-term contracts because each buyer, in signing a contract, ignores the externality imposed on other buyers from its decision to accept the contract and consequent reduction in the probability of successful entry. Each additional contract reduces the number of free buyers, thus dampening the discipline that the incumbent faces in competing for the free buyers ex post from potential entry. Each contract with a buyer allows the entrant to extract additional profits from the free buyers.
This theory is developed in refs. [158] and [169].
If buyers compete, however, the Aghion–Bolton theory can break down [62]. A single buyer downstream may hold-out from joining the contract, and then is available for the entrant. The entrant can charge a
price that allows the single buyer to undercut the remaining buyers and capture the entire market. As Fumagalli and Motta demonstrate, this possibility eliminates the exclusionary effect of contracts when buyers compete downstream.4 Simpson and Wickelgren [177] offer additional insights in analyzing exclusionary contracts in the case of competing downstream buyers.
4Wright [208] and Abito and Wright [1] offer an alternative analysis of the impact of buyer competition downstream in the Fumagalli–Motta model.