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Article Excerpt
We examine situations in which a party must make a sunk investment prior to contracting with a second party to purchase an essential complementary input. We study how the resulting hold-up problem is affected by the seller's information about the investing party's likely returns from its investment. Our principal focus is on the effects oft he investment's being observable by the noninvesting party. We establish conditions under which the seller's ability to observe the buyer's investment harms the seller, benefits the buyer, and reduces equilibrium investment and total surplus. We also note conditions under which investment and welfare rise when investment is observable.
1. Introduction
The hold-up problem is a central issue in economic analysis. (1) It arises when one party makes a sunk, relationship-specific investment and then engages in bargaining with an economic trading partner. That partner may be able to appropriate some of the gains from the sunk investment, thus distorting investment incentives, either toward too little investment or toward investments that are less subject to appropriation. Examples include a buyer that requires the seller's facility to market the buyer's products (e.g., a coal mine reliant on the local railroad or a web-based application provider reliant on an Internet service provider), a buyer that must invest in complementary assets to be used in conjunction with the seller's product (e.g., a firm undertaking marketing expenditures or investment in specialized facilities in order to distribute a manufacturer's product), investment in R&D or specialized production assets early on in a procurement process, and private investment subject to later government regulation (e.g., construction of a regulated oil or gas pipeline).
In the present article, we analyze the effects of the information structure on the hold-up problem when pre-investment contracting is infeasible. (2) Our principal focus is on the effects of the investment's being observable by the noninvesting party. The situation we have in mind is the following. There is an initial stage in which a buyer invests in complementary assets that are necessary to generate value from a seller's product and which have no value in alternative uses. After the results of the buyer's investment have been realized, the seller makes the buyer a take-it-or-leave-it offer. (3) In deciding the price to offer, the seller may have information about (i.e., receive a signal of) the buyer's realized value for the seller's product. At one extreme, the signal could be perfect and reveal the buyer's realized value. Then, absent any ex ante pricing commitments to do otherwise, the seller will set a price that fully extracts the buyer's surplus. Anticipating such pricing, the buyer expects to earn zero profits gross of its investment expenses regardless of its level of investment. Hence, a rational buyer makes no investment. In other words, as is well known, perfect information leads to complete holdup and destroys buyer investment incentives.
It is readily shown that both the buyer's profits and investment incentives can be positive when the seller is perfectly ignorant of the buyer's realized value. Given that perfect information drives both to zero, one might suspect that improving the seller's information lowers the buyer's profits and investment incentives, even when the improved information is itself imperfect. As we will demonstrate, however, there are important circumstances in which neither comparative static obtains. It is perhaps not surprising that "anything can happen" absent sufficient structure. Suppose one restricts attention to settings in which investment improves the distribution of the buyer's returns in the sense of first-order stochastic dominance and a higher value of the seller's signal leads to an improvement in the conditional distribution of the buyer's returns in the sense of first-order stochastic dominance. With this structure, it seems intuitively clear that the seller's price is increasing in the signal value and that, in comparison with an uninformative signal, an informative signal lowers the equilibrium levels of investment, buyer profits, and joint profits. (4) As we will show, however, all of these claims are false.
Our analysis proceeds as follows. After describing the model and characterizing a baseline case in which the seller is perfectly uninformed about the buyer's investment level and the realized value of trading, we examine settings in which the seller can observe--and condition its price on--the buyer's investment level. We demonstrate that, when the seller cannot commit to a price schedule prior to the buyer's sinking its investment, the observability of investment may, in general, raise or lower the buyer's equilibrium investment level and the seller's price may be increasing or decreasing in investment level. We derive conditions under which the seller's price is increasing in investment and the additional information reduces equilibrium buyer investment, in accord with the common intuition that additional information allows the seller to appropriate more of the returns to investment and thus reduces the buyer's investment incentives. Even in this case, however, we obtain the surprising--but quite general--result that the additional information results in the buyer k equilibrium profits rising vis-a-vis the situation in which the seller cannot observe investment. We also derive conditions under which the observability of investment reduces the seller's profits. In other words, we show that, even when the additional information gives the seller a greater ability to extract rents from the buyer at the margin, the additional information reduces the seller's ability to extract rents overall.
We also show that, because there are two opposing forces at work, the net effect of investment-based pricing on total surplus is ambiguous even when such pricing lowers buyer investment further below the efficient level. First, investment-based pricing induces the buyer to invest less, which tends to lower welfare. But, second, the seller lowers its price in response to lower investment, which increases the social benefits associated with a given level of investment because the seller is less likely to inefficiently price the buyer out of the market (i.e., to cause the buyer to shut down). We demonstrate that a necessary condition for investment-based pricing to increase welfare is that it raise the equilibrium probability of trade.
Last, we briefly examine markets in which the seller conditions its price on a general, noisy signal of the returns realized from the buyer's investment. We derive conditions under which the seller's price is an increasing function of the signal's value and the buyer's equilibrium investment is less than the second-best level. However, we also observe that the investment and welfare effects of increased seller information are generally ambiguous even under strong regularity conditions.
Before presenting our analysis, it is useful to put it in context. Economists have devoted considerable attention to the hold-up problem under various assumptions concerning the information structure and contracting institutions. (5) Like us, Rogerson (1992) and Hermalin and Katz (1993) consider situations in which the buyer's value of trade remains his private information. Unlike us, they assume that contracting prior to the buyer's investment is feasible, and they establish conditions under which the first-best outcome is attainable.
Tirole (1986), Gul (2001), and Lau (2008) examine situations in which contracting prior to investment is infeasible. Inter alia, these authors demonstrate how the observability of investment affects the equilibrium outcome. Specifically, Tirole focuses on the change in equilibrium investment when observability implies the parties can contract on the level of investment. (6) In contrast, we assume observability does not imply contractibility. Gul shows that the hold-up problem is solved when the buyer's investment is unobservable, repeated offers are made by the seller, and the time between offers is small. Lau looks at an intermediate case in which--at the time that the buyer invests--it is uncertain whether the seller will observe the buyer's investment. She shows that welfare can be greater than at either of the extremes of no information (less holdup but less efficient trade) and perfect information (complete holdup but efficient trade) because intermediate information "balances" the conflicting tensions. Both Gul and Lau assume that the buyer's value of the seller's product is a deterministic function of investment. (7) In a departure from these authors, we allow for the more realistic case of stochastic returns to investment. In this setting, even when the noninvesting party observes the investing party's level of investment and the noninvesting party has all the bargaining power, the noninvesting party is typically unable to appropriate the investing party's surplus fully.
Like us, Skrzypacz (2005) allows for investment with noisy returns. However, Skrzypacz focuses on the limiting case of a bargaining process in which the degree of ex post inefficiency goes to zero. In contrast, we limit ourselves to letting the noninvesting party make a single, take-it-or-leave-it offer. Our simpler bargaining process gives rise to the possibility of ex post inefficiency, which we believe is an important feature of many settings of interest.
2. The model
* We examine a setting in which there is a single buyer that requires the output of an upstream monopoly seller to generate value by selling a downstream product. For example, the monopoly seller might control a bottleneck facility through which the buyer reaches its market. Alternatively, the buyer might be a distributor of a monopoly manufacturer's product. Or the buyer might need to license the seller's intellectual property. We assume the buyer is a monopoly provider of its downstream product. This assumption avoids complications that arise when there are multiple buyers that are downstream competitors and, consequently, have interdependent demands.
The timing of the baseline game is as follows:
* The buyer chooses and sinks its investment, I, in its product. The buyer's investment yields a conditional distribution of product-market quasi-rents (i.e., buyer profits gross of the investment cost and any payments to the seller). As a shorthand, we refer to these quasi-rents as the buyer's return, r [member of] [R.sub.+]. We assume r is the buyer's private information.
* The seller observes a signal, s, which may contain information about the buyer's benefit of trade, r. The seller then makes a take-it-or-leave-it offer to sell one unit of its output at price p(s).
* After observing the realized values of r and p(s), the buyer chooses whether to shut down or continue. If the buyer shuts down, it loses its investment, I, earns no returns, and makes no payment to the seller. If the buyer continues operation, it earns profits of r--p(s)--I and the seller receives payment p(s). For simplicity, we assume the seller incurs no marginal costs to produce output. (8)
Formally, returns have the conditional distribution F(r, s | I) with the corresponding density function f(r, s | I). (9) We assume F(r, s | I) is at least twice differentiable in I for all I [member of] (0, [infinity]), r, and s. Let [F.sub.r](r | I)...
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