Efficient durable good pricing and aftermarket tie-in sales.

Kaserman, David L.

I. INTRODUCTION

A number of alternative theories currently exist to explain the use of tying arrangements in general. Incentives involving price discrimination, foreclosure, variable proportions, protection of franchise system goodwill, and so on have all been shown to motivate tying under various market conditions. (1) Interestingly, however, most of these theories do not appear to apply directly to the tying of aftermarket sales to the purchase of a durable good in a competitive environment. Such tying (or, equivalently, aftermarket monopolization) was a central issue in the widely debated Kodak case and continues to be a highly controversial aspect of a series of subsequent antitrust cases. (2)

The two predominant theories employed by opposing parties at trial in the Kodak case were the so-called installed-based opportunism theory and the systems theory. (3) The former posits conditions under which a durable good producer may find it profitable to raise aftermarket prices for maintenance and repair services above the competitive level to its locked-in customers, regardless of the intensity of competition in the equipment (or fore-) market. The latter, in turn, demonstrates the conditions under which such opportunistic behavior is either (a) not profitable or (b) profitable but very limited in its competitive effects. (4) While both these theories provide some useful guidance regarding the question of post-sale exploitation of purchasers of durable goods, neither provides an explicit theory of aftermarket tie-in sales that is driven by any sort of efficiency considerations.

In the wake of the controversy sparked by the Kodak decision, two important developments have emerged. First, the courts have demonstrated a strong reluctance to embrace the economic logic embodied in that decision. Despite a large number of similar claims that have subsequently been filed, there have not yet been any decisions that clearly adopt the customer lock-in argument that prevailed in Kodak. (5)

Second, in response to some dissatisfaction with the state of the economic theory relevant to aftermarket tying or monopolization at the time the case was decided, a series of articles has emerged that present newer (and, perhaps, more relevant) theories of Kodak-type behavior. (6) These include, inter alia, aftermarket monopolization incentives that derive from (a) variable proportions production as in Elzinga and Mills (2001), (b) the time inconsistency problem of durable good pricing as in Morita and Waldman (2004), (c) price discrimination as in Klein (1995) and Chen and Ross (1993, 1999), (d) socially excessive maintenance as in Carlton and Waldman (2001), and (e) economies of scope in remanufacturing of used parts as in Carlton and Waldman (2001). The common thread that connects these theories is that most contain some sort of efficiency-based motivation for aftermarket monopolization, which results in an unambiguous improvement in social welfare. (7) As a consequence, considerable doubt has been cast on the legitimacy of Kodak's broad condemnation of aftermarket monopolization.

This article attempts to contribute to this general line of research. Like the above-mentioned articles, it offers an efficiency-driven motivation for aftermarket tie-in sales or monopolization. Unlike these articles, however, the incentive arises directly from the contracting problem faced by buyers and sellers of durable goods. Specifically, like the systems theory, the model presented here assumes that buyers make their purchase decisions rationally on the basis of the expected life cycle (or total ownership) costs of the competing durable goods available at the time of purchase. Similarly, sellers make offers that incorporate the life cycle profits anticipated from the sale, including both the price received for the initial durable good purchase and the future stream of revenues from any subsequent aftermarket services provided by the seller. The two parties then negotiate over the relevant fore- and aftermarket prices.

The novel aspect introduced here is that we allow the discount rates applied to the future expenditures and revenues of the buyer and seller to differ. (8) In theory, these different discount rates can arise from a number of potential sources. For example, the contracting parties may have (a) different rates of time preference, (b) different degrees of uncertainty regarding future period costs and revenues, (c) different attitudes toward risk, (d) different degrees of control over the level of post-sale maintenance and repair services, and/or (e) different costs of capital. The simple convention of allowing these rates to differ obviously cannot distinguish which of these underlying sources dominates. Nonetheless, whatever the source, the presence of different discount rates provides another plausible incentive for durable good suppliers to pursue aftermarket tying or monopolization.

Given this simple framework, we derive the optimal structure of equipment and aftermarket prices, which, together, allocate the present and future costs and revenues efficiently between the contracting parties. We are then able to explore the conditions under which tying will necessarily be an essential component of that optimal contract.

II. THE CONTRACTING PROBLEM AND SOLUTION

We assume a simple two-period model in which a durable good is sold in the first period and that good is then serviced and/or repaired in the second period. A single unit of the good is purchased by a buyer, B, and sold by a seller, S. The sale takes place under the terms of a contract that specifies both the initial, Period 1, purchase price and the post-sale, Period 2, service/repair price.

We assume that both contracting parties are rational. Specifically, they both recognize that the purchase/sale of this good will generate both benefits (or revenues) and costs in both periods--that is, each party recognizes the life cycle effects of the terms of the negotiated contract, Additionally, we assume that the durable good market is competitive, although the model could easily be extended to incorporate imperfect competition.

Next, as described above, we allow the discount rates that are applied to Period 2 benefits and costs to differ between the buyer and the seller. We specify these discount rates as [r.sub.B] and [r.sub.S], where [r.sub.B] may be greater than, less than, or equal to [r.sub.S]. Thus, we make no prior assumption regarding the relative magnitude of these discount rates. We shall see, however, that that magnitude has a profound effect on the price structure of the negotiated contract and, through that, the incentive to tie.

Turning to that contract, we let [P.sub.D] be the initial purchase price of the durable good and [P.sub.A] be the per-unit aftermarket price of repair and maintenance services. (9) The buyer and seller thus negotiate these two prices simultaneously prior to the purchase, and their values are incorporated in the resulting contract. Finally, we assume that constant costs of CD and CA apply to production of the durable good and related aftermarket services, respectively.

Given the assumptions and notations mentioned above, the present value of the life cycle costs incurred by the buyer is

(1) [L.sub.B] = [P.sub.D] + [1/(1 + [r.sub.B])][P.sub.A][Q.sub.A]([P.sub.A]),

where [Q.sub.A]([P.sub.A]) is the quantity of aftermarket services purchased. The present value of the seller's life cycle profits is given by

(2) [[pi].sub.S]: ([P.sub.D] - [C.sub.D]) + [1/(1 + [r.sub.S])]([P.sub.A] - [c.sub.A]) x [Q.sub.A] ([P.sub.A]).

With a competitive durable good market, the terms of the efficient contract are given by the solution to

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The resulting set of fore- and aftermarket prices leads to an efficient allocation of present and future revenues and costs between the contracting parties and, as we shall see, the potential incentive to tie.

The Lagrangean for this problem is

(4) [pounds sterling] = [P.sub.D] + [1/(1 + [r.sub.B])][P.sub.A][Q.sub.A]([P.sub.A]) - [lambda]{([P.sub.D] - [c.sub.D]) + {1/(1 + [r.sub.S])] x ([P.sub.A] - [c.sub.A])[Q.sub.A]([P.sub.A])},

with first-order conditions

(5) [partial derivative][pounds sterling]/[partial derivative][P.sub.D] = 1 - [lambda] = 0

(6) [partial derivative][pounds sterling]/[partial derivative][P.sub.A] = [1/(1 + [r.sub.B])][([Q.sub.A] + [P.sub.A] ([partial derivative][Q.sub.A]/[partial derivative][P.sub.A])] - [lambda][1/(1 + [r.sub.S])][([Q.sub.A] + [P.sub.A]([partial derivative][Q.sub.A]/[partial derivative][P.sub.A]) - [c.sub.A]([partial derivative][Q.sub.A]/[partial derivative][P.sub.A])] = 0

(7) [partial derivative][pounds sterling]/[partial derivative][lambda] = ([P.sub.D] - [c.sub.D]) + [1/(1 + [r.sub.S)] x ([P.sub.A] - [c.sub.A])[Q.sub.A] = 0.

As explained in greater detail below, the need for the durable good supplier to tie aftermarket purchases to the original sale will hinge on the value of [P.sup.*.sub.A] relative to [c.sub.A]. Specifically, only in situations where [P.sup.*.sub.A] > CA will tying be a necessary component of the optimal contract. Focusing, then, on [P.sup.*.sub.A], the above system yields

(8) [P.sub.A] = - [[d.sub.S]/([d.sub.B] - [d.sub.S])][c.sub.A] - [Q.sub.A]/([partial derivative] /[partial derivative][P.sub.A]),

where [d.sub.B] = 1/(1 + [r.sub.B]) and [d.sub.S] = 1/(1 + [r.sub.S]). Rearranging Equation (8), we have

(9) [P.sub.A] - [c.sub.A] = [[d.sub.B]/([d.sub.S] - [d.sub.B])][c.sub.A] - [Q.sub.A] /([partial derivative][Q.sub.A]/[partial derivative][P.sub.A]).

Because the demand for maintenance is downward sloping, the second term on the right is positive. Therefore, if [d.sub.S] > [d.sub.B], then [P.sub.A] > [c.sub.A] will hold. That condition, in turn, requires [r.sub.B] > [r.sub.S]. Thus, only in situations in which the buyer exhibits a higher discount rate than the seller is it likely that the efficient contract will contain aftermarket prices that exceed costs. (10) Importantly, this result can occur in the absence of either (a) market power on the part of the seller or (b) postcontractual opportunism in which locked-in customers are exploited by suppliers reneging on either an explicitly or an implicitly negotiated contract. Rather, [P.sup.*.sub.A] > [c.sub.A] can emerge directly from efficient contracting in cases where [r.sub.B] > [r.sub.S] holds. (11)

III. THE NEED TO TIE

Having established the conditions under which efficient competitive contracting can result in aftermarket prices that exceed costs, we have also established the need for the efficient contract to contain a tying provision or an equivalent mechanism that binds the customer to the original equipment supplier for aftermarket sales. In the absence of such a provision, buyers will obviously have an incentive to switch to independent, third-party suppliers of aftermarket services due to the markup being charged by the original equipment manufacturer. Moreover, such suppliers will have an incentive to enter the market for these services due to the post-sale markup being charged. As a result, the efficient contract is not sustainable in the absence of the tying (or equivalent) requirement in cases where that contract requires [P.sup.*.sub.A] > [c.sub.A].

In all other cases (e.g., where [P.sup.*.sub.A] [less than or equal to] [c.sub.A]), however, tying is not required. Specifically, where [P.sup.*.sub.A] < [c.sub.A], aftermarket services are supplied below cost. In this case, customers will voluntarily purchase such services from the original durable good supplier. In addition, because post-sale profits are negative, alternative suppliers of such services will not arise to vie for aftermarket sales, and where [P.sup.*.sub.A] = [c.sub.A], both the durable good suppliers and their customers will be largely indifferent regarding the source of aftermarket suppliers. Independent suppliers of post-sale services and repair parts may compete alongside the original equipment manufacturers as occurs, for example, in the automobile market.

Finally, while we have focused here on tying as the (contractual) mechanism used to bind customers to durable good suppliers for their aftermarket purchases, that is obviously not the only (or necessarily most efficient) approach to achieve that end. Specifically, alternative strategies include (a) design compatability of aftermarket equipment, (b) refusals to deal with independent service organizations, (c) free (or below cost) provision of service, and (d) explicit contractual provisions. Regardless of the particular mechanism chosen, however, the basic point remains--efficient contracting between buyers and sellers of durable goods may require some sort of binding mechanism such as tying between fore- and aftermarket sales.

IV. CONCLUSION

The analysis presented here demonstrates that aftermarket tie-in requirements can be an important component of an efficient multi-period contract between buyers and sellers of durable goods under competitive market conditions. In particular, where buyers exhibit relatively high discount rates, the optimal contract can contain aftermarket prices that exceed costs. In such cases, a tying arrangement (or equivalent mechanism) is needed to bind aftermarket sales to the original durable good supplier in order to permit the efficient combination of prices to emerge.

REFERENCES

Blair, R. D., and D. L. Kaserman. "Vertical Integration, Tying, and Antitrust Policy." American Economic Review, 68, 1978, 266-72.

--. "Optimal Franchising." Southern Economic Journal, 49, 1982, 494-505.

Borenstein, S., J. K. MacKie-Mason, and J. S. Netz. "Antitrust Policy in Aftermarkets." Antitrust Law Journal, 63, 1995, 455-82.

Carlton, D. "A General Analysis of Exclusionary Conduct and Refusal to Deal--Why Aspen and Kodak are Misguided." Antitrust Law Journal, 68, 2001, 659-83.

Carlton, D., and M. Waldman. "Competition, Monopoly, and Aftermarkets." National Bureau of Economic Research Working Paper 8086, 2001.

Chen, Z., and T. W. Ross. "Refusals to Deal, Price Discrimination and Independent Service Organizations." Journal of Economics and Management Strategy, 2, 1993, 593-614.

--. "Refusals to Deal and Orders to Supply in Competitive Markets." International Journal of Industrial Organization, 17, 1999, 399-417.

Elzinga, K. G., and D. E. Mills. "Independent Service Organizations and Economic Efficiency." Economy Inquiry, 39, 2001, 549-60.

Friedman, M., and L.J., Savage. "The Utility Analysis of Choices Involving Risk." Journal of Political Economy, 56, 1948, 279-304.

Hansen, R., and R. B. Roberts. "Metered Tying Arrangements, Allocative Efficiency, and Price Discrimination." Southern Economic Journal 47, 1980, 73-83.

Hovenkamp, H. "Post-Chicago Antitrust: A Review and Critique." Columbia Business Law Review, 2001, 2001, 257-337.

Klein, B. "'Market Power in Antitrust: Economic Analysis After Kodak." Supreme Court Economic Review, 3, 1995, 43-92.

Klein, B., and L. F. Saft. "The Law and Economics of Franchise Tying Contracts." Journal of Law and Economics, 28, 1985, 345-61.

Liebowitz, S. J. "Tie-In Sales and Price Discrimination." Economic Inquiry, 21, 1983, 387-99.

Machina, M. J. "Choice Under Uncertainty: Problems Solved and Unsolved." Journal of Economic Perspectives, 1, 1987, 121-54.

MacKie-Mason, J. K., and J. Metzler. "Links between Vertically Related Markets: Kodak (1992)," in The Antitrust Revolution." Economics. Competition. and Policy, 3rd ed., edited by J. E. Kwoka, and L. J. White. New York: Oxford University Press, 1999, 386-408.

Morita, H., and M. Waldman. "Durable Goods, Monopoly Maintenance, and Time Inconsistency." Journal of Economics and Management Strategy, 13, 2004, 273-302.

Shapiro, C., "Aftermarkets and Consumer Welfare: Making Sense of Kodak." Antitrust Law Journal, 63, 1995, 483-504.

Shapiro, C., and D. Teece. "Systems Competition and Aftermarkets: An Economic Analysis of Kodak." Antitrust Bulletin, 39, 1994, 135-62.

Whinston, M. D. "Tying, Foreclosure, and Exclusion." American Economic Review, 80, 1990, 837-59.

(1.) See, for example, Liebowitz (1983). Hansen and Roberts (1980), Whinston (1990), Blair and Kaserman (1978), and Klein and Salt (1985).

(2.) Eastman Kodak Co. v. Image Technical Services, Inc., 112 S. Ct. 2072 (1992). For a list of 10 related subsequent cases, see Hovenkamp (2001, ft. 67, 283-284).

(3.) See MacKie-Mason and Metzler (1999).

(4.) At trial and, later, in a subsequent series of articles, several variants of these two theories were presented to support or reject the basic proposition that equipment market competition may be a sufficient condition to protect aftermarket customers from supracompetitive pricing. See Mackie-Mason and Metzler (1999); Shapiro and Teece (1994): Shapiro (1995): Borenstein, MacKie-Mason, and Netz (1995): and Carlton (2001).

(5.) Hovenkamp (2001, 285-286) writes that: "The Kodak decision will soon be a decade old. Notwithstanding thousands of pages of law review articles and hundreds of millions of dollars in litigation costs, there has not been a single defensible plaintiff's victory in a case where the defendant's market power depended on a Kodak-style lock-in theory. Most lower courts have bent over backwards to construe Kodak as narrowly as possible." (Footnotes omitted.)

(6.) Both Elzinga and Mills (2001) and Carlton and Waldman (2001) contain a brief survey of this literature.

(7.) The sole exception is price discrimination, which yields ambiguous social welfare effects. Thus. all these theories admit the possibility that welfare will be improved by aftermarket monopolization.

(8.) Blair and Kaserman (1982) adopted this approach to explain the terms of franchise contracts.

(9.) We interpret the aftermarket sales broadly. They may include, for example, repair parts, supplies needed to operate the durable good. maintenance services, and so on.

(10.) To the extent that the two discount rates reflect the contracting parties' attitudes toward risk, one might expect [r.sub.B] < [r.sub.S] to be the typical case, because the buyer is discounting future costs, while the seller is discounting future profits. This reflects the so-called loss-aversion principle. See, for example, Friedman and Savage (1948) and Machina (1987). Moreover, because we find that when [r.sub.B] < [r.sub.S], tying does not arise, this observation may help explain the relatively low incidence of tying arrangements in aftermarkets. Nonetheless, this need not always be the case due to the dependence of [r.sub.B] and [r.sub.S] on other factors (e.g., the presence of moral hazard).

(11.) Equation (7) also yields the result

[P.sup.*.sub.D] = - [d.sub.S]([P.sup.*sub.A] - [c.sub.A][Q.sub.A] + [c.sub.D].

Thus, if [P.sup.*.sub.A] > [c.sub.A] , then [P.sup.*.sub.A] < [c.sub.D]. That is, under competitive market conditions, a positive markup on aftermarket price will be accompanied by a discount below costs in the equipment market. This appears to be the proverbial case in which razors are priced below costs (perhaps even given away free) in order to earn profits in subsequent periods on the sale of blades.

DAVID L. KASERMAN *

* I would like to acknowledge the helpful comments provided by my colleagues, Randy Beard, Richard Beil, and Mike Stern, as well as those of Tom Saving and the two anonymous referees. Any remaining errors, of course, are mine.

Kaserman: Torchmark Professor, Department of Economics, Auburn University, Auburn, AL 36849-5242. Phone 1-334-844-2905, Fax 1-334-844-4615, E-mail kaserman@auburn.edu