Self-Sabotage and Durable-Goods Monopoly

Abstract

We analyze a simple two-period linear demand durable-goods monopoly model with “self-sabotage.” The firm has the ability to sabotage its own production by increasing its future (period two) manufacturing costs. We find that an uncommitted monopoly seller has an incentive to engage in such self-sabotage, while a committed seller or renter has no such incentive. Unlike the previous papers on self-sabotage, we show this occurs even though the firm faces no rivals in the output market. In our durable-goods setting, the incentive for self-sabotage arises from the seller’s commitment problem with period-one buyers (the so-called Coase conjecture). Interestingly, we also find that this sort of self-sabotage can not only be profit enhancing for the uncommitted firm, but may also increase social welfare (in contrast to the earlier models on self-sabotage.)

Key Words:

• Monopoly
• Durable-Goods
• Self-Sabotage.

JEL classifications:

• L1
• D4.

The author gratefully acknowledges the helpful comments and suggestions of the Editor on an earlier draft of this paper and those received in the anonymous refereeing process. Any remaining errors or omissions are solely the author’s responsibility.

Notes

1. Of course, if the firm rents or leases all units, it owns the circulating stock at all future points and does not face any expectation problem with potential buyers that a seller does. Thus, in durable-goods models, there are substantial differences in renting and selling solutions.

2. Hence, backward induction is the current standard for solving the durable-goods monopoly models.

3. A large number of studies have examined the mechanisms available for the firm to commit itself credibly to a future time path. See, for example, Arya and Mittendorf (2006), Butz (1990), Chen, Esteban, and Shum (2010), Goering and Pippenger (2002), Goering and Sarangi (2012), Kahn (1986), and Olsen (1992). These analyses show, among other things, that when the seller can fully commit itself to potential buyers, the selling solution approaches the pure rental solution (where no commitment problem exists). Hence, fully committed sales solutions are typically the same as the pure renting solution.

4. The durable-goods analysis nearest to ours is likely that of Karp and Perloff (1996). However, their model, although related, is very different. In particular, they assume that only perfectly durable goods are sold, and that the monopolist has an “infinitesimal period of commitment” by assumption. In other words, they “assume the monopoly cannot make a binding choice of technology in the initial period.” Hence, they do not allow the choice of a future cost technology to provide any commitment effect for the firm by design. Consequently, they find that in perfect foresight rational expectations (Markov) equilibria, an uncommitted seller will always choose the most efficient (lowest average cost) technology. In contrast to this, we assume that the firm can bind itself to higher future costs through “self-sabotage” (as in Sappington and Weisman 2005), and show that such a strategy maybe profit maximizing.

5. See Goel and Hsieh (1999), Malueg and Solow (1989), Usategui (2007), and Utaka (2006) for welfare analyses of renting and selling durable goods in nonsabotage settings.

6. Of course, the firm, in most instances, can not only choose its output levels but also the durability of its product (e.g., Bulow 1986; Goering and Sarangi 2012). As in Bulow (1982), we abstract away from the choice of durability in the current paper. This allows us to focus more narrowly on the self-sabotage aspect of the model. The generalization of the model to both the choice of product durability and self-sabotage is left to future research.

7. Note that, in this formulation, we are assuming that the firm starts with zero manufactured units in period one, so the stock in period one is simply their production, , in this period. However, in period two, the stock of available units is the surviving durable period-one units plus any period-two production ().

8. It is worth noting that, in any of the durable-goods analysis cited, if we assume that buyers cannot observe or correctly forecast firm costs or future demand, the Coase conjecture itself breaks down, since it is unclear what rationale/mechanism buyers will use to predict the firm’s future behavior, and the analysis tends to become very ad-hoc.

9. The first- and second-order conditions are omitted for brevity but are available by request. Also, the superscript * denotes the profit-maximizing level of the given variable.

10. Obviously, if second-period output is zero, this change in cost has no impact whatsoever on the committed seller’s profit. This implies the firm has no incentive for self-sabotage even with such a corner solution.

11. It is worth stressing once again that, as is standard in the literature, we are examining perfect foresight rational expectations equilibria. This indicates that the high marginal cost committed to by the monopolist (through self-sabotage) is known or observable to potential period-one buyers. If this is not the case then, as an anonymous referee pointed out, a high future marginal cost will not provide any commitment ability. Although we do not analyze such asymmetric imperfect information equilibria, it does raise the interesting question of how a durable-goods monopolist may communicate to potential buyers that it has committed itself to higher costs in the future (through self-sabotage). One way this may occur is if the firm adopts a “green” production technology that reduces environmental pollutants and waste, but increases the firm’s production cost in the future period. The firm would then have an incentive to communicate to buyers, through advertising and so on, that it will be using a “green” or “socially responsible” production method in the future, thereby gaining the needed credibility with these buyers.

12. Indeed, Bulow (1982, 1986) argues that if the goods are perfectly durable, it may be optimal for a selling firm that is endowed with commitment power not to produce any future output at all. This illustrates that high future marginal production costs likely have strong commitment power if the goods themselves are highly durable.

13. As equation (9(9) ) formally indicates, increasing period-two costs decreases the firm’s profit directly, since it is more expensive to manufacture period-two output (), but it also provides a strategic commitment benefit and increases profit when the goods are durable, . Either of these two effects may dominate, depending upon the durability of the goods (among other things). Unfortunately, even in this stylized two-period model, it is not possible to “pin down” the magnitude of the two opposing forces any more than equation (9(9) ) illustrates. Hence, we turn to specific numerical examples in the text.

14. Note, for completeness, we have included the calculations for . This final row in Table 1 illustrates that second period output does indeed become negative after the point at which . Obviously, the firm cannot actually produce such a negative quantity, and these calculated values for profit and so on are not relevant.

15. Remember a pure renter, by definition, owns the entire stock of durables in every period (sells no units) and, consequently, has no such commitment problem.

16. As in Table 1, for completeness, in Table 2, the final row simply illustrates that for , second-period output becomes negative. Once again, such a negative quantity is not feasible, and the calculated values for profit and so on are not relevant.

17. Note, many durable-goods studies (e.g., Butz [1990] best-price provisions) implicitly assume that the monopolist can use a given commitment mechanism for free. Such a costless instrument typically guarantees the firm the fully committed seller’s (pure renter’s) maximal profit. In our model, self-sabotage is clearly not costless to the firm per se. The firm must pay the higher period-two costs for any unit produced. Consequently, the selling monopolist will not earn the full rental profits it would if it were, in effect, simply endowed with commitment ability.

18. They show an uncommitted seller tends to produce a lower level of output than a renter in period one, but a higher stock of output in period two. Hence, social welfare maybe maximized under either a rental or sales scenario.

19. Unfortunately, as the cited durability literature shows, even in simple stylized two-period durable-goods models, it is often very difficult to make general conclusions due to the complexity of the dynamic interactions (e.g., either sales or rentals in a durable-goods monopoly may yield higher social welfare). Even with our assumption of linear service demand, categorizing the welfare impacts (proposition four) and the profitability (or lack thereof) of self-sabotage (proposition three) more fully is not possible without further restricting and simplifying the analysis.