nach oben

Quantitative Marketing and Economics

Erschienen in:

01.06.2016

The strategic use of early bird discounts for dealers

verfasst von: Desmond (Ho-Fu) Lo, Stephen W. Salant

Erschienen in: Quantitative Marketing and Economics | Ausgabe 2/2016

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

We study a widely used ordering process (“Early Bird Discounts”) whereby a profit-maximizing manufacturer permits his dealers to place advance orders at a discount before they set retail prices. We show that such discounts may be used to shift just enough channel profits to dealers to enable them to cover their fixed costs and stay in business. If the manufacturer instead simply cut his wholesale price in order to generate gross margins for his dealers, these margins would soon dissipate as price competition among dealers selling the same product forced retail prices back down to the per-unit cost. We show that when dealer fixed costs are low, the manufacturer offers an Early Bird Discount to his multiple dealers that induces all but two of them to exit; when fixed costs are high, the manufacturer offers no preorder discount (i.e. switches to linear pricing) and induces all but one dealer to exit. Although uniform slotting allowances could also be used to reward dealers, a sales-based alternative like an Early Bird Discount sometimes has a key advantage when the manufacturer has dealers in cities of different sizes. If the same Early Bird Discount is offered, dealers in markets with more consumers, who typically have larger fixed costs, will preorder larger amounts and will automatically receive higher gross margins. To duplicate such payments with slotting allowances, non-uniform allowances would have to be offered to firms in different markets, which is divisive and possibly illegal.

Nächster Artikel Mixed pricing in online marketplaces

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Nur mit Berechtigung zugänglich

Slotting allowances are lump-sum transfers or negative access fees in a two-part pricing scheme between a manufacturer and a retailer (e.g., Shaffer 1991; Kuksov and Pazgal 2007). When a manufacturer offers the same amount of slotting allowance to dealers, we call it a “uniform slotting allowance.” This is to distinguish it from the notion of “non-uniform slotting allowances” defined in the text.

If accelerating production would raise per-unit costs, then it is less costly for the manufacturer to have at least some production occur prior to the realization of uncertain demand (e.g., Eichenbaum 1989). Stockouts are costly to dealers due to the loss of both immediate and long-term sales (Anderson et al. 2006). Preordering and inventory commitment may eliminate stockouts, avoiding situations where consumers would switch to competing products (McCardle et al. 2004). None of these self-insurance behaviors (Ehrlich and Becker 1972) involves strategic considerations on the manufacturer’s part.

At the owner’s request, we have replaced the name of his firm with the pseudonym “Computec.” Computec’s executives said that they intentionally installed the three-stage sales process to alter the strategic interaction downstream and to increase dealer margins. Further evidence that production smoothing is not the company’s motivation is that the company allows its dealers to take deliveries immediately after the last opportunity to preorder (see Appendix A).

As is standard in their businesses, Computec, Kaspersky, Toshiba, Hitachi, and Carrier—at least in some of their international markets—prohibit dealer returns of preorders unless the products are defective. For higher-education book distributors/publishers such as NACSCORP and Kendall Hunt, returns policies for bookstores vary but can be restrictive, and some merchandise is simply nonreturnable. For fruit farms, according to those we interviewed, it is logistically difficult to return fresh fruits such as melons, and thus returns are rarely accepted by growers.

Of course, when accelerating production raises per-unit costs, both cost and strategic considerations may motivate the manufacturer to offer preorder discounts. Hence, in some of the examples we first cited, we cannot rule out the possibility that the manufacturers were motivated to some extent by the desire to avoid higher per-unit costs or dealer stockouts.

We define gross margin as the difference between the sales revenue earned by a dealer and his total variable cost of acquiring the merchandise. Gross margin does not include the dealer’s fixed costs.

This may seem paradoxical since the profits of a firm who has more customers than he can serve will be the same no matter which customers he turns away. However, his rival’s strategy may no longer be profit-maximizing depending on which customers the first firm turns away. In that case, what was an equilibrium under one rationing rule ceases to be an equilibrium under the other rationing rule.

The same issue of observability arises in, for instance, Kreps and Scheinkman (1983), Davidson and Deneckere (1986), Maggi (1996), Padmanabhan and Png (1997, 2004), and Wang (2004). Although the role of observability of firm capacities or preorders is not always explicitly discussed in these models, some mechanism through which each firm or dealer learns the capacities or preorders must be implicitly assumed. This is because, as Tirole emphasizes on capacity-constrained games in his textbook (Tirole 1988, p. 217), to influence subsequent behavior, prior actions must be observable. Dixit (1982) and Shapiro (1989) make the same point.

We are assuming that distribution is not the manufacturer’s forte. That is, even if channel profits were maximized, the revenue net of production costs would be insufficient to cover the additional costs the manufacturer would incur if he tried to distribute the product himself. Thus, he is dependent on one or more dealers for distribution (Coughlan et al. 2006).

In other words, we assume that dealers preorder and distribute the manufacturer’s product if and only if they expect their profit (the difference between gross margins and fixed costs) to be weakly positive. Symmetrically, we also assume the manufacturer remains in business if and only if he earns a weakly positive profit.

If customers could instead not observe the quantity preordered by each dealer, demand would more plausibly be divided equally across the lowest-priced dealers, so that each would have demand, D(p)/R.

The other known alternative in capacity-constrained oligopoly games such as ours is to assume one of several ad hoc rationing rules as in Kreps and Scheinkman (1983) and the subsequent literature (see Tirole 1988, p. 212–3). Our results would then depend on which arbitrary rationing rule we adopted (Davidson and Deneckere 1986, p. 404). We instead follow Maggi (1996) in incorporating into the “rules of the game” the assumption that dealers must augment to satisfy unmet demand. As a shorthand, we refer to the Kreps-Schenkman assumption as the “no rainchecks” assumption and to Maggi’s alternative as the “rainchecks” assumption. We make the latter assumption because (i) augmentation is a key feature in many of the real-world examples cited in the introduction, and (ii) requiring it also avoids equilibrium predictions that, as Davidson-Deneckere showed, depend on the arbitrary rationing rule that must be specified under the “no rainchecks” approach. The equilibrium may change because an equilibrium strategy profile under one rationing rule may not form an equilibrium under a new rationing rule since under the new rationing rule a rival firm inherits a different set of discarded customers and may have a profitable deviation where none existed under the old rule. The third option – allowing dealers to choose whether or not to issue rainchecks – requires a dealer to compare the payoff from each alternative and therefore again involves the adoption of an arbitrary rationing rule in the “no rainchecks” subgames.

Nevertheless, it is logically possible that some dealer would strictly prefer to turn away a customer unilaterally rather than offer him a raincheck if the rules of the game permitted such behavior. In our equilibrium, every dealer preorders enough to serve every customer (see Proposition 1). If a dealer nonetheless turned away a customer unilaterally under these circumstances, the dealer would be strictly worse off: he would forego the retail price the customer would pay but could not get any refund from the manufacturer on the preordered merchandise since the manufacturer has a “no returns” policy. We thank the associate editor and an anonymous referee for encouraging us to clarify these issues.

As shown in Proposition 1, when retail prices are below the level that maximizes channel profits, those prices are Cournot prices. Therefore, they decrease in the number of dealers.

Suppose the unique solution to the manufacturer’s profit-maximization problem formalized above occurs on the R-dealer CB boundary. There is then also a continuum of optima that can be achieved by taking the same c but raising θ, since changing θ has no effect when the dealers are behaving like “Cournot competitors.”

Dealer gross margins in the Cournot region equal the profits of Cournot competitors with marginal cost c. As discussed in Kotchen and Salant (2010), Cournot profits increase as c decreases given our assumption that inverse demand is weakly concave.

In Appendix F, we review Spengler’s solution and extend it to the case where the dealer cannot cover his fixed cost out of the gross margin in Spengler’s solution. Readers interested in more detailed calculations for this example should consult Appendix F.

Early Bird Discounts degenerate into linear pricing when θ = c. If a single dealer can preorder at c per unit and augment at the per-unit cost θ = c, we envision him as preordering what is profit-maximizing for a monopolist dealer to sell if product can be acquired at marginal cost c. The dealer would make a strict loss by preordering more. If he preordered less, he would earn an unchanged profit since it would then be profit-maximizing to acquire the remainder by augmenting at θ = c. If F = 0 the equilibrium payoff of the manufacturer and his single dealer is the same as in Spengler (1950).

The last equality follows since θ^* = (a + m) / 2 ⇒ b(a – θ^*) / b = (θ^* – m) ⇒ D(θ^*) / –D'(θ^*) = (θ^*– m) ⇒ (D(θ^*))² / –D'(θ^*) = (θ^*– m)D(θ^*) = П_max.

In the smaller city, the Cournot price solves the equation \( \mathrm{p}+\frac{\widehat{\mathrm{D}}\left(\mathrm{p}\right)}{2\widehat{\mathrm{D}}^{\prime}\left(\mathrm{p}\right)}=\mathrm{c} \). Since \( \widehat{\mathrm{D}}\left(\mathrm{p}\right) \) = χD(p), this equation can be rewritten as \( \mathrm{p}+\frac{\upchi \mathrm{D}\left(\mathrm{p}\right)}{2\upchi \mathrm{D}^{\prime}\left(\mathrm{p}\right)}=\mathrm{c} \). This simplifies to precisely the equation determining the Cournot price in the larger city. Hence the two Cournot prices are the same.

Notice that if demand were the same in the two cities, contrary to our assumption, then χ = 1 and the derivation shows that Early Bird Discounts and slotting allowances are equally profitable. This confirms our conclusion in the one-city case.

See Coughlan et al. (2006, pp. 83–89) for a detailed discussion on the process and the high cost of handling and restocking returned merchandise in marketing channels.

To make this as clear as possible, we have adopted Maggi’s notation with two minor exceptions. First, we denote the preorder cost as c, which is equivalent to his original cost of building capability, denoted as c₀ in his paper. Second, Maggi has another variable c as firms’ selling cost, which we set as zero. Of course, the proof of our proposition is entirely different, because we are dealing with an arbitrary number of players, a wider class of inverse demand curves, and perfect substitutes.

At Cournot equilibrium, no oligopolist would strictly benefit from increasing or decreasing his production. So p^Cournot(c;R) + q^Cournot(c;R) · P'(R · q^Cournot(c;R)) – c = 0. Since θ < p^Cournot(c;R), D(θ)/R > q^Cournot(c;R), and P'(·) < 0 is strictly decreasing, it follows that θ + (D(θ)/R) · P'(D(θ)) – c < 0. This last expression is the marginal change in dealer i’s gross margin if he unilaterally increased his preorder in the neighborhood of his proposed equilibrium strategy. Given strict concavity of his gross-margin function, non-local increases in his preorder are also unprofitable.

Suppose the contrary: c – m = 0 in the interior of the Bertrand region. (E1) yields (θ – m)D'(θ) + D(θ) = 0, which by definition implies θ = θ^*. However, it is well known that the price charged in a Cournot oligopoly (with two or more dealers) is strictly smaller than the price a monopolist would charge, p^Cournot (m;R) < θ^*, so (E4) would be violated. Therefore, we must have c > m in the interior of the Bertrand region.

Anderson, E., Fitzsimons, G. J., & Simester, D. (2006). Measuring and mitigating the costs of stockouts. Management Science, 52(11), 1751–1763.CrossRef

Bertrand, J. (1883). Revue de la théorie de la recherche sociale and recherches sur les principes mathématiques de la théorie des richesses. Journal des Savants. 499–508.

Blattberg, R., & Neslin, S. (1990). Sales promotion: Concepts, methods, and strategies. Englewood Cliffs: Prentice Hall.

Carlton, D., & Perloff, J. (2005). Modern industrial organization. New York: Addison-Wesley.

Coughlan, A. T., Anderson, E., Stern, L. W., & El-Ansary, A. I. (2006). Marketing channels. Upper Saddle River: Prentice Hall.

Davidson, C., & Deneckere, R. (1986). Long-term competition in capacity, short-run competition in price, and the Cournot model. RAND Journal of Economics, 17, 404–415.CrossRef

Desai, P. S. (2000). Multiple messages to retain retailers: signaling new product demand. Marketing Science, 19(4), 381–389.CrossRef

Dixit, A. (1982). Imperfect competition and public policy: recent developments in oligopoly competition. American Economic Review, 72, 12–17.

Dutta, S., Bergen, M., & John, G. (1994). The governance of exclusive territories when dealers can bootleg. Marketing Science, 13, 83–89.CrossRef

Ehrlich, I., & Becker, G. (1972). Market insurance, self-insurance, and self-protection. Journal of Political Economy, 80, 623–648.CrossRef

Eichenbaum, M. (1989). Some empirical evidence on the production level and production cost smoothing models of inventory investments. American Economic Review, 79, 853–864.

FTC (Federal Trade Commission) (2003). Slotting allowances in the retail grocery industry: selected case studies in five product categories.

Ingene, C., & Parry, M. (1995). Channel coordination when dealers compete. Marketing Science, 14(4), 360–377.CrossRef

Katz, M. (1989). Vertical contractual relations. In R. Schmalensee, R. Willig, eds. Handbook of industrial organization. Vol. 1, Chapter 11. Elsevier Science, New York.

Kotchen, M., & Salant, S. (2010). A free lunch in the commons. Journal of Environmental Economics and Management, 61, 245–253.CrossRef

Kreps, D. M., & Scheinkman, J. A. (1983). Quantity precommitment and Bertrand competition yield Cournot outcomes. Bell Journal of Economics, 14(2), 326–337.CrossRef

Kuksov, D., & Pazgal, A. (2007). The effect of costs and competition on slotting allowances. Marketing Science, 26(2), 259–267.CrossRef

Lo, D., Salant, S. (2015). Early bird discounts for dealers. Santa Clara University discussion paper.

Maggi, G. (1996). Strategic trade policies with endogenous mode of competition. American Economic Review, 86, 237–258.

Mathewson, R., & Winter, F. (1984). An economic theory of vertical restraints. RAND Journal of Economics, 15, 27–38.CrossRef

McCardle, K., Rajaram, K., & Tang, C. (2004). Advance booking discount programs under retail competition. Management Science, 50(5), 701–708.CrossRef

Padmanabhan, V., & Png, I. P. L. (1997). Manufacturer’s returns policies and retail competition. Marketing Science, 16(1), 81–94.CrossRef

Padmanabhan, V., & Png, I. P. L. (2004). Reply to “Do returns policies intensify retail competition?”. Marketing Science, 23(4), 614–618.CrossRef

Shaffer, G. (1991). Slotting allowances and resale price maintenance: a comparison of facilitating practices. RAND Journal of Economics, 22, 120–135.CrossRef

Shapiro, C. (1989). Theories of oligopoly behavior. In R. Schmalensee, R. Willig, eds. Handbook of industrial organization. Vol. 1, Chapter 6. Elsevier Science, New York.

Spengler, J. (1950). Vertical integration and anti-trust policy. Journal of Political Economy, 58, 347–352.CrossRef

Tirole, J. (1988). The theory of industrial organization. Cambridge: MIT Press.

Viscusi, W., Vernon, J., & Harrington, J. (2005). Economics and regulation of antitrust. Cambridge: MIT Press.

Vives, X. (1985). On the efficiency of Bertrand and Cournot equilibria with product differentiation. Journal of Economic Theory, 36, 166–175.CrossRef

Wang, H. (2004). Do returns policies intensify retail competition? Marketing Science, 23(4), 611–613.CrossRef

Titel: The strategic use of early bird discounts for dealers
verfasst von: Desmond (Ho-Fu) Lo
Stephen W. Salant
Publikationsdatum: 01.06.2016
Verlag: Springer US
Erschienen in: Quantitative Marketing and Economics / Ausgabe 2/2016
Print ISSN: 1570-7156
Elektronische ISSN: 1573-711X
DOI: https://doi.org/10.1007/s11129-016-9167-4