Price Quantity Discounts_ Some Implications for Buyers and Sellers
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James B. Wilcox, Roy D. Howell, Paul Kuzdrall, & Robert Britney
Price Quantity Discounts:Some Implications for
Buyers and SellersPrice quantity discount schedules are shown to present opportunities to buyers beyond those explicit inthe discount schedule itself. The authors propose a taxononny of price quantity discount schedules, andwithin that taxonomy examine the implications of price quantity discounts for the ordering behavior ofbuyers and the formation of alternative channels of distribution.
BECAUSE of industry practice, for convenience,for marketing purposes, or for all of those rea-sons, the use of price quantity discount schedules hasbecome common in many industries. These sched-ules, intended to act as 24-hour salespersons, presentquantity-related prices and savings to potential buy-ers. Though the rationale for offering such discountshas been debated (Crowther 1964; Dolan 1978; Jeu-land and Shugan 1983; Lai and Staelin 1984; Monroeand Delia Bitta 1978), the practice has become ac-cepted and in many cases exf)ected in marketing.
Price quantity discounts may give buyers cost-lowering opportunities beyond those explicit in thediscount schedule itself. To lower cost per unit, buy-ers may order in quantities larger than they need andenter prearranged resale (pooled buying) agreementsor ad hoc brokerage situations. Additionally, more
James B. Wilcox and Roy D. Howell are Professors of Marketing, TexasTech University. Paul Kuzdrall is Associate Professor of Management,Uniyersity of Akron. Robert Britney is Professor of Production/Opera-tions Management, Uniyersity of Western Ontario. The authors grate-fully acknowledge the partial support of this work under Natural Sci-ences and Engineering Research Council of Canada Grant A-5311. Theyare also indebted to the numerous firms whose schedules were madeavailable for the research.
formal mechanisms for the distribution of the "ex-cess" merchandise may develop. Price quantity dis-counts recently have been criticized as one of the ma-jor factors contributing to the emergence of graymarkets (Donath 1985; Litley 1985), wherein the"surplus" units reenter the market through perhapsunanticipated and frequently unauthorized channels.Interestingly, with the exception of some caveats byeconomists (Buchanan 1953; Oi 1970), this possibil-ity has not been addressed adequately. The commonpractice of offering price quantity discounts has notbeen examined as a mechanism favoring the devel-opment of such markets.
To address the issues raised by price quantity dis-counts, we first briefly review the literature to developa framework. We then describe a taxonomy of modelsthat have been found to fit actual price quantity dis-count schedules. Next, within the context of thesemodels, the characteristics of discounts that give riseto the issues are examined. Finally, the seller's ra-tionale for offering price quantity discounts is recon-sidered.
Why Price Quantity Discounts?Several reasons for the use of price quantity discountshave been identified. Crowther (1964) suggests that
60 / Journal of Marketing, July 1987Journal of MarketingVol. 51 (July 1987), 60-70
sellers save in several ways by selling fewer, largerorders to their customers. One saving is from lowersales costs in that fewer sales calls are made, fewerorders are processed, and so on. A second is fromlowered costs for raw materials because quantity dis-counts are often available to the seller. Third, the timevalue of money is taken into account because largerrevenues are available for reinvestment for longer pe-riods. Finally, longer production runs without atten-dant increases in holding costs are possible (see alsoMonahan 1984). Monroe and Delia Bitta (1978) ex-tend Crowther's model to recognize the interactive ef-fects of these factors, though the reasoning behind thediscounts remains unchanged.
More recently, quantity discounts have been viewedas a tool for achieving channel cooperation. Jeulandand Shugan (1983), for example, see such discountsas a subtle form of profit sharing between levels inthe channel. In their model for optimizing channelprofits they propose negotiations between the sellerand each individual buyer to allocate optimally thesavings referred to by Crowther (1964). Though theybase their work on a different theory and make dif-ferent assumptions, Zusman and Etgar (1981) providea similar perspective.
Perhaps the most complete model has been offeredby Lai and Staelin (1984). They argue that thoughquantity discounts are believed to arise as a result ofpressure from large buyers, discounts also are offeredat small quantities. They conclude that effort on thepart of the seller to maximize profits by modifying thebuyers' order policy is a more likely explanation forthe use of discounts.
One additional reason for using price quantity dis-counts, addressed primarily by economists, is pricediscrimination. Gabor (1955) has shown that such dis-counts are actually two-part prices composed of a fixedand variable component. Oi (1970) has demonstratedthat, in comparison with a single-price strategy, a two-part price is an effective means for monopolists to in-crease profit. The two parts are a lump sum tax orfranchise fee paid for the right to purchase the mo-nopolist's product and a per-unit fee. The lump sumis the mechanism used to reduce consumer surplus.Oi notes, however, that such a strategy should seldombe employed because of the inability of the monop-olist to prevent resale. That is, in the absence of hightransaction costs of some sort, " . . . a single con-sumer could pay the lump sum tax and purchase largequantities for resale to others" (1970, p. 88).
Though in some of Oi's examples the franchisefee is a one-time payment (e.g., initiation fees for acountry club), that is not a necessary condition. Allthat is required is a fixed and variable component. Inthe models described hereafter, we demonstrate thatprice quantity discounts meet this requirement.
A Taxonomy of Price QuantityDiscount Models
According to Fartuch, Kuzdrall, and Britney (1984;see also Britney, Kuzdrall, and Fartuch 1983a,b) thereare two basic approaches to the presentation of pricequantity discounts and variations for each approach.The two major models are per-unit pricing (model I)and package pricing (model II). The variations withineach type include the presence (second degree) or ab-sence (first degree) of quantity intervals over which acertain price per unit applies. The models and theirvariations are shown graphically in Figure 1.
Model IModel I price schedules are characterized by per-unit,all-unit prices. That is, as the buyer orders largerquantities, the price per unit charged applies to all unitspurchased. First degree model I pricing is the limitingcase in which a unique price is associated with eachunit. Such price schedules may be presented as a longlist of quantities with the price at each quantity or maybe offered simply in terms of the fixed (F) and vari-able (V) components (e.g., $29 per day and 30 centsper mile). This model is shown in Figure 1 as havinga smooth, curvilinear price-quantity relationship. If asimilar approach is used but each price applies to arange or interval of quantities, the schedule becomesa second degree model I. For example, any quantityordered in the range of 50 to 75 units would carry thesame price per unit. These schedules also can be de-scribed by a fixed and variable component. In this case,price is held constant over a range, giving rise to the"stairstep" schedules shown in Figure 1. Note that thesteps originate from the continuous curve, either pro-jected backward (I-A), forward (I-B), or somewherebetween (I-A/B). Techniques for determining aschedule's fixed and variable components (F and V)are discussed in the Appendix. Forms of model I pric-ing are common and are used for such products assteel bars, stud bolts, recording tape, integrated cir-cuits, photocopying, stationery, office equipment, andexpendable computer supplies (see Table 1).Model IModel II pricing schedules refer to package pricing inwhich the buyer receives no credit for taking deliveryof fewer units than the maximum quantity in the pack-age. This type of pricing is usually the result of in-dustry practice and perhaps physical packaging re-quirements. Like model I, model II has a range ofvariations. Model II first degree schedules quote aunique package price for each quantity, as indicatedby the straight-line price-quantity relationship shownin Figure 1. Second degree schedules involve inter-vals of package quantities to which a single price ap-
Price Quantity Discounts / 61
FIGURE 1Forms of Price Quantity Discounts
plies and hence show a stairstep price-quantity rela-tionship. Again, the schedule is a projection from thecontinuous case. The techniques in the Appendix canbe used to decompose the schedules into F and Vcomponents, but the type A, B, and A/B distinctionsdo not apply to model II second degree schedules.Though not as common as model I, model II sched-ules are used in pricing paper, photographic film,transistors, capacitors, and electrical components.
In addition to models I and II, non-all-unit modelsare possible. For example, block pricing schedules areused by electric utilities. To get to a lower price onthe schedule, the buyer first must acquire the lowerquantities at higher prices. Such schedules are beyondthe scope of our discussion.
As shown in the Appendix, most quantity discountschedules can be decomposed into fixed (F) and vari-able (V) components following either model I or model
n pattems. As we discuss in more detail subse-quently, an examination of a large number of pub-lished price lists shows a surprisingly high proportionof schedules that "fit" one of the models depicted inFigure 1 (r^ > .95). The discovery