# Potential profitability and decreased consumer welfare through manufacturers' cents-off coupons.

It seems peculiar that so little attention has been paid to
potential adverse effects of manufacturers' cents-off couponing policies especially considering the volume and cost of their
distribution. In fact, it has been reported that in 1985 a total of
$180 billion worth of coupons was issued. The majority were distributed
blindly--approximately 60 percent in freestanding inserts, 31 percent
printed in newspapers and magazines, and the remaining nine percent by
mail or attached to the product package itself. Thus, given the
reported four percent redemption rate, approximately $7.2 billion worth
of coupons was used in 1985 (Clements 1986).

On the cost side, one survey estimated the cost of freestanding newspaper inserts to be approximately $7 per thousand with the cost increasing for other types of distribution (Clements 1986). If it is assumed that the average coupon value is $0.30 and the cited cost figure is employed, a low estimate of the fixed cost of coupon distribution in 1985 would be $4.2 billion. Clearly, even this rough estimate demonstrates that couponing costs are not a trivial use of resources.

Although the formal model of third-degree price discrimination employed in this paper occupies a time-honored position in the literature of economics, its implications in this area appear to have been widely ignored by consumer advocates. The fact that potential losses resulting from cents-off couponing are is some sense voluntary (all consumers have the option of redeeming coupons) may account for this lack of interest because this type of price discrimination is not prohibited under the Robinson-Patman Act. Also, the view that manufacturers' cents-off coupons are mainly promotional may alleviate concern over the types of losses discussed here.

This paper examines the potential magnitude of the increase in oligopolistic manufacturers' profits due to a policy cents-off couponing and the resulting changes in consumer welfare and resource allocation. In addition, evidence is presented in support of the hypothesis that observed couponing policies of U.S. manufacturers are motivated by their desire to increase profits through third-degree price discrimination--a practice that results in welfare losses to consumers.

Third-degree price discrimination involves the ability of a producer to separate customers into two (or more) distinct demand groups and charge two (or more) different prices to members of each group. In contrast, first-degree price discrimination or perfect price discrimination involves selling each unit of a good at its demand price with the last unit being sold at marginal cost. Second-degree price discrimination or block pricing entails selling the first block of output associated with the price of say, [P.sub.1] or greater at [P.sub.1], the second block associated with a demand price less than [P.sub.1] but greater than or equal to [P.sub.2] at [P.sub.2]([P.sub.1] > [P.sub.2]), and so on until the last block is sold at marginal cost.

While some of the conclusions of this paper have been dealt with by other researchers (Narasimhan 1984; Phlips 1983; Robinson 1933; Schmalensee 1981; Tirole 1988; Vilcassim and Wittink 1987; Yamey 1974), the approach taken here differs in that it attempts to quantify the probable magnitudes of the welfare effects and profit potential of oligopolistic manufacturers' couponing policies within the framework of a third-degree price discrimination model.

An innovative simulation approach which offers a useful alternative methodology for future research is introduced. Moreover, the idea that products redeemed with a coupon carry additional marginal cost of redemption is incorporated into the analysis. As is expected, this will lower the quantity produced when compared to the outcome under single oligopolistic pricing. This investigation will be limited to markets in which products are already well established and the demand curves facing each firm in a market will be assumed to be constant. This view is not unreasonable since "92 percent of blind-distributed coupons are redeemed by customers who have used the product before" (Clements 1986). This study will abstract from the promotional and advertising or inventory reducing aspects associated with couponing.(1)

One way to delineate between coupons motivated by promotional or inventory reducing considerations is whether they carry an expiration date. As a practical matter, continual reissuing of dated coupons leads to the suggestion that expiration date serves as a monitor to track purchases made with and without coupons. Thus, it is difficult to distinguish between coupons issues that are purely promotional and those that are discriminatory unless they are for newly introduced products or brands. For a complete discussion of possible objectives of coupon promotional programs, see Vilcassim and Wittink (1987), Narasimhan (1984), and Chapman (1986).

Under these assumptions, the analysis will be based on the Pigouvian model of third-degree price discrimination (Pigou 1932) within a market structure characterized by n identical Cournot oligopolists. The higher of the two prices will correspond to the shelf price of a product and the lower will measure the shelf price minus the coupon discount. Consumers independently separate themselves into two distinct groups, coupon users and nonusers, based on their own subjective valuation of the value of their time, their income, product prices, and their tastes. In general, one expects a major determinant of time costs to be reflected in the wage rate earned by a consumer. Thus, it is expected that higher wage earners would be less likely to be coupon users than consumers with lower wage rates and corresponding lower opportunity costs. Although on the surface this appears reasonable, Narasimhan (1984) finds inconclusive evidence in her quantitative analysis to support this hypothesis.

This reasoning may shed light on the tremendous increase of 500 percent in coupon distribution over the last ten years (Narasimhan 1984). Traditionally, women have been the grocery shoppers in the United States. As the number of professional women in the labor market has risen over the last decade, the number of potential noncoupon users or price inelastic consumers may have also increased, making it more profitable in some situations to price discriminate. This proposition will be demonstrated analytically in the next section.

It should be noted that redemption of coupons by customers not only increases marginal costs associated with production vis-a-vis redemption, but also represents a negative externality to noncoupon users. Time spent in a supermarket checkout queue increases as more customers submit more coupons to the cashier. These couponing costs cannot be measured, but it is felt that they are not trivial.

LINEAR MODEL AND RESULTS

Basic Framework and Assumptions

The first complete discussion of the welfare effects of third-degree price discrimination can be attributed to Joan Robinson (1933). Assuming linear demand curves, a single monopolist supplier, and employing a graphical approach, she derived many of the basic results presented here. The results derived in this paper are somewhat more general since oligopoly instead of strict monopoly is assumed. Results presented will generally depend on the number of oligopolistic suppliers, n. Although many of these results may be found in somewhat different forms elsewhare, they are included in order to give a cohesive and comprehensive presentation. The particular attention devoted to the magnitudes of potential profits, consumer surplus, and dead weight loss is original.

With this in mind, let there exist two types of consumers in a market, those with a lower price elasticity of demand and those with a higher price elasticity of demand. Throughout this paper elasticity is assumed to refer to elasticity at a given price value. Specifically, the following continuous downward sloping inverse demand functions represent the two demand segments where [P.sub.L] represents the shelf price or full pay and [P.sub.H] represents [P.sub.L] minus the coupon value. The two respective market quantities demanded are denoted as [Q.sub.H] and [Q.sub.L].(2)

[P.sub.L] = [[alpha].sub.L] - [[beta].sub.L[Q.sub.L]] [[alpha].sub.L], [[beta].sub.L] > 0 (1)

[P.sub.H] = [[alpha].sub.H] - [[beta].sub.H[Q.sub.H]] [[alpha].sub.H], [[beta].sub.H] > 0 (2)

where

[Mathematical Expression Omitted]

n = number of oligopolistic suppliers in a market, [q.sub.Li] = output of the [i.sup.th] firm in the low elasticity market, and [q.sub.Hi] = output of the [i.sup.th] firm in the high elasticity market.

For simplicity, it is initially assumed that no costs are associated with the production or sale of the products in question. It is easy to show that the introduction of constant marginal costs into this analysis only increases the percentage changes in profits due to price discrimination.(3) In addition, it is assumed that because of other noncouponing types of advertising and promotion strategies, each producer views the demand curve as constant and the quantity produced by rivals as invariant to decisions made. It is also assumed that all firms are idential and that each of the n firms make their production decisions as would a standard Cournot oligopolist. It should be clear that under these assumptions, if couponing is profitable for one firm it will be profitable for all firms. In fact, it can be easily argued that if one firm chooses to issue coupons, all firms will be forced to do so. Therefore the standard type of Cournot noncooperative equilibrium market output and price values will be computed.

Given this framework, each oligopolistic manufacturer faces the following set of maximization problems. On one hand, each of the n identical Cournot oligopolists could choose a single output strategy that solves the following optimization problem given below for the [i.sup.th] firm. This will be referred to as case I.

[Mathematical Expressions Omitted]

Here, the term in brackets is simply the total market inverse demand function for P [is less than or equal to] min([[alpha].sub.L], [[alpha].sub.H]). This condition insures that both markets must be served under a single pricing policy. Otherwise, third-degree price discrimination would generally be preferable. Under the assumption of zero-marginal cost, the optimal price will indeed always satisfy this condition. Because this study is mainly interested in market equilibrium values, firm level output, and profit, although they may be easily computed by dividing the market values by n, will not be explicitly reported.

The resulting Cournot equilibrium values for price ([P.sub.o]), output ([Q.sub.o]), and profits ([[pi].sub.o]) can be computed as (footnote 3)

[Mathematical Expressions Omitted]

It will become obvious that if [[alpha].sub.L] = [[alpha].sub.H], the single pricing strategy (case I) will be optimal when compared to the two-tier strategy (case II). Intuitively, if [[alpha].sub.L] = [[alpha].sub.H], both demand curves will be equally elastic at each particular price. Therefore, the potential to price discriminate vanishes.

On the other hand, if the oligopolistic firms are able to issue coupons, and as generally is assumed (Narasimhan 1984), coupon users correspond to high price elasticity of demand consumers, then each firm may be thought of as simultaneously solving the following two maximization problems. This will be referred to as case II.

[Mathematical Expressions Omitted]

As before, optimal values of the prices ([P.sub.L], [P.sub.H]), market outputs ([Q.sub.L], [Q.sub.H]), and market profits ([[pi].sub.L], [[pi].sub.H]) for high and low elasticity customers may be computed as

[Mathematical Expressions Omitted]

The combined profits earned through price discrimination, II = [[pi].sub.L] + [[pi].sub.H], may be written as (4)

[Mathematical Expressions Omitted]

Comparison of Prices and Profits

A major concern is the magnitude of the potential difference in profits and prices under a couponing strategy (case II) and a single-price strategy (case I). Given the analytical expressions computed previously, the difference and percentage difference in profits may be written as

[Mathematical Expressions Omitted]

If [[alpha].sub.L] > [[alpha].sub.H], a costless couponing policy will increase profits due purely to the reconfiguration of price and addition of coupon distribution without any change in total quantity sold. Invariance of total output sold can be found by adding [Q.sub.H] and [Q.sub.L] from equation (10) and comparing it to equation (5). Total quantity will be reduced when constant marginal costs differ between the consumer groups served. Thus, equation (14) reflects an increase in profits with quantity held constant. Generally, equation (14) is an underestimate of the percentage change in potential profits under constant common marginal costs and an overestimate when constant marginal costs differ across consumer groups. (5)

As is apparent from either equation (13) or (14), if [[alpha].sub.L] = [[alpha].sub.H], then profits (assuming zero couponing costs) are equivalent and it would be desirable for the oligopolistic firms to charge a single price. If there are fixed costs associated with a coupon distribution policy, a single-price policy will be optimal if the associated fixed costs are greater than the increase in profits associated with the couponing policy. The corresponding percentage difference in prices may be expressed as (6)

[Mathematical Expressions Omitted]

By inspection of equations (15) and (16), it should be clear that [[alpha].sub.H] must be less than [[alpha].sub.L] if in fact higher elasticity consumers or coupon users are to pay a lower net price for the commodity. It is assumed that [[alpha].sub.L] > [[alpha].sub.H] throughout this paper. In addition, equation (14) depends only on the relative magnitudes of [[alpha].sub.H], [[alpha].sub.L], [[beta].sub.H], and [[beta].sub.L]. Formally, let [[alpha].sub.H] = [[theta] [alpha].sub.L], where 0 < [theta] < 1 and [[beta].sub.H] = [unkeyable] [[beta].sub.L], where [unkeyable] > 0.

Making appropriate substitutions the percentage change in profits may be written as

[Mathematical Expressions Omitted]

Table 1 contains simulated values for equation (14) and (14'). Notice that the percentage change in profits applies to both market and firm level profits and does not depend on number of firms in an industry.

Making appropriate substitution in equation (9), the percentage coupon discount may be written as (1 - [theta]). Thus, [theta] values of less than perhaps .6 yield somewhat unreasonable results. However, it does not appear unreasonable to observe coupon discounts in the neighborhood of 30 percent. From Table 1, one can see that couponing, when [theta] = .7 and [unkeyable] ranges from 0.2 to 0.29, will yield nontrivial increases in profits. If the fixed cost associated with couponing is less than say two percent of precouponing profits, couponing can substantially raise profits. From these simulated results, it is evident that couponing can indeed be motivated by the desire to increase profits through a policy of third-degree price discrimination.

[TABULAR DATA OMITTED]

From Table 1, the effect of increasing the percentage of potential coupon users can also be evaluated. The reader is reminded that [[beta].sub.H] and [[beta].sub.L] can be interpreted as [b.sub.L]/N(1 - [lambda]) and [b.sub.H]/N[lambda] where [b.sub.L] and [b.sub.H] are the slope coefficients from a high and low elasticity consumer's individual demand schedules, respectively. The total number of consumers that the firm faces is assumed to be a constant, N, and [lambda] is the percentage of potential coupon users. Although one might view [lambda] as a random variable, it is assumed that each firm makes its decisions as if [lambda] were known with certainty. Holding [b.sub.L], [b.sub.H], and N constant, increases in [lambda] can be thought of as decreases in [unkeyable]. For example, if the initial demand configuration is characterized by [theta] = .7 and [unkeyable] = 0.9, the effect of increases in the percentage of coupon users can be seen from reading up the [theta] = .7 column from [unkeyable] = 0.9. From Table 1 it can be seen that the percentage change in profits due to couponing will increase from 3.16 percent when [unkeyable] = 0.9 to 3.21 percent when [unkeyable] = 0.7 and then decline for [unkeyable] < 0.7. This is a somewhat general result. It will be shown that the maximum percentage change in profits occurs when [unkeyable] = [theta] or equivalently when [[alpha].sub.L]/[[beta].sub.L] = [[alpha].sub.H]/[[beta].sub.H].

If firms are motivated by potential percentage increases in potential maximum profits, these results may in part explain the increased implementation of couponing by U.S. manufacturers. As [unkeyable] rises, ceteris paribus, the percentage of noncoupon users (1 - [lambda]) rises as does the associated percentage change in profits when [unkeyable] [is less than or equal to] [theta].

Even within this simplified analytical framework a graphical representation of the relationship between the two types of consumers is useful. The possible demand configurations that are consistent with price discrimination must be isolated. Figures 1(A) through 1(D) illustrate these possible relationships between demands of high and low elasticity consumers.

To fix a point of reference, the bold lines in Figure 1(A) through 1(D) represent the demand curve for low elasticity customers (labeled as [D.sub.L]). These illustrations are static in the sense that they do not capture changes in the proportion of high and low elasticity consumers. Therefore, the differences between the individual demands can be examined. Thus, the slope is - [[beta].sub.L], the maximum reservation price of low elasticity consumers is [[alpha].sub.L], and the quantity demanded at a zero price would be [[alpha].sub.L]/[[beta].sub.L]. In each case [[alpha].sub.L] must be greater than [[alpha].sub.H].

Given the arbitrary position of this demand segment, there are three distinct possible ranges for the value of [[alpha].sub.H]/[[beta].sub.H] for which it will be useful to distinguish. In terms of Table 1, range 1 implies [phi] = [theta], range 2 implies [phi] < [theta], and range, 3, [phi] > [theta].

range 1: [alpha]L/[beta]L = [alpha]H/[beta]H [alpha]L > [alpha]H

range 2: [alpha]L/[beta]L < [alpha]H/[beta]H [alpha]L > [alpha]H

range 3: [alpha]L/[beta]L > [alpha]H/[beta]H [alpha]L > [alpha]H

Figure 1(A) illustrates the effect of changes in [[beta].sub.H] holding [[beta].sub.L] and [[alpha].sub.L] > [[alpha].sub.H] constant. As [[beta].sub.H] falls, the high elasticity demand increases. Elasticity at each price, however, remains unaltered. As long as [[alpha].sub.L] > [[alpha].sub.H], the high demand will be more elastic than the low demand.

Figure 1(B) through 1(D) illustrate the effects of changes in [[alpha].sub.H] holding [[beta].sub.H], [[beta].sub.L], and [[alpha].sub.H] constant. Figure 1(B) represents demand configurations where [[beta].sub.H] < [[beta].sub.L]; 1(C), [[beta].sub.H] > [[beta].sub.L]; and 1(D), [[beta].sub.H] = [[beta].sub]L]. As [[alpha].sub.H] increases, high elasticity demand increases and high price elasticity declines. At a given price, as [[alpha].sub.H] approaches [[alpha].sub.L], the two price elasticities approach each other and as demonstrated previously, there will be no profit gain resulting from couponing. Thus, in all cases, [P.sub.H] is less than [P.sub.L]. These four configurations illustrate changes in high elasticity demand that correspond to the partial derivatives with respect to [[alpha].sub.H] and [[beta].sub.H]. This interpretation will be examined further. Intuitively, Figure 1(C) and 1(D) represent a situation where "low" demand is larger than "high" demand. Thus, the demand is greater for low elasticity consumers. Data are unavailable that would shed light on the previously mentioned demand configurations, however, they do not seem probable. For products in this study (laundry, dish, and bath soaps, certain brands of breakfast cereals, etc.), Figure 1(A) and 1(B) may be more relevant. Here, at least for fairly low prices, the "high" demand is larger than the "low" demand. In fact, from equation (10) it is clear that when demand is configured as in Figure 1(A) or 1(B) and [[alpha].sub.H]/[[beta].sub.H] > [[alpha].sub.L]/[[beta].sub.L] (range 3), the quantity sold with a coupon discount will be larger than noncoupon purchases. The percentage of coupon transactions is greater than percentage of noncoupon transactions.

Having formalized the linear model, the following four questions will be addressed. (1) Under what demand configurations will the incentive to engage in a cents-off couponing policy be greatest? The answer to this question could allow the direct profit incentive in certain markets where couponing is observed to be ruled out. In these markets, it will be likely that couponing is a promotional or inventory reducing device. (2) Under which demand configurations will profits be greatest? (3) How are the face value and percentage coupon discount affected by the demand configuration? and (4) How is the change in the shelf price affected by the demand configuration? Is the Vilcassim-Wittink hypothesis that increases in the percentage of coupon usage lead to higher shelf prices supported?

In regard to the first and second questions, it must be made clear that it is assumed that the overriding goal of the firm is profit maximization rather than, for example, sales maximization. Therefore, the demand configuration that will yield the highest change in profits would be the one where the incentive to coupon would be greatest. It is interesting to note that as the higher elasticity approaches the lower elasticity or, as [[alpha].sub.H] approaches [[alpha].sub.L], the change in profits due to couponing goes to zero, and obviously the incentive to coupon evaporates. On the other hand, this situation, given [[beta].sub.H] and [[beta].sub.L], corresponds to the highest attainable profits (given [[alpha].sub.L] > [[alpha].sub.H]. Thus, it is most profitable for the demand configurations to imply a noncouponing policy.

Returning to questions (1) and (2), it has been assumed that [[alpha].sub.L] > [[alpha].sub.H] and the change in profits will reflect the effects of [[beta].sub.H]. It is easy to see from equation (13) that smaller values of [[beta].sub.H] yield higher additional profits due to couponing while increasing the elasticity at each price. Thus, demand configurations illustrated by Figure 1(A) and 1(B) result in a higher incentive to coupon and concurrently yield lower profit levels. Given nonzero costs of couponing, it may be concluded that when [[alpha].sub.H] is close to [[alpha].sub.L] or when [[beta].sub.H] is large relative to [[beta].sub.L], couponing policies are not directly related to profit maximization through price discrimination and must therefore be related to profit maximization via other avenues.

If the incentive to coupon is determined by the highest percentage change in potential profits due to couponing, then it would be expected that couponing policies would be most prevalent when [[alpha].sub.L]/[[beta].sub.L] = [[alpha].sub.H]/[[beta].sub.H]. To see this, equation (14) may be maximized with respect to [[beta].sub.H]. The appropriate first-order condition is

[Mathematical Expression Omitted]

Rearranging equation (17) it can be shown that [[alpha].sub.L/[[beta].sub.L] = [[alpha].sub.H]/[[beta].sub.H] when [Delta][pi]/[pi] is at its maximum. (7)

The third question regarding the face value of a coupon and the percentage coupon discount is easily answered by referring back to equation (9). It is clear that these values depend only on [[alpha].sub.L] and [[alpha].sub.H] or on the maximum reservation prices of the two consumer classes when n is held constant. The face value of the coupon may be written as

[Mathematical Expression Omitted]

and the percentage coupon discount is

[Mathematical Expression Omitted]

Again, these results are not surprising. The divergence in optimal prices is determined by the divergence in the maximum reservation prices of the two groups and n, number of firms. (8) With this in mind, observing coupon discounts or more than say 30 percent would shed doubt on the direct profit motive behind price discrimination because it does not, to the casual observer, seem likely to find larger average discrepancies such that [[alpha].sub.H] is less than say 70 percent of [[alpha].sub.L] in reservation prices. It is interesting to note that while the number of firms does not affect the percentage coupon discount, the face value of a coupon will decrease as industry concentration declines.

The last question to be addressed is whether or not the model presented supports the Vilcassim-Wittink hypothesis that increases in the percentage of coupon usage lead to higher shelf prices. Given the demand configuration, the percentage of coupon usage for a particular product will rise whenever [Q.sub.H]/[Q.sub.L] rises. Thus, from equation (10), the following is derived.

[Mathematical Expression Omitted]

The change in shelf price, computed by taking the difference in the single Cournot oligopoly price and the price charged to low elasticity customers, may be written as

[Mathematical Expression Omitted]

The inclusion of constant marginal costs leaves (21) unaltered. Taking the partial derivatives with respect to [[alpha].sub.H] and [[beta].sub.H], it is clear that the shelf price increase is positively related to decreases in [[alpha].sub.H] and [[beta].sub.H].

[Mathematical Expression Omitted]

From equations (21), (22), and (23) it is evident that, given [[alpha].sub.L] and [[beta].sub.L], increases in percentage of coupon usage occur when [[alpha].sub.H]/[[beta].sub.H] increases. Thus, the increase in coupon usage is caused by a decrease in [[beta].sub.H] and the Vilcassim-Wittink hypothesis is supported. Increases in percentage of coupon usage caused by increases in [[alpha].sub.H] are, however, not supported.

Comparison of Consumer Welfare and Resource Allocation

The last question to be answered, given the profitability of couponing already established under the linear model, is whether couponing leaves consumers, as a whole, better or worse off. In addition, the effect of a couponing policy on allocation of resources within a particular market and among consumer classes will be discussed. As is generally done, consumer welfare is measured by Consumer Surplus (CS) and resource misallocation by Dead Weight Loss (DWL). Any redistributional issues associated with transferring consumer surplus between consumer groups are ignored.

It will be demonstrated that, when couponing is profitable and high price elasticity consumers pay a lower price via couponing, lower CS and higher DWL will result when compared to an oligopolistic sinigle price equilibrium. Couponing, given the constrained relationship between high and low elasticity demands, leads to higher profits. This increase in profits can be accompanied by decreased consumer welfare and increased resource misallocation between consumer groups. The common assumption that a dollar's worth of CS is valued identically by both high and low elasticity consumers is implicitly being made in this analysis. Moreover, the decrease in consumer surplus is underestimated because the present framework does not capture the user costs incurred by consumers who clip, organize, and redeem coupons nor the negative externalities coupon users inflict on nonusers at redemption. In addition, incorporating the plausible presumption that products redeemed with a coupon have higher marginal costs associated with them, it will be argued that the net welfare loss due to couponing is exacerbated.

To facilitate the discussion of the propositions outlined, Figure 2(A) and 2(B) will be useful. Positioning of the two demand curves is arbitrary except that [[alpha].sub.L] > [[alpha].sub.H]. The line LL represents low elasticity demand and HH represents high elasticity demand.

The net loss in CS may be computed by subtracting the loss in CS suffered by low elasticity consumers due to couponing from the gain enjoyed by high elasticity consumers. Specifically, the absolute value of the loss in CS is represented by the shaded region in Figure 1(A) and may be written as

[Mathematical Expression Omitted]

In equation (24), [P.sub.o], [P.sub.L], and [Q.sub.L] refer to values given by equations (4), (9), and (10), respectively, and [Q.sub.L]([P.sub.o]) is the quantity demanded by low elasticity consumers when price equals [P.sub.o]. The absolute value of the gains in CS is represented by the shaded region in Figure 2(B) and is computed as

[Mathematical Expression Omitted]

Again, [P.sub.o], [P.sub.H], and [Q.sub.H] refer to equations (4), (9), and (10) and [Q.sub.H]([P.sub.o]) is the quantity demanded by high elasticity consumers when price equals [P.sub.o]. Subtracting (24) from (25) the net [Delta]CS due to couponing is given by

[Mathematical Expression Omitted]

As before, [Delta][pi] refers to increase in profits under couponing when compared to a single Cournot equilibrium price, equation (13).

It should be clear that in the model presented, loss in CS due to couponing entails not only a transfer of benefits from consumers to producers, but a net welfare loss of 1/2n([Delta][pi]). The [Delta]DWL due to couponing is

[Mathematical Expression Omitted]

Thus, couponing will lead to a decrease in total welfare. This loss in total welfare is due purely to a misallocation of the product among consumers because output remains constant in the case of either zero or constant common marginal costs.

If the practical presumption that products redeemed with a coupon carry higher marginal costs is incorporated into the model, welfare loss increases. As can be seen from footnote 6, [P.sub.o] - [P.sub.H] will be lower and [Q.sub.H] will decline, thus lowering the resulting increase in the gain in CS that high elasticity consumers would enjoy (loss remains the same). In this case, misallocation of resources reflects not only a sub-optimal distribution of the product among consumers, but also the contraction of output. To compound the reduction in the gain to CS, losses to CS associated with time costs incurred by customers who redeem coupons and the externalities imposed on nonusers during redemption must be included, at least theoretically.

CONCLUSION

This study has lent support to the arguments of Vilcassim and Wittink (1987) concerning potential profitability of couponing--an issue that appears to be of interest in marketing. Specifically, it has been shown that couponing policies can indeed raise profits substantially and increase shelf price of the product in question. Effects of higher marginal costs due to redemption have been formally introduced as has the idea that nonmeasurable redemption costs, borne by both users and nonusers, must be considered. A major conclusion is the demonstration that couponing policies of American oligopolistic manufacturers are potentially harmful to consumers as a whole and aggravate resource misallocation. These losses are not offset by increased profits.

In general, of major concern to economists is resource misallocation, not the transfer of profits and consumer surplus. What cents-off couponing leads to under the present framework is a situation in which the good in question is not fully allocated among consumers who value it most highly. Some low elasticity consumers will not purchase the product as [P.sub.L] even though they have a demand price greater than some high elasticity consumers who purchase the good at [P.sub.H].

Noncoupon users have little room to improve their situation. They made the decision to be low elasticity consumers based on subjective evaluation of the costs and benefits of using coupons. The transactions or arbitrage costs that a low elasticity consumer would incur when trying to "buy" the good from a high elasticity purchaser would certainly be too steep to warrant the trade because, on an individual level, savings would be limited to the coupon value.

Therefore, limited expenditure savings of an individual associated with cents-off couponing serves as an effective arbitrage barrier. This barrier is further enhanced by the difficulty of identifying arbitrage partners. Cents-off couponing fulfills two important prerequisites to price discrimination--identification and separation of consumer classes. There seems to be little room for the situation to be remedied by unilateral behavior of individuals.

Under the simplifying assumptions made in this paper, the evidence supports the prohibition of cents-off couponing. In a single-price equilibrium, total output probably would be expanded (assuming noncommon constant marginal costs), consumer surplus would increase, and the good would be allocated to those who receive the highest benefit from its consumption.

By employing a model of Cournot oligopoly it has been demonstrated that the benefits to society of banning cents-off couponing policies are positively related to the industry concentration. If number of firms in an industry is small, there will be higher losses incurred by society under cents-off couponing. Cents-off couponing can be viewed as an extension of market power not as a vehicle with which to obtain or maintain it.

REFERENCES

Chapman, Randall (1986), "Assessing the Probability of Retailer Couponing with a Low-Cost Field Experiment," Journal of Retailing, 62(1, Spring): 19-40.

Clements, Jonathan (1986), "The Increasing Payoff in Cents-off," Forbes (December 29): 40.

Narasimhan, Chakravarthi (1984), "A Price Discrimination Theory of Coupons," Marketing Science (3, Spring): 128-147.

Pigou, A. C. (1932), The Economics of Welfare, London: Macmillan.

Phlips, Louis (1983), The Economics of Price Discrimination, Cambridge, MA and New York: Cambridge University Press.

Robinson, Joan (1933), The Economics of Imperfect Competition, London: Macmillan.

Schmalensee, Richard (1981), "Output and Welfare Implications of Monopolistic Third-Degree Price Discrimination," American Economic Review (71):242-247.

Tirole, Jean (1988), Industrial Organization, Cambridge, MA: MIT Press.

Vilcassim, Naufel and Dick Wittink (1987), "Supporting a Higher Shelf Price Through Coupon Distributions," Journal of Consumer Marketing (4, Spring): 29-39.

Yamey, Basil (1974), "Monopolistic Price Discrimination and Economic Welfare," Journal of Law and Economics (17, October): 277-280.

Jamie Howell is Assistant Professor of Economics, Department of Economics, Haverford College, Haverford, PA.

The author wishes to thank Haverford College, The Dana Foundation, and The Mellon Fund for the 80's for their support in this research, in addition to the four anonymous referees and the editor for their very helpful comments on this paper.

On the cost side, one survey estimated the cost of freestanding newspaper inserts to be approximately $7 per thousand with the cost increasing for other types of distribution (Clements 1986). If it is assumed that the average coupon value is $0.30 and the cited cost figure is employed, a low estimate of the fixed cost of coupon distribution in 1985 would be $4.2 billion. Clearly, even this rough estimate demonstrates that couponing costs are not a trivial use of resources.

Although the formal model of third-degree price discrimination employed in this paper occupies a time-honored position in the literature of economics, its implications in this area appear to have been widely ignored by consumer advocates. The fact that potential losses resulting from cents-off couponing are is some sense voluntary (all consumers have the option of redeeming coupons) may account for this lack of interest because this type of price discrimination is not prohibited under the Robinson-Patman Act. Also, the view that manufacturers' cents-off coupons are mainly promotional may alleviate concern over the types of losses discussed here.

This paper examines the potential magnitude of the increase in oligopolistic manufacturers' profits due to a policy cents-off couponing and the resulting changes in consumer welfare and resource allocation. In addition, evidence is presented in support of the hypothesis that observed couponing policies of U.S. manufacturers are motivated by their desire to increase profits through third-degree price discrimination--a practice that results in welfare losses to consumers.

Third-degree price discrimination involves the ability of a producer to separate customers into two (or more) distinct demand groups and charge two (or more) different prices to members of each group. In contrast, first-degree price discrimination or perfect price discrimination involves selling each unit of a good at its demand price with the last unit being sold at marginal cost. Second-degree price discrimination or block pricing entails selling the first block of output associated with the price of say, [P.sub.1] or greater at [P.sub.1], the second block associated with a demand price less than [P.sub.1] but greater than or equal to [P.sub.2] at [P.sub.2]([P.sub.1] > [P.sub.2]), and so on until the last block is sold at marginal cost.

While some of the conclusions of this paper have been dealt with by other researchers (Narasimhan 1984; Phlips 1983; Robinson 1933; Schmalensee 1981; Tirole 1988; Vilcassim and Wittink 1987; Yamey 1974), the approach taken here differs in that it attempts to quantify the probable magnitudes of the welfare effects and profit potential of oligopolistic manufacturers' couponing policies within the framework of a third-degree price discrimination model.

An innovative simulation approach which offers a useful alternative methodology for future research is introduced. Moreover, the idea that products redeemed with a coupon carry additional marginal cost of redemption is incorporated into the analysis. As is expected, this will lower the quantity produced when compared to the outcome under single oligopolistic pricing. This investigation will be limited to markets in which products are already well established and the demand curves facing each firm in a market will be assumed to be constant. This view is not unreasonable since "92 percent of blind-distributed coupons are redeemed by customers who have used the product before" (Clements 1986). This study will abstract from the promotional and advertising or inventory reducing aspects associated with couponing.(1)

One way to delineate between coupons motivated by promotional or inventory reducing considerations is whether they carry an expiration date. As a practical matter, continual reissuing of dated coupons leads to the suggestion that expiration date serves as a monitor to track purchases made with and without coupons. Thus, it is difficult to distinguish between coupons issues that are purely promotional and those that are discriminatory unless they are for newly introduced products or brands. For a complete discussion of possible objectives of coupon promotional programs, see Vilcassim and Wittink (1987), Narasimhan (1984), and Chapman (1986).

Under these assumptions, the analysis will be based on the Pigouvian model of third-degree price discrimination (Pigou 1932) within a market structure characterized by n identical Cournot oligopolists. The higher of the two prices will correspond to the shelf price of a product and the lower will measure the shelf price minus the coupon discount. Consumers independently separate themselves into two distinct groups, coupon users and nonusers, based on their own subjective valuation of the value of their time, their income, product prices, and their tastes. In general, one expects a major determinant of time costs to be reflected in the wage rate earned by a consumer. Thus, it is expected that higher wage earners would be less likely to be coupon users than consumers with lower wage rates and corresponding lower opportunity costs. Although on the surface this appears reasonable, Narasimhan (1984) finds inconclusive evidence in her quantitative analysis to support this hypothesis.

This reasoning may shed light on the tremendous increase of 500 percent in coupon distribution over the last ten years (Narasimhan 1984). Traditionally, women have been the grocery shoppers in the United States. As the number of professional women in the labor market has risen over the last decade, the number of potential noncoupon users or price inelastic consumers may have also increased, making it more profitable in some situations to price discriminate. This proposition will be demonstrated analytically in the next section.

It should be noted that redemption of coupons by customers not only increases marginal costs associated with production vis-a-vis redemption, but also represents a negative externality to noncoupon users. Time spent in a supermarket checkout queue increases as more customers submit more coupons to the cashier. These couponing costs cannot be measured, but it is felt that they are not trivial.

LINEAR MODEL AND RESULTS

Basic Framework and Assumptions

The first complete discussion of the welfare effects of third-degree price discrimination can be attributed to Joan Robinson (1933). Assuming linear demand curves, a single monopolist supplier, and employing a graphical approach, she derived many of the basic results presented here. The results derived in this paper are somewhat more general since oligopoly instead of strict monopoly is assumed. Results presented will generally depend on the number of oligopolistic suppliers, n. Although many of these results may be found in somewhat different forms elsewhare, they are included in order to give a cohesive and comprehensive presentation. The particular attention devoted to the magnitudes of potential profits, consumer surplus, and dead weight loss is original.

With this in mind, let there exist two types of consumers in a market, those with a lower price elasticity of demand and those with a higher price elasticity of demand. Throughout this paper elasticity is assumed to refer to elasticity at a given price value. Specifically, the following continuous downward sloping inverse demand functions represent the two demand segments where [P.sub.L] represents the shelf price or full pay and [P.sub.H] represents [P.sub.L] minus the coupon value. The two respective market quantities demanded are denoted as [Q.sub.H] and [Q.sub.L].(2)

[P.sub.L] = [[alpha].sub.L] - [[beta].sub.L[Q.sub.L]] [[alpha].sub.L], [[beta].sub.L] > 0 (1)

[P.sub.H] = [[alpha].sub.H] - [[beta].sub.H[Q.sub.H]] [[alpha].sub.H], [[beta].sub.H] > 0 (2)

where

[Mathematical Expression Omitted]

n = number of oligopolistic suppliers in a market, [q.sub.Li] = output of the [i.sup.th] firm in the low elasticity market, and [q.sub.Hi] = output of the [i.sup.th] firm in the high elasticity market.

For simplicity, it is initially assumed that no costs are associated with the production or sale of the products in question. It is easy to show that the introduction of constant marginal costs into this analysis only increases the percentage changes in profits due to price discrimination.(3) In addition, it is assumed that because of other noncouponing types of advertising and promotion strategies, each producer views the demand curve as constant and the quantity produced by rivals as invariant to decisions made. It is also assumed that all firms are idential and that each of the n firms make their production decisions as would a standard Cournot oligopolist. It should be clear that under these assumptions, if couponing is profitable for one firm it will be profitable for all firms. In fact, it can be easily argued that if one firm chooses to issue coupons, all firms will be forced to do so. Therefore the standard type of Cournot noncooperative equilibrium market output and price values will be computed.

Given this framework, each oligopolistic manufacturer faces the following set of maximization problems. On one hand, each of the n identical Cournot oligopolists could choose a single output strategy that solves the following optimization problem given below for the [i.sup.th] firm. This will be referred to as case I.

[Mathematical Expressions Omitted]

Here, the term in brackets is simply the total market inverse demand function for P [is less than or equal to] min([[alpha].sub.L], [[alpha].sub.H]). This condition insures that both markets must be served under a single pricing policy. Otherwise, third-degree price discrimination would generally be preferable. Under the assumption of zero-marginal cost, the optimal price will indeed always satisfy this condition. Because this study is mainly interested in market equilibrium values, firm level output, and profit, although they may be easily computed by dividing the market values by n, will not be explicitly reported.

The resulting Cournot equilibrium values for price ([P.sub.o]), output ([Q.sub.o]), and profits ([[pi].sub.o]) can be computed as (footnote 3)

[Mathematical Expressions Omitted]

It will become obvious that if [[alpha].sub.L] = [[alpha].sub.H], the single pricing strategy (case I) will be optimal when compared to the two-tier strategy (case II). Intuitively, if [[alpha].sub.L] = [[alpha].sub.H], both demand curves will be equally elastic at each particular price. Therefore, the potential to price discriminate vanishes.

On the other hand, if the oligopolistic firms are able to issue coupons, and as generally is assumed (Narasimhan 1984), coupon users correspond to high price elasticity of demand consumers, then each firm may be thought of as simultaneously solving the following two maximization problems. This will be referred to as case II.

[Mathematical Expressions Omitted]

As before, optimal values of the prices ([P.sub.L], [P.sub.H]), market outputs ([Q.sub.L], [Q.sub.H]), and market profits ([[pi].sub.L], [[pi].sub.H]) for high and low elasticity customers may be computed as

[Mathematical Expressions Omitted]

The combined profits earned through price discrimination, II = [[pi].sub.L] + [[pi].sub.H], may be written as (4)

[Mathematical Expressions Omitted]

Comparison of Prices and Profits

A major concern is the magnitude of the potential difference in profits and prices under a couponing strategy (case II) and a single-price strategy (case I). Given the analytical expressions computed previously, the difference and percentage difference in profits may be written as

[Mathematical Expressions Omitted]

If [[alpha].sub.L] > [[alpha].sub.H], a costless couponing policy will increase profits due purely to the reconfiguration of price and addition of coupon distribution without any change in total quantity sold. Invariance of total output sold can be found by adding [Q.sub.H] and [Q.sub.L] from equation (10) and comparing it to equation (5). Total quantity will be reduced when constant marginal costs differ between the consumer groups served. Thus, equation (14) reflects an increase in profits with quantity held constant. Generally, equation (14) is an underestimate of the percentage change in potential profits under constant common marginal costs and an overestimate when constant marginal costs differ across consumer groups. (5)

As is apparent from either equation (13) or (14), if [[alpha].sub.L] = [[alpha].sub.H], then profits (assuming zero couponing costs) are equivalent and it would be desirable for the oligopolistic firms to charge a single price. If there are fixed costs associated with a coupon distribution policy, a single-price policy will be optimal if the associated fixed costs are greater than the increase in profits associated with the couponing policy. The corresponding percentage difference in prices may be expressed as (6)

[Mathematical Expressions Omitted]

By inspection of equations (15) and (16), it should be clear that [[alpha].sub.H] must be less than [[alpha].sub.L] if in fact higher elasticity consumers or coupon users are to pay a lower net price for the commodity. It is assumed that [[alpha].sub.L] > [[alpha].sub.H] throughout this paper. In addition, equation (14) depends only on the relative magnitudes of [[alpha].sub.H], [[alpha].sub.L], [[beta].sub.H], and [[beta].sub.L]. Formally, let [[alpha].sub.H] = [[theta] [alpha].sub.L], where 0 < [theta] < 1 and [[beta].sub.H] = [unkeyable] [[beta].sub.L], where [unkeyable] > 0.

Making appropriate substitutions the percentage change in profits may be written as

[Mathematical Expressions Omitted]

Table 1 contains simulated values for equation (14) and (14'). Notice that the percentage change in profits applies to both market and firm level profits and does not depend on number of firms in an industry.

Making appropriate substitution in equation (9), the percentage coupon discount may be written as (1 - [theta]). Thus, [theta] values of less than perhaps .6 yield somewhat unreasonable results. However, it does not appear unreasonable to observe coupon discounts in the neighborhood of 30 percent. From Table 1, one can see that couponing, when [theta] = .7 and [unkeyable] ranges from 0.2 to 0.29, will yield nontrivial increases in profits. If the fixed cost associated with couponing is less than say two percent of precouponing profits, couponing can substantially raise profits. From these simulated results, it is evident that couponing can indeed be motivated by the desire to increase profits through a policy of third-degree price discrimination.

[TABULAR DATA OMITTED]

From Table 1, the effect of increasing the percentage of potential coupon users can also be evaluated. The reader is reminded that [[beta].sub.H] and [[beta].sub.L] can be interpreted as [b.sub.L]/N(1 - [lambda]) and [b.sub.H]/N[lambda] where [b.sub.L] and [b.sub.H] are the slope coefficients from a high and low elasticity consumer's individual demand schedules, respectively. The total number of consumers that the firm faces is assumed to be a constant, N, and [lambda] is the percentage of potential coupon users. Although one might view [lambda] as a random variable, it is assumed that each firm makes its decisions as if [lambda] were known with certainty. Holding [b.sub.L], [b.sub.H], and N constant, increases in [lambda] can be thought of as decreases in [unkeyable]. For example, if the initial demand configuration is characterized by [theta] = .7 and [unkeyable] = 0.9, the effect of increases in the percentage of coupon users can be seen from reading up the [theta] = .7 column from [unkeyable] = 0.9. From Table 1 it can be seen that the percentage change in profits due to couponing will increase from 3.16 percent when [unkeyable] = 0.9 to 3.21 percent when [unkeyable] = 0.7 and then decline for [unkeyable] < 0.7. This is a somewhat general result. It will be shown that the maximum percentage change in profits occurs when [unkeyable] = [theta] or equivalently when [[alpha].sub.L]/[[beta].sub.L] = [[alpha].sub.H]/[[beta].sub.H].

If firms are motivated by potential percentage increases in potential maximum profits, these results may in part explain the increased implementation of couponing by U.S. manufacturers. As [unkeyable] rises, ceteris paribus, the percentage of noncoupon users (1 - [lambda]) rises as does the associated percentage change in profits when [unkeyable] [is less than or equal to] [theta].

Even within this simplified analytical framework a graphical representation of the relationship between the two types of consumers is useful. The possible demand configurations that are consistent with price discrimination must be isolated. Figures 1(A) through 1(D) illustrate these possible relationships between demands of high and low elasticity consumers.

To fix a point of reference, the bold lines in Figure 1(A) through 1(D) represent the demand curve for low elasticity customers (labeled as [D.sub.L]). These illustrations are static in the sense that they do not capture changes in the proportion of high and low elasticity consumers. Therefore, the differences between the individual demands can be examined. Thus, the slope is - [[beta].sub.L], the maximum reservation price of low elasticity consumers is [[alpha].sub.L], and the quantity demanded at a zero price would be [[alpha].sub.L]/[[beta].sub.L]. In each case [[alpha].sub.L] must be greater than [[alpha].sub.H].

Given the arbitrary position of this demand segment, there are three distinct possible ranges for the value of [[alpha].sub.H]/[[beta].sub.H] for which it will be useful to distinguish. In terms of Table 1, range 1 implies [phi] = [theta], range 2 implies [phi] < [theta], and range, 3, [phi] > [theta].

range 1: [alpha]L/[beta]L = [alpha]H/[beta]H [alpha]L > [alpha]H

range 2: [alpha]L/[beta]L < [alpha]H/[beta]H [alpha]L > [alpha]H

range 3: [alpha]L/[beta]L > [alpha]H/[beta]H [alpha]L > [alpha]H

Figure 1(A) illustrates the effect of changes in [[beta].sub.H] holding [[beta].sub.L] and [[alpha].sub.L] > [[alpha].sub.H] constant. As [[beta].sub.H] falls, the high elasticity demand increases. Elasticity at each price, however, remains unaltered. As long as [[alpha].sub.L] > [[alpha].sub.H], the high demand will be more elastic than the low demand.

Figure 1(B) through 1(D) illustrate the effects of changes in [[alpha].sub.H] holding [[beta].sub.H], [[beta].sub.L], and [[alpha].sub.H] constant. Figure 1(B) represents demand configurations where [[beta].sub.H] < [[beta].sub.L]; 1(C), [[beta].sub.H] > [[beta].sub.L]; and 1(D), [[beta].sub.H] = [[beta].sub]L]. As [[alpha].sub.H] increases, high elasticity demand increases and high price elasticity declines. At a given price, as [[alpha].sub.H] approaches [[alpha].sub.L], the two price elasticities approach each other and as demonstrated previously, there will be no profit gain resulting from couponing. Thus, in all cases, [P.sub.H] is less than [P.sub.L]. These four configurations illustrate changes in high elasticity demand that correspond to the partial derivatives with respect to [[alpha].sub.H] and [[beta].sub.H]. This interpretation will be examined further. Intuitively, Figure 1(C) and 1(D) represent a situation where "low" demand is larger than "high" demand. Thus, the demand is greater for low elasticity consumers. Data are unavailable that would shed light on the previously mentioned demand configurations, however, they do not seem probable. For products in this study (laundry, dish, and bath soaps, certain brands of breakfast cereals, etc.), Figure 1(A) and 1(B) may be more relevant. Here, at least for fairly low prices, the "high" demand is larger than the "low" demand. In fact, from equation (10) it is clear that when demand is configured as in Figure 1(A) or 1(B) and [[alpha].sub.H]/[[beta].sub.H] > [[alpha].sub.L]/[[beta].sub.L] (range 3), the quantity sold with a coupon discount will be larger than noncoupon purchases. The percentage of coupon transactions is greater than percentage of noncoupon transactions.

Having formalized the linear model, the following four questions will be addressed. (1) Under what demand configurations will the incentive to engage in a cents-off couponing policy be greatest? The answer to this question could allow the direct profit incentive in certain markets where couponing is observed to be ruled out. In these markets, it will be likely that couponing is a promotional or inventory reducing device. (2) Under which demand configurations will profits be greatest? (3) How are the face value and percentage coupon discount affected by the demand configuration? and (4) How is the change in the shelf price affected by the demand configuration? Is the Vilcassim-Wittink hypothesis that increases in the percentage of coupon usage lead to higher shelf prices supported?

In regard to the first and second questions, it must be made clear that it is assumed that the overriding goal of the firm is profit maximization rather than, for example, sales maximization. Therefore, the demand configuration that will yield the highest change in profits would be the one where the incentive to coupon would be greatest. It is interesting to note that as the higher elasticity approaches the lower elasticity or, as [[alpha].sub.H] approaches [[alpha].sub.L], the change in profits due to couponing goes to zero, and obviously the incentive to coupon evaporates. On the other hand, this situation, given [[beta].sub.H] and [[beta].sub.L], corresponds to the highest attainable profits (given [[alpha].sub.L] > [[alpha].sub.H]. Thus, it is most profitable for the demand configurations to imply a noncouponing policy.

Returning to questions (1) and (2), it has been assumed that [[alpha].sub.L] > [[alpha].sub.H] and the change in profits will reflect the effects of [[beta].sub.H]. It is easy to see from equation (13) that smaller values of [[beta].sub.H] yield higher additional profits due to couponing while increasing the elasticity at each price. Thus, demand configurations illustrated by Figure 1(A) and 1(B) result in a higher incentive to coupon and concurrently yield lower profit levels. Given nonzero costs of couponing, it may be concluded that when [[alpha].sub.H] is close to [[alpha].sub.L] or when [[beta].sub.H] is large relative to [[beta].sub.L], couponing policies are not directly related to profit maximization through price discrimination and must therefore be related to profit maximization via other avenues.

If the incentive to coupon is determined by the highest percentage change in potential profits due to couponing, then it would be expected that couponing policies would be most prevalent when [[alpha].sub.L]/[[beta].sub.L] = [[alpha].sub.H]/[[beta].sub.H]. To see this, equation (14) may be maximized with respect to [[beta].sub.H]. The appropriate first-order condition is

[Mathematical Expression Omitted]

Rearranging equation (17) it can be shown that [[alpha].sub.L/[[beta].sub.L] = [[alpha].sub.H]/[[beta].sub.H] when [Delta][pi]/[pi] is at its maximum. (7)

The third question regarding the face value of a coupon and the percentage coupon discount is easily answered by referring back to equation (9). It is clear that these values depend only on [[alpha].sub.L] and [[alpha].sub.H] or on the maximum reservation prices of the two consumer classes when n is held constant. The face value of the coupon may be written as

[Mathematical Expression Omitted]

and the percentage coupon discount is

[Mathematical Expression Omitted]

Again, these results are not surprising. The divergence in optimal prices is determined by the divergence in the maximum reservation prices of the two groups and n, number of firms. (8) With this in mind, observing coupon discounts or more than say 30 percent would shed doubt on the direct profit motive behind price discrimination because it does not, to the casual observer, seem likely to find larger average discrepancies such that [[alpha].sub.H] is less than say 70 percent of [[alpha].sub.L] in reservation prices. It is interesting to note that while the number of firms does not affect the percentage coupon discount, the face value of a coupon will decrease as industry concentration declines.

The last question to be addressed is whether or not the model presented supports the Vilcassim-Wittink hypothesis that increases in the percentage of coupon usage lead to higher shelf prices. Given the demand configuration, the percentage of coupon usage for a particular product will rise whenever [Q.sub.H]/[Q.sub.L] rises. Thus, from equation (10), the following is derived.

[Mathematical Expression Omitted]

The change in shelf price, computed by taking the difference in the single Cournot oligopoly price and the price charged to low elasticity customers, may be written as

[Mathematical Expression Omitted]

The inclusion of constant marginal costs leaves (21) unaltered. Taking the partial derivatives with respect to [[alpha].sub.H] and [[beta].sub.H], it is clear that the shelf price increase is positively related to decreases in [[alpha].sub.H] and [[beta].sub.H].

[Mathematical Expression Omitted]

From equations (21), (22), and (23) it is evident that, given [[alpha].sub.L] and [[beta].sub.L], increases in percentage of coupon usage occur when [[alpha].sub.H]/[[beta].sub.H] increases. Thus, the increase in coupon usage is caused by a decrease in [[beta].sub.H] and the Vilcassim-Wittink hypothesis is supported. Increases in percentage of coupon usage caused by increases in [[alpha].sub.H] are, however, not supported.

Comparison of Consumer Welfare and Resource Allocation

The last question to be answered, given the profitability of couponing already established under the linear model, is whether couponing leaves consumers, as a whole, better or worse off. In addition, the effect of a couponing policy on allocation of resources within a particular market and among consumer classes will be discussed. As is generally done, consumer welfare is measured by Consumer Surplus (CS) and resource misallocation by Dead Weight Loss (DWL). Any redistributional issues associated with transferring consumer surplus between consumer groups are ignored.

It will be demonstrated that, when couponing is profitable and high price elasticity consumers pay a lower price via couponing, lower CS and higher DWL will result when compared to an oligopolistic sinigle price equilibrium. Couponing, given the constrained relationship between high and low elasticity demands, leads to higher profits. This increase in profits can be accompanied by decreased consumer welfare and increased resource misallocation between consumer groups. The common assumption that a dollar's worth of CS is valued identically by both high and low elasticity consumers is implicitly being made in this analysis. Moreover, the decrease in consumer surplus is underestimated because the present framework does not capture the user costs incurred by consumers who clip, organize, and redeem coupons nor the negative externalities coupon users inflict on nonusers at redemption. In addition, incorporating the plausible presumption that products redeemed with a coupon have higher marginal costs associated with them, it will be argued that the net welfare loss due to couponing is exacerbated.

To facilitate the discussion of the propositions outlined, Figure 2(A) and 2(B) will be useful. Positioning of the two demand curves is arbitrary except that [[alpha].sub.L] > [[alpha].sub.H]. The line LL represents low elasticity demand and HH represents high elasticity demand.

The net loss in CS may be computed by subtracting the loss in CS suffered by low elasticity consumers due to couponing from the gain enjoyed by high elasticity consumers. Specifically, the absolute value of the loss in CS is represented by the shaded region in Figure 1(A) and may be written as

[Mathematical Expression Omitted]

In equation (24), [P.sub.o], [P.sub.L], and [Q.sub.L] refer to values given by equations (4), (9), and (10), respectively, and [Q.sub.L]([P.sub.o]) is the quantity demanded by low elasticity consumers when price equals [P.sub.o]. The absolute value of the gains in CS is represented by the shaded region in Figure 2(B) and is computed as

[Mathematical Expression Omitted]

Again, [P.sub.o], [P.sub.H], and [Q.sub.H] refer to equations (4), (9), and (10) and [Q.sub.H]([P.sub.o]) is the quantity demanded by high elasticity consumers when price equals [P.sub.o]. Subtracting (24) from (25) the net [Delta]CS due to couponing is given by

[Mathematical Expression Omitted]

As before, [Delta][pi] refers to increase in profits under couponing when compared to a single Cournot equilibrium price, equation (13).

It should be clear that in the model presented, loss in CS due to couponing entails not only a transfer of benefits from consumers to producers, but a net welfare loss of 1/2n([Delta][pi]). The [Delta]DWL due to couponing is

[Mathematical Expression Omitted]

Thus, couponing will lead to a decrease in total welfare. This loss in total welfare is due purely to a misallocation of the product among consumers because output remains constant in the case of either zero or constant common marginal costs.

If the practical presumption that products redeemed with a coupon carry higher marginal costs is incorporated into the model, welfare loss increases. As can be seen from footnote 6, [P.sub.o] - [P.sub.H] will be lower and [Q.sub.H] will decline, thus lowering the resulting increase in the gain in CS that high elasticity consumers would enjoy (loss remains the same). In this case, misallocation of resources reflects not only a sub-optimal distribution of the product among consumers, but also the contraction of output. To compound the reduction in the gain to CS, losses to CS associated with time costs incurred by customers who redeem coupons and the externalities imposed on nonusers during redemption must be included, at least theoretically.

CONCLUSION

This study has lent support to the arguments of Vilcassim and Wittink (1987) concerning potential profitability of couponing--an issue that appears to be of interest in marketing. Specifically, it has been shown that couponing policies can indeed raise profits substantially and increase shelf price of the product in question. Effects of higher marginal costs due to redemption have been formally introduced as has the idea that nonmeasurable redemption costs, borne by both users and nonusers, must be considered. A major conclusion is the demonstration that couponing policies of American oligopolistic manufacturers are potentially harmful to consumers as a whole and aggravate resource misallocation. These losses are not offset by increased profits.

In general, of major concern to economists is resource misallocation, not the transfer of profits and consumer surplus. What cents-off couponing leads to under the present framework is a situation in which the good in question is not fully allocated among consumers who value it most highly. Some low elasticity consumers will not purchase the product as [P.sub.L] even though they have a demand price greater than some high elasticity consumers who purchase the good at [P.sub.H].

Noncoupon users have little room to improve their situation. They made the decision to be low elasticity consumers based on subjective evaluation of the costs and benefits of using coupons. The transactions or arbitrage costs that a low elasticity consumer would incur when trying to "buy" the good from a high elasticity purchaser would certainly be too steep to warrant the trade because, on an individual level, savings would be limited to the coupon value.

Therefore, limited expenditure savings of an individual associated with cents-off couponing serves as an effective arbitrage barrier. This barrier is further enhanced by the difficulty of identifying arbitrage partners. Cents-off couponing fulfills two important prerequisites to price discrimination--identification and separation of consumer classes. There seems to be little room for the situation to be remedied by unilateral behavior of individuals.

Under the simplifying assumptions made in this paper, the evidence supports the prohibition of cents-off couponing. In a single-price equilibrium, total output probably would be expanded (assuming noncommon constant marginal costs), consumer surplus would increase, and the good would be allocated to those who receive the highest benefit from its consumption.

By employing a model of Cournot oligopoly it has been demonstrated that the benefits to society of banning cents-off couponing policies are positively related to the industry concentration. If number of firms in an industry is small, there will be higher losses incurred by society under cents-off couponing. Cents-off couponing can be viewed as an extension of market power not as a vehicle with which to obtain or maintain it.

REFERENCES

Chapman, Randall (1986), "Assessing the Probability of Retailer Couponing with a Low-Cost Field Experiment," Journal of Retailing, 62(1, Spring): 19-40.

Clements, Jonathan (1986), "The Increasing Payoff in Cents-off," Forbes (December 29): 40.

Narasimhan, Chakravarthi (1984), "A Price Discrimination Theory of Coupons," Marketing Science (3, Spring): 128-147.

Pigou, A. C. (1932), The Economics of Welfare, London: Macmillan.

Phlips, Louis (1983), The Economics of Price Discrimination, Cambridge, MA and New York: Cambridge University Press.

Robinson, Joan (1933), The Economics of Imperfect Competition, London: Macmillan.

Schmalensee, Richard (1981), "Output and Welfare Implications of Monopolistic Third-Degree Price Discrimination," American Economic Review (71):242-247.

Tirole, Jean (1988), Industrial Organization, Cambridge, MA: MIT Press.

Vilcassim, Naufel and Dick Wittink (1987), "Supporting a Higher Shelf Price Through Coupon Distributions," Journal of Consumer Marketing (4, Spring): 29-39.

Yamey, Basil (1974), "Monopolistic Price Discrimination and Economic Welfare," Journal of Law and Economics (17, October): 277-280.

Jamie Howell is Assistant Professor of Economics, Department of Economics, Haverford College, Haverford, PA.

The author wishes to thank Haverford College, The Dana Foundation, and The Mellon Fund for the 80's for their support in this research, in addition to the four anonymous referees and the editor for their very helpful comments on this paper.

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Author: | Howell, Jamie |
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Publication: | Journal of Consumer Affairs |

Date: | Jun 22, 1991 |

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