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A Price Discrimination Theory of Coupons

Author(s): Chakravarthi NarasimhanSource: Marketing Science, Vol. 3, No. 2 (Spring, 1984), pp. 128-147Published by: INFORMSStable URL: http://www.jstor.org/stable/183747.

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MARKETING SCIENCEVol. 3, No. 2, Spring 1984Printed in U.S.A.

A PRICE DISCRIMINATION THEORY OF COUPONSCHAKRAVARTHINARASIMHAN

Universityof ChicagoThe objective of this paper is to analyze the consumer's decision in electing to use cents-offcoupons distributed by manufacturers of consumer products. Arguing that the decision to usecoupons is based on the tradeoff between costs of using coupons and the savings obtained, it isshown that coupons can serve as a price discrimination device to provide a lower price to a

particular segment of consumers. Based on a price theoretic model, it is shown that the usersof coupons are more price elastic than nonusers of coupons and that the opportunity cost oftime and other household resource variables are determinant factors in consumers' decisions.Implications derived from the model are tested using diary panel data.(Price-Discrimination;Cents-Off Coupons; Theory Testing)

1. IntroductionA cefrts-off coupon promises the consumer a reduced price on the next purchase ofa specified product. The practice of offering a reduced price through such instrumentsis prevalent in the consumer goods industries, more noticeably in the frequentlypurchased nondurable products and service markets. Examples of such categoriesinclude: grocery products, meals in restaurants, hair cutting services, laundry andcleaning services, photographic supplies, film processing, etc. Cents-off coupons aredistributed in the newspapers, magazines, by mail, in/on packages. The number.ofcoupons have grown by more than 500%in the last decade and the average face valuehas doubled in the same period. Thus, coupons are an important promotionalmechanism.There are many interesting research issues in the study of cents-off coupons. Themore important ones are:(i) Why do manufacturers offer such coupons? Why not reduce the price of theproduct at the retail outlet?(ii) Who are the more intense users of coupons if not all consumers? Whichdemographic variables have predictable impact on the usage?(iii) Why does the savings offered through coupons vary across brands and sizes?On the managerial side one would like to answer questions such as how to evaluatethe profitability of couponing, how to determine the cents off value, what tradeoffsexist between distributing coupons in different media, etc.In this paper, we argue that one reason why a firm will offer coupons is to pricediscriminate between the more elastic and less elastic demanders. Hypotheses concern-ing the difference between users and nonusers of coupons in terms of observabledemographic variables will be offered. And finally, hypotheses consistent with the

1280732-2399/84/0302/0128$01.25Copyright ? 1984, The Institute of Management Sciences/Operations Research Society of America

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PRICE DISCRIMINATION THEORY OF COUPONSmodel developed in this paper will be offered to explain systematic differences incents-off values offered by different brands in a product category and different sizeswithin a brand. The rest of the paper is organized as follows. In ?2, past literature incouponing and alternative explanation to the existence of coupons are examined. In?3, the basic hypothesis of this paper is developed. ?4 contains a description of theconsumer model; ?5 contains the empirical tests of the implications derived from theconsumer model. ?6 outlines managerial implications from the theory and ?7 con-cludes the paper with a summary and directions for further work.

2. BackgroundPast research in marketing on coupons and their effects on consumers is ratherscanty. Nielson (1965) discusses the market research aspects of coupons and argues

that this could be a prime factor for the manufacturers to distribute coupons. Wardand Davis (1978) argue that coupons influence consumers through their redemptivevalue and their informational value (i.e., informing the consumers of the existence ofthe product). They construct a regression model with consumption as the dependentvariable and price, income, savings given through coupons, and a host of demographicvariables as independent variables. They break down the increase in consumption intotwo parts: a price effect and an informational effect. From the empirical estimates ofthe regression model, they show that both effects exist. Dodson, Tybout, and Sternthal(1978) examine the impact of retracting a deal on brand loyalty. Based on self-perception theory, they conclude that while media distributed coupons may encourageswitching, once the coupons are retracted, the consumers who switched did notrepurchase at the regular price. Precisely the opposite effects were encountered forin/on package coupons. Teel, Williams and Bearden (1980) conducted a survey offemale heads of household to study the characteristicsof coupon users. The focus wason characterizing the profile of coupon users who would try a new product with acoupon. They report, based on the survey results, that coupon users have significantlylarger family sizes, larger incomes and are significantly younger than nonusers ofcoupons. Bearden, Teel and Williams (1981) report the results of another survey theydid to study the relationship between the percentage price reduction and willingness totry a new brand among female grocery shoppers. They computed the percent of peoplewho would buy the new product using coupons for different levels of price reduction.Such a relationship is obviously useful for planning purposes. Neslin and Shoemaker(1983) describe a computer based simulation model that can be used to calculate theprofitability of couponing. Based on a decision calculus approach, the parameters ofthe model are estimated.More recently White (1983) and Levedahl (1983) have addressed the issue of the useof cents-off coupons. White argued that coupons can be a means to discriminatebetween those consumers who comparison shop and those who do not. The proportionof consumers who comparison shop is assumed to be exogenous to the model. Sheshows that as a result of entry and exit, the relative profit positions of the differentfirms in the industry are unaffected but the structure of price changes, viz., someconsumers pay higher prices and some (those who use coupons) pay lower prices.Levedahl compares the price discrimination hypothesis (see below) with what he calls"multipart pricing"-charging a lower price for the first unit and higher price foradditional units. (This definition is different from the definition of multipart pricing inthe economics literature.)He uses the data derived from a panel supplied by NPD. Forthe paper towels category, the average full price with coupon (price paid plus the valueof coupon) is significantly higher for all the national brands than the average pricepaid when there was no coupon. This is consistent with the price discrimination

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hypothesis and not the "multipart pricing" hypothesis. He further argues that recur-rence of coupons periodically is consistent with the price discrimination hypothesisand not with the "multipart pricing" hypothesis.As can be seen from the above review, no one has explicitly modelled the consum-ers' usage of cents-off coupons and empirically tested any proposition. In this paper,we propose to advance a price discrimination hypothesis and offer some empiricalsupport to this hypothesis. Before we do this, we review some alternative explanations.Couponsfor Gathering Market Research Data. By coding the coupons for themedia and geographic regions in which they are distributed, a manufacturer can gainvaluable insights into the price sensitivity of different consumer segments. Further, hecan learn about the pattern of redemption and plan the coupon drop more effectivelyand organize his cash flows. Coupons can also be used to test advertising copies. By a"split run test" wherein alternate copies of a single issue of a magazine carry different

advertising copies, and by monitoring the redemption of coupons included in theseadvertisements, a manufacturer can ascertain the relative effectiveness of copy themes.Thus, the market research benefits of coupons cannot be ignored.Can this be an explanation of the incentive of the manufactureres to issue coupons?Not likely. Cents-off labels on packages are probably a less costly mechanism ofoffering a price cut since the manufacturerdoes not incur redemption costs paid to theretailer, cost of misredemption, etc. Further, this hypothesis cannot explain thevariation in coupon usage across consumers nor does it prove useful in predicting thesavings to be offered through coupons relative to competing brands.CouponsInduce Trials and Hence Repeat Purchases. Coupons represent a price cutto consumers. The consumer incurs a cost in trying a product whose value he isuncertain about. Therefore, if he can be compensated for this cost, at least partially, atrial may take place and this would increase the probability of future sales.The above hypothesis would therefore predict that over the brand's life the coupon-ing intensity must gradually decrease since firms benefit from inducing an early trial.Now, there are many other alternative mechanisms available for inducing trial. Someof these are: Using cents-off labels, small sample sizes, trade promotions, etc. Thishypothesis fails to explain why these alternative mechanisms are less efficient thancents-off coupons for inducing trial. Further and most importantly, the hypothesis hasno prediction on the intensity of coupon usage across consumers. Note that the crucialquestion here is not why a price cut is given but rather why the price cut takes aparticular form. In other words, given the cost of couponing, viz., cost for distributingcoupons, redemption cost paid to retailers, clearing houses, etc., why does a firmchoose this strategy as opposed to say, cents-off labels and advertising about this offer?The hypothesis proposed in this paper (see next section) is also consistent with theproposition that coupons can be used to induce trial. But unlike this hypothesis, theprice discrimination hypothesis predicts why, in a positive sense, the intensity of usageof coupons is likely to differ across consumers. And finally, the trial-repeat purchasehypothesis does not have predictions on the cents-off to be offered through couponsand how the savings given should vary across brands and package sizes.

This does not necessarily mean that the trial-repeat purchase hypothesis cannotexplain some form of couponing. In product categories where the purchaser is not theconsumer, coupons can serve as a reminder to the purchaser of the product's utility tothe consuming person and thus coupons can serve to induce repeat purchase.' Pet'One could argue that this statement would, in general, be true. The point that is being made here is thatin the absence of self-evaluation of a product by the purchaser, an on/in pack coupon can influcence thenest purchase more heavily than in other product categories. Dodson et al.'s article seems to partiallysupport this assertion.

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PRICE DISCRIMINATION THEORY OF COUPONSfoods and ready to eat cereals are good examples of such a category and in/onpackage coupons is a major form of couponing in these categories.

3. Couponsas Price DiscriminationDevicesThe basic argument in the explanation offered in this paper is that to enjoy thesavings from using coupons, the consumer incurs some cost and the decision to usecoupons is made by trading off the savings obtained against the cost of using coupons.There are many costs that can be identified. These are the cost of organization (cost oforganizer, time spent in periodically organizing the coupons, etc.), cost of lookingthrough magazines, time spent in storing and retrieving the coupons, etc. The chiefcomponent of this cost is the cost of time. This cost will also be affected by otherhousehold resource variables like the education level of the housewife, the presence ofchildren and the manner in which the household derives its income. For example, ahousewife who is employed is bound to treat her time as more valuable than anonworking housewife belonging to another household with identical income andother household resource variables.2 Similarly, the presence of children could have animpact on the cost imputed to the time available to the housewife. In general, as timebecomes more and more of a scarce resource, the value attached to successive units ishigher.Blattberg, Buesing, Peacock and Sen (1978), in their study on deal prone segments,use similar arguments to identify the consumers that are likely to be deal prone. Theyshow that presence of children and the wife being employed have a negative impact onthe ability to take advantage of deals, since this latter activity is time intensive.Now, assume for a moment that a household can buy one unit of a product usingone coupon. Let c(n) be the cost function reflecting the cost of using n coupons. Let Sbe the savings obtained per coupon assumed constant. Therefore the optimal numberof units the household will buy under this simple situation can be characterized by thefollowing first order condition, viz.,

S = c'(n) (1)where c'(.) is the marginal cost of using one coupon. If all households in thepopulation face the same savings S (i.e., benefit) from coupons but differ in their costfunction then it is easy to see from (1) that different households will be exhibitingdifferent intensities of coupon usage.3 Those households for whom c'(n) > S for alln > 0 choose not to use coupons. Thus, given heterogeneity in the cost of usingcoupons across consumers, one should observe differing patterns of usage of coupons.The decision to use coupons is purely by self-selection and not due to any constraintsimposed by the firm.4Why is the firm interested in providing a price cut to those consumers with lowercosts of usage? Now suppose it can be established that the consumers with lower costsare more price elastic than those who do not use coupons, it then follows that the firmis selling the same product at a lower price to the more elastic consumers relative tothe segment who have higher costs (and less elastic demand). It is in this sense thatcoupons behave as price discrimination devices and that such a mechanism is profitmaximizing has been well established in the price theory literature (see, for example,Becker 1971, pp. 102-105). One important point regarding the formation of the

2Given a fixed number of hours per day, a working woman has less time to do household activities than anonworking woman ceteris paribus. Similar arguments apply to the next two assertions as well.3We also assume that all consumers know and expect to receive savings S from a coupon.4Since some consumers acting in their self-interest choose not to use coupons, the question of arbitragedoes not arise. That is, the manufacturer need not take any explicit action to isolate the segments.

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CHAKRAVARTHI NARASIMHANsegments is worth emphasizing here. The segments are formed on the basis of rationalself-selection and not on the basis of preferences. That is, the differences in demandelasticities (this is rigorously established in the next section) is driven by opportunitycost differences and not due to taste differences.The differences between the price discrimination hypothesis and trial-repeat pur-chase hypothesis are the following. If firms want to induce trial through coupons, firmswould like to limit the use of coupons only on the first unit bought (for example, a"mail-in refund" program can be used where it is possible to restrict the refund to oneper household.) Whereas under the price discrimination hypothesis the firm does nothave an incentive to restrict such use. The recurring use of coupons seems to beconsistent with price discrimination hypothesis and inconsistent with trial-repeathypothesis (Levedahl 1983). Further, Dodson, Tybout and Sternthal (1978) concludethat at least as far as media distributed coupons are concerned, cents-off couponsundermined repeat purchases. If firms know this, it is not clear why they continue tocoupon. Secondly, if consumers are uncertain about a product, one would expect themto use coupons on small sizes, since it involves less outlay and, consequently, firms torestrict coupons to only small sizes (thereby restricting the use of coupons by regularusers of the product who may be buying larger sizes). We do not observe this inpractice.5In this paper, evidence will be presented that is consistent with the price discrimina-tion hypothesis. Some of this evidence may be consistent with other theories. Clearly,further tests are needed to discriminate between competing hypotheses.

4. Model of ConsumerBehaviorIn this section a formal model of the consumer is presented. The model's implica-tions regarding coupon usage, differences in elasticities between users and nonusers,and implications for couponing across sizes and across different brands of a productclass are derived. As detailed in the previous section, it is assumed that a consumertrades off the savings he/she obtains from a coupon with the cost of using a coupon.The consumer's decision on using coupons is analyzed using a simple price-theoreticframework.

AssumptionsA . The consumer maximizes a well-defined utility function (for other assumptionson the nature of this utility function see below), defined over two goods denoted as Xand L. The good X is available for purchase with coupon, and L can represent acomposite good or leisure.6A2. The consumer knows the price of good X with certainty and he also knows thequality of the product. That is, we assume a world of costless information on pricesand quality.A3. If the consumer decides to buy X with a coupon, he uses one coupon for oneunit of the product and obtains a savings of S. This assumes that products areavailable in one "size" only. While this is obviously restrictive, it simplifies thetreatment. We will return to the issue of sizes later.A4. The utility function U (defined over X and L) is continuous, twice-differentiableand the Hessian of U is negative definite. That is,Uxx, ULL < 0 andUxx ULL - UXL5This is based on anecdoctal evidence. Further, in the empirical testing section, we will see that brandscoupon for different sizes (see Table 3).6This is essentially a mathematical simplification. Even though a consumer purchases a number of goodsin the economy, to study the price effects on one good, one can conveniently combine the all other goods inone category and classify this as a composite good.

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PRICE DISCRIMINATION THEORY OF COUPONS> 0 where the subscripts refer to the variables with respect to which the partialderivative of U is considered.A5. Both X and L are "normal" goods, i.e., as income increases holding everythingelse constant, the consumer consumes more of X and L.Assumptions A4 and A5 are made for tractability. A5 is a strong sufficient (notnecessary) condition to assure that the demand curves are sloping downwards.Mathematical Notation

Let:PI = price of one unit of X,P2 = price of one unit of L,Xl = quantity of X bought with coupon,S = saving/unit of the quantity bought from using a coupon,H = number of hours the consumer spends in the labor market,ti = time input into the consumption of X,t2= time input for using one coupon,A = nonwage income,w(H) = a scaling function transforming the hours worked, H, into "effective"number of hours,a = wage rate,T= total number of hours available to the consumer in some particular timehorizon.Thus, aw(H) is the total income derived from the labor market. This representation

is chosen for mathematical simplicity so that it is easy to analyze the behavior ofconsumers differing in their wage income by looking at changes in a.A6. aw/aH > 0 and a2w/aH2 < 0. In other words, by spending more hours in thelabor market the consumer increases his wage income, but at a decreasing rate. Thisassumption relies on the fact that the consumer is likely to exhaust more beneficial (tohim) sources of employment first before turning to less income yielding opportunities.A7. All third-order derivatives of U and w are zero. This assumption is made formathematical tractability.The consumer model can be represented by the following nonlinear constrainedmaximization problem:Max U(X,L)s.t. (a) aw(H) + A = P,X - SX, + P2L,

(b) T= tlX + t2X, + L + H,(c) X > X,,(d) X, > 0.

The thrust of the modelling here is to see how (i) Xl, the quantity bought usingcoupons, varies across consumers holding everything else constant and (ii) how theprice elasticity of demand varies across consumers using coupons with differentintensity. That is, we are interested in the signs of dX*/aa andarpl(X*)/aa whererp,(X*) is the elasticity of demand. Narasimhan (1982) has shown that7

aX?/aa < 0, (3)arnl(x*)/aa > 0. (4)

Now since aw' in this model captures the opportunity cost of the marginal unit of time,7A sketch of the proof of (3) and (4) is available from the author upon request.

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CHAKRAVARTHI NARASIMHANthe first inequality implies that as the opportunity cost of time increases, the intensityof coupon usage decreases. The second inequality implies that the more intense usersof coupons (those with a lower a) are more price elastic ('qp,(x) is a negative number)than the less intense users of coupons.Other ImplicationsCouponing Across Brands. Consider a product class with a number of brandsdifferentiated on some set of characteristics. To simplify, let R denote a compositecharacteristic on which brands are differentiated. The brands in this product class aresold at different prices, and let P,(R) represent the market price function, which isassumed to be well-defined continuous and twice differentiable over the relevant rangeof analysis. Since different brands will be couponed at different values, let S(R)represent the savings per coupon offered by different brands. The consumer modelunder this situation can be formulated as:Max U(X,L,R)s.t. (a) aw(H)+ A = XPI(R)+ P2L - S(R)X,,

(b) T= tlX + t2X + L + H,(c) X > X,,(d) X 0O.

It is easy to see that this framework is very similar to Rosen's (1974, p. 40)"extended" model. As discussed by Rosen (1974), it is possible to derive a 0 functionwhich traces out indifference curves in the P - R plane describing the price theconsumer is willing to pay for various values of R, holding his income and utility levelconstant. The optimum R the consumer selects is obtained at the tangency of the P(R)function and the indifference curves described by the 0 function.Far less can be said in this case than in the conventional utility maximization model.However, this model has some very important contributions, such as describing therelevance of the market price function, the location of consumers and producers atvarious points in the characteristic spectrum, and the formulation of market segments.Rosen also established that assuming the characteristicsare normal (i.e., higher-incomeconsumers demand larger amounts of the characteristics), on the average higher-income consumers will be consuming brands with higher levels of R or which arepriced higher. Of course, taste differences could, to the extent it is the more dominat-ing force, lessen the above effect. Since it is hard to theorize on the variation of tastes,this effect will be ignored. Therefore, holding nonwage income constant, one wouldexpect consumers with higher wage rates or opportunity costs of time to be located athigher levels of R in the characteristic spectrum or consuming higher-priced brands.Thus, if the brands coupon at different values, the higher-priced brands on averagewill coupon at higher values. This effect is reinforced by the following reasoning aswell. In Figure 1, the choice of a consumer selecting a brand (a particular value of R)is illustrated. P(R) describes the market price function; i.e., the price at which brandswith differing R sell. 0(U, R, Y) describes the price a consumer is willing to pay fordifferent R, holding is utility (U) and income (Y) fixed. The consumer selects thebrand Ro paying price PO.Consider two other brands R1 and R2 priced at P1 and P2such that P2 > Pl > PO.Now the 0 function which describes the consumers' tradeoffof R against price is a concave function of R (see Rosen 1974). Therefore, if thehigher-pricedbrands P, and P2 were to coupon so as to make the consumer buying Roto buy their brand, they have to offer a net savings of 8, and 82, respectively, at whichthe consumer would be just about indifferent between Ro or switching to one of thehigher-priced brands. From Figure 1, it is clear that 82 > 86 or that the net savings

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PRICE DISCRIMINATION THEORY OF COUPONSp

P(R)

p2P . e/ (R,U,Y)

PO - /- -- - - - - -- - - --? - 61p0

R' R0 R1 2 R

FIGURE . Consumer Tradeoffs and Couponing Across Brands.from the higher-priced brand (P2, R2) is greater than the net savings from a lower-priced brand (P,, R,). Since the marginal cost for using coupons is assumed to be thesame regardlessof which brand's coupon the consumer uses, this would imply that thehigher-priced brand should offer higher savings through coupons than a lower-pricedbrand. What drives this implication is that the 0 function is concave and the marketprice function P(R) is convex.In Figure 1, another brand (P', R') is shown. This brand is priced lower than thebrand the consumer is currently buying; i.e., (P, Ro). It appears as though it couldoffer a higher savings equal to 82, say, to make the consumer buying (PO,RO) o buy itsbrand. However, given our assertion that consumers buying (P', R') on the averagehave a lower opportunity cost of time, such a move would lead to enormous "leakage"between the two consumer segments; i.e., the brand (P', R') cannot prevent its presentconsumers from buying its product with a coupon. This may inhibit such "large"couponing (in terms of value offered) by relatively lower-priced brands.Thus, the implication derivable from the hypothesis proposed is that, on the average,higher-priced brands will offer larger savings through coupons than lower-pricedbrands.8

CouponingAcross Sizes. Until now it was assumed that the consumer buys one unitthrough a coupon, no more or no less. However, a manufacturer may issue a couponfor different sizes of the same product, offering different absolute discounts (15? off a12-oz. box and 254 off on a 24-oz. box).Consider one particular brand and two different sizes: L (large) and S (small). Forexpositional convenience, assume the large box is twice the size of the small box. Let Cbe the marginal cost for collecting and using a coupon, assumed to be constant. Toremove price effects, assume that the price per unit is the same forL and S. In otherwords, if the small size sells for Ps and the large size for PL, then PL= 2Ps. Now, ifthe manufacturer offers coupons both for large and small sizes with savings SL and Ss,then SL must be greater than Ss since otherwise no one would buy the large size(remember, the price per unit is the same). However, in equilibrium to preventarbitrage, the net benefit from using a coupon on the large size and using two couponsto buy two small sizes must be the same:Net benefit from buying large size = (SL - C).8The argument presented above is somewhat incomplete. We only considered the demand side effects andthus, it is only a partial equilibrium analysis. One should establish why in equilibrium the firm is interestedin offering coupons in the manner argued above by "closing" the market. This, however, is beyond the scopeof this paper.

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Net benefit from buying two small sizes = 2(Ss - C). Therefore,SL-C=2Ss-2C or SL=2Ss-C i.e.,

(5)SL < 2Ss (C > 0), implying SL/2 < S .Since the definition of a unit of a product is rather arbitraryif one treats the smallsize as a unit, (5) implies that the savings per unit on a large size box must be smallerthan the savings per unit on a smaller size box. Note that the above result is notaffected by the assumption that C is a constant or by the assumption that L = 2S.In the next section, the following implications that are described above will beempirically tested.(i) The users of coupons have a more elastic demand than the nonusers;(ii) The intensity of usage of coupons is inversely related to opportunity cost of time;(iii) Within a product class, the price of a brand and the savings offered throughcoupons will be positively correlated(iv) Across different sizes of a brand, the savings per unit of the product bought willbe inversely related to the size.

5. EmpiricalAnalysisIn this section the implications derived from the consumer model are tested withdiary panel data. The panel contains purchase records of about 1,000 consumers in 20product categories.

1. Testing Differencesin Demand Elasticities.A key implication of the consumer model described in ?4 was that there should be asystematic difference in demand elasticities between users and nonusers. More specifi-cally, it was shown (see (4)) that the users of coupons are more price elastic thannonusers of coupons. The null hypothesis, then, is that users of coupons are more priceelastic than nonusers of coupons.To test this hypothesis, it is necessary to estimate demand equations for "users" and"nonusers" separately and compare their elasticities. This brings up the definition of a"user" of coupons. This is an empirical question and was resolved in a simple andstraightforwardmanner. A user was defined as one who made at least one purchasewith a coupon. This is a conservative definition and would bias the test (to bedescribed below) towards rejecting the null hypothesis:9Ln( QTY,) = a,Ln(PRICE,) + a2Ln(INCOME,) + a3Ln(FAMSIZ,)

+ a4Ln(EDUFEM ) + caLn(FEMEMP, )+ a6Ln(A GEFEM, ) + Ec where: (6)

QTYi = Annual quantity purchased by the ith household;PRICEi = Average price paid by the ith household;INCOME, = Annual income of the ith household;FAMSIZ, = Number of members in the ith household;EDUFEMi = Educational level of the female head of the ith household;AGEFEM, = Age of the female head of the ith household;Ei= A disturbance term, assumed to be independent and identically distributed,satisfying the usual properties.

91f consumers who are not regular users of coupons are considered as users, then the price elasticity willbe lower than it would be if the null hypothesis were true. Thus, this minimizes the chances of finding agreater elasticity for the users of coupons, making the test conservative.

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PRICE DISCRIMINATION THEORY OF COUPONSTABLE I

Results of Regressionto Test Differencesin Demand Elasticities BetweenUsers and Nonusersof CouponsProduct N R2 Price DPR Income

Toilet Tissues 979 0.21 - 0.596 (-5.35)b - 0.060 (-4.66) 0.009 (0.27)Paper Towels 932 0.09 -0.518 (-3.18) 0.062 (-0.22) 0.163 (1.96)Stuffing/Dressing 434 0.15 - 0.711 (-5.50) - 0.245 (-5.42) 0.077 (1.18)Hair Coloring 205 0.09 - 0.455 (-2.70) 0.032 (0.80) 0.166 (1.65)Hair Spray 450 0.13 -0.0648 (-7.13) -0.202 (-2.74) -0.003 (-0.04)Shampoo 834 0.37 -0.838 (-16.02) - 0.200 (-5.60) 0.256 (4.96)Cooking/Salad Oil 946 0.21 - 1.221 (-9.85) -0.099 (-5.29) 0.129 (-2.64)Ready to Eat Cereal 952 0.29 - 1.577 (-5.96) 0.856 (2.28) 0.22 (-2.91)Dog Foodc 432 0.42 - 1.498 (-9.69) 0.63 (2.64) 0.202 (2.45)Dry Mix Dinners 647 0.24 -0.876 (-9.42) -0.210 (-6.23) -0.217 (-3.04)Bars and Squares 247 0.14 0.546 (2.16) - 0.348 (-5.35) -0.123 (-1.06)Cake Mix 886 0.18 - 0.210 (-1.35) -0.219 (-10.71) -0.153 (-2.82)Cat Food' 329 0.21 -0.485 (-2.13) -0.642 (-3.96) 0.235 (2.07)Frozen Entrees 715 0.16 -0.601 (-5.30) -0.346 (-8.46) -0.044 (-0.59)Gelatin 773 0.23 - 0.971 (-11.05) - 0.278 (-8.57) -0.067 (-1.09)Spaghetti Sauces 619 0.48 - 1.653 (-20.94) - 0.161 (-4.88) 0.045 (0.60)Creme Rinse/ 493 0.34 -0.824 (-12.44) - 0.295 (-4.60) 0.202 (2.62)ConditionersSoups 959 0.30 - 1.052 (-15.27) - 0.165 (-8.73) - 0.027 (-8.73)Other Mixes 596 0.22 - 0.958 (-9.68) - 0.244 (-9.13) -0.159 (-2.60)Hot Dogs 884 0.20 -0.585 (-4.08) - 0.182 (-6.20) -0.162 (-2.94)aDPR is 0 for nonusers and equals price for users.bFigures in parentheses are t-values.'For dog food and cat food, family size was replaced by number of dogs and number of catsrespectively.

The above functional form was used since we are primarily interested in testingdifferences in demand elasticities. The coefficients in a log-log model directly yield theestimates of elasticities of the dependent variable with respect to the independentvariable. In equation (6), FAMSIZ is included since consumption will be affected bythe number of members in a household. EDUFEM, FEMEMP and ADEFEM areincluded to control for "taste" differences across households.The model specified by equation (6) was estimated at the product category level forthe user and nonuser segment respectively. The null hypothesis that coefficients of allvariables but prices were equal across the segments was not rejected (at the 0.05 level)in all but the following four categories: paper towels, ready to eat cereals, dog foodand cat food. Thus, except for the above four, for the rest of the product categories,the estimation was done by pooling the two segments together and adding an extraprice term as follows: DPR, = a7[8iLn(PRICE)] where 8; takes on a value of 1 if theith household is a coupon user and 0 otherwise. For the four categories, where thehomogeneity test was rejected, the individual constraints were tested and only thosethat could not be rejected were imposed and the estimation was done including the

extra price term.In the above regression, note that a, is the estimate of the price elasticity of thenonusers of coupons and (a, + a7) is the estimate of the price elasticity of the users ofcoupons. Since the null hypothesis is that users are more price elastic than nonusers,the statistical test is H : a7, < 0.The results of this estimation are summarized in Table 1 for 19 product categories.For expositional purposes only the price and income coefficients are listed. It is seenfrom this table that the hypothesis that users of coupons are more price elastic cannotbe rejected in most of the product categories.

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CHAKRAVARTHI NARASIMHANFrom Table 1 we see that in the case of the following product categories: papertowels, hair coloring, ready to eat cereals and dog food, the null hypothesis wasrejected. There apparently does not seem to be much commonality between these.

Ready to eat cereals and dog food are categories where in/on pack coupons is adominant force.10 But this is true in the case of cat food also in which the nullhypothesis could not be rejected. Overall, we could say that the results in generalconfirm that users of coupons are more price elastic than nonusers.2. Testing the Intensity of Usage of CouponsAcross Consumers

Recall from t l sctn tha X 0 (e eon ( w i theast section that 0 (see equation (3)) where X is thequantity bought using coupons and a is the wage rate to reflect the opportunity cost oftime. In testing this relationship we have to model the relationship between X* andvariables that are likely to affect the opportunity cost of time. We first discuss theselection of variables, the regression model and finally present the results.Selection of Variables. The dependent variable to test the above implications is thequantity bought using coupons. One of the independent variables selected is the totalquantity bought in this product category. The reason for this is the following: in thetheoretical development, consumption was modelled only as a function of price andincome. But households can vary in their consumption due to other factors such as thenumber of members in a household and of course due to taste differences. Thehouseholds with greaterconsumption in the product class are more often in the marketand can consequently take advantage of the coupon offerings more easily." In fact, asimple t test of the means of quantity bought between user and nonuser segmentrevealed that the users of coupons have a significantly higher average consumptionthan nonusers of coupons. The other independent variables are those that capture theopportunity cost of time. In deciding on these variables, the following issues have to beconsidered. These are (i) whether both husband and wife are employed or whetheronly one is employed, (ii) the educational level of the female head of the household,and (iii) the presence of children. The reason is that the above variables may affect theintensity of coupon usage either in terms of the levels or in the responsiveness of thehousehold to a change in any of these variables. For example, it was argued in anearlier section that a housewife who works is bound to treat her time as more valuablethan another with the same income from her husband. The educational level will affectthe "efficiency" of the housewife in organizing her time. The presence of children willput additional strain on the housewife's time and will consequently be reflected on theopportunity cost of time of the housewife. All these assumptions are consistent withBlattberg et al.'s (1978) work on deal prone consumers.To carry out the test, the sample was divided into three groups as follows: (i) nomale head of the household, (ii) married couple, wife not employed and (iii) marriedcouple, wife employed. In selecting the independent variables the presence of childrenand the educational status of the housewife are relevant for all three groups. Theemployment status of the female head is relevant only for the first and third group.Income is appropriate only for the first group since this is the group where thehousewife is the only source of income. For the second group, income is notappropriate since it does not reflect the housewife's opportunity cost of time. Similar

'?The in/on pack coupon purchases as a percentage of total purchases (deal purchases) for ready to eatcereals, dog food and cat food were 5.55 (20.31), 6.40 (25.31), and 4.69 (17.74), respectively. These wereamong the highest of all the categories in the panel data."For example, if a household buys the product regularly, the housewife is more likely to remember totake the coupons for redemption. In general, the cost of using the coupon is likely to be less the morefrequently one buys the product (higher consumption rates), since many cost components associated withstoring, retrieval, redemption of coupons, etc. are going to be less because of better organization.

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reasoning holds for the third group since the household income overstates the incomeof the wife. For the second group, two dummy variables were selected to control forthe husband's occupation status. The reason for controlling this is because it was feltthat the husband's occupational status will have a bearing on the wife's opportunitycost of time. For example, an executive's wife may have to allocate a portion of hertime to activities (party going, office organizations, etc.) which may be specific to herhusband's occupational status. Thus, in estimating across households with differingoccupational status of the male head of the household, controlling for this aspect isnecessary. The two dummies were labelled OCC1 and OCC2. OCC1 takes on a value 1if the husband is a professional, proprietor, manager or farm owner. OCC2 takes on avalue I if the male head of the household has one of the following job classifications:clerical, sales, skilled foreman, unskilled operator, private household worker, serviceworker. The omitted category is retired, unemployed students, laborers and those inmilitary service.Having selected the independent variables, the next task was to select the functionalform. Since the price theoretic model does not prove useful in selecting a functionalform it was decided to choose a functional form that fits best among some commonlyused relationships. A multiplicative model is ruled out since the dependent variabletakes on a value of 0 for nonusers. A semilog form where the independent variableswere transformed to their logarithms did not improve over a simple linear model.Finally, it was decided to use the squared values of independent variables and retainonly those that improved the R2. This was determined by the traditional F test foradding variables and an F value of greater than I was the critical level.12 In order thatthe significance levels should not be overstated, the experimentation with differentfunctional forms was done with one product category (toilet tissue) and the functionalform that fit the data best was used for all other product categories. The functionalform selected was:

CUPUNTi = ao + a L(INCOME,) + a2(INCOME,)2+ a3(EDUFEM,)+ a4(FEMEMP, ) + a5( QTY,) + a6( QTY,)2+ aT(DUMCHD )+ a8OCC 1 + aO9CC2i + c, where (7)

CUPUNT, is the quantity bought using coupons by the ith household,DUMCHDi is a dummy that takes on the value i if the ith household has nochildren below 18, 0 otherwise.Note that in the above model, FEMEMP takes on the value 0 if the householdbelongs to group (ii) (married couple, wife not unemployed), INCOME takes on thevalue of 0 for groups (ii) and (iii) (both employed) and OCCI and OCC2 havemeaning only for group (ii).Finally, one has to ascertain whether the groups are homogeneous in their responsesto the common variables: EDUFEM, DUMCHD, FEMEMP, QTY, QTY2. Themodel as given by (7) was estimated by assuming homogeneity of response for thesecommon variables. Where the null hypothesis of homogeneity was rejected, theindividual variables were examined and only those constraints that were appropriatewere imposed. The results of the estimation for different product categories are givenin Table 2. The coefficients of only these variables that are tested are given in thetable. The null hypothesis is that the usage is negatively affected by income andemployment hours of the female and positively influenced by the absence of childrenand educational level of the housewife. Thus the null hypothesis a1,a2, a4 < 0 anda3, a7 > 0.

'2An F value of greater than 1 implies that the adjusted R2 is increasing. See Maddala (1977, Chapter 8).

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TABLE 2Test of Intensity of CouponUsage

EDUFEMProduct N R2 Income Income2 Ia I III I

Toilet Tissues 979 0.32 8.2 x 10-3 - 2.58 x 10-7 8.43 -C 9.2(2.54) (-2.18) (2.80)b (1.4

PaperTowels 933 0.43 0.0001 - 3.89 x 10-3 0.67 - 0.3(0.57) (-0.52) (3.30) (0.2Stuffing/Dressing 434 0.20 0.0002 - 4.55 x 10-9 0.51 - 0.9(0.55) (-0.45) (1.49) (1.3Hair Coloring 205 0.12 - 8.67 x 107 1.86 x 10-1 0.0007 0.0007 -0.0006 0.0(- 1.88) (1.58) (1.83) (1.83) (-1.23) (0.0Shampoo 845 0.18 -4.9 x 10-9 1.43 x 108 0.98 -- 0.1(-0.97) (0.70) (2.27) (0.1Cooking/Salad Oil 946 0.27 0.001 - 6.36 x 10-8 3.25 - - 1.8(0.65) (-1.05) (2.04) (0.5Ready to Eat Cereal 952 0.55 0.0665 - 2.91 x 10-7 23.3 5.01 18.29 17.2

(0.76) (-1.12) (1.18) (0.83) (2.60) (1.7Dog Food 492 0.34 0.039 - 1.5 x 10-5 100.67 - 87.7(1.03) (-1.27) (2.83) (1.3Dry Mix Dinners 648 0.23 1.6 x 104 2.68 x 10-9 - 0.62 0.39 1.68 3.0(0.15) (0.09) (-0.22) (0.44) (1.69) (2.3Bars and Squares 247 0.33 2.2 x 104 - 4.82 x 10-9 0.07 - 1.9(0.24) ( - 0.16) (-0.05) ( - 0.79



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886 0.50 0.008(1.88)328 0.43 0.008(0.49)715 0.18 0.005(2.31)

774 0.28 4.5 x 10-5(0.06)620 0.22 - 0.0003

(-0.14)499 0.21 0.0002

(0.50)959 0.17 0.0016(1.27)596 0.33 0.003(1.65)885 0.20 0.0037(2.34)

- 1.61x 10-7(-1.18)-7.90x 10-7

(-1.40)- 7.9 x 10-8

(-0.91)- 4.07 x 10-9

(-0.17)1.67x 10-8(0.25)-6.8 x 10-9

(-0.38)-4.72 x 10-8(-0.92)- 5.55 10-8(-1.12)- 9.47 x 10-8(-2.07)

9.50(0.89)8.07(0.42)1.35(0.77)0.65

(1.41)5.25(1.25)1.39(3.46)- 1.49(1.14)- 1.05

(-0.34)- 0.91(-0.33)

4.11 8.39 - 10.4(1.25) (2.29) (0.6- -31.27

(-0.16)- -1.76

(-0.48)- -0.83

(0.20.50 4.1 4.2

(0.32) (2.74) (1.5- ((.(0.1- 5.3(1.90.32 3.34 4.6

(0.40) (2.66) (2.00.24 2.33 2.0(0.20) (1.69) (1.0

aI and III refer to the following groups respectively: Household with no malehead, household with female notbFigures in parentheses are t-values.'A "-" means that the hypothesis of homogeneity of response across groups could not be rejected and conseqvariable. The critical value of t (for large degrees of freedom) for a one-tailed test is 1.29 at 0.10 level of significa

Cake MixCat FoodFrozen EntreesGelatinSpaghetti SaucesCreme RinseConditionersSoupsOther MixesHot Dogs



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CHAKRAVARTHI NARASIMHANDiscussion. Examination of Table 2 reveals that the income effect is nonlinear. Inall product categories a1 and a2 have different signs. Only in three product categoriesboth are significant. In general, the signs of the coefficient seem to suggest that usage

of coupons tends to increase with income first and after some critical income levelseems to fall as predicted by the theoretical model. For example, this critical incomelevel is $16,206 for toilet tissue. But the lack of significance of the income coefficient issomewhat disappointing. The coefficient of FEMEMP has the wrong sign in threeproduct categories for both groups. For group one only in the case of one productcategory (hair coloring) and for group three only in one category (frozen entree). Innine of the 19 product categories, the coefficients are significantly negative. Thecoefficient of EDUFEM in general has the correct sign. Only six out of 31 estimateshave the wrong sign (none significant) and 16 are significantly positive. The coefficientof DUMCHD has the correct sign in 20 out of 27 different estimates and 13 of themare significantly positive.Looking across at the three demographic groups, the model seems to predict best forthe third group (both husband and wife employed). This is probably understandablegiven the greater time constraint a working couple will face in general than otherhouseholds, ceteris paribus. Overall, one can say that the evidence presented here isstrangely suggestive but in terms of statistical significance of the variables examined,only moderately supportive of the hypothesis proposed in this paper.In evaluating these results, we have to consider the possibility of whether theassumptions underlying the model are too restrictive to yield meaningful results. Twoassumptions are particularlyrestrictive. These are:

(i) only one couponed product was available, and(ii) there are no supply side constraints, i.e., coupons are freely available if one iswilling to put in the effort to clip and redeem them.When the household faces coupons from many product categories, it is not going tospend the same amount of effort in each category. Frequency of purchase and theexpenditure in the product category are some important determinants.13The QTYvariable used in (7) partially captures this but it is difficult to judge how well thevariation in coupon usage across product categories is captured by this variable. Givenpanel data, it is impossible to check, for example, whether condition (ii) above wassatisfied. If there had been a systematic difference in the distribution of coupons acrossdemographic regions (for example, due to differences in product availability acrossregions), assumption (ii) above is very restrictive. Again it is hard to speculate on theeffect of this violation on the results.3. Testing CouponingAcross Brands and Sizes

In this model, predictions regarding couponing across brands in a product class andacross sizes within a brand are tested. The predictions were (1) higher priced brandsshould offer higher savings per unit through coupons, and (2) across sizes, the savingsper unit must be negatively correlated with the size of the package. To test theseimplications, only coupons from newspapers, magazines, mail and from prior pur-chases are considered. Since coupons used in conjunction with other deals wouldreflect savings more than the actual value mentioned on the coupon, such purchaseswere deleted.Within each product category, a model relating the savings per unit, the price perunit and the package size were estimated. The general model was

S, = f(P,,Z,) where (8)13Among the 19 product categories in the panel, the number of product categories in which at least onecoupon purchase was made by a typical household was 6.13.

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S, = savings/unit for thejth size of the ith brand,Pi = price/unit for the jth size of the ith brand,Zj = package size for thejth size of the ith brand.

For each brand and size, the price and savings obtained were averaged acrossconsumers yielding one observation per brand per size. The above model was esti-mated by specifying different functional forms for "f." Specifically, the following werechosen.Model I. Linear: S,j = ao+ a1P . + a2j + ci.Model II. Log-Log: Ln(S) = a0 + a,Ln(P) + a2Ln(z,) + rc.Model III. Semilog: S,j = a0 + acPij + a2Ln(z.) + ei.Model IV. Ln(S,j) = ao + aiP. + a2z,C+ Ei.In all models, the a priori predictions were ae > 0 and a2 < 0.The four models differ in their representation of the curvature properties of f (seeequation (8)) with respect to P, and z,. Model I assumes that the relationship is linear.Model II uses a constant elasticity function implying that a percentage change in thesavings per unit for one percent change in price (or the size) is constant. In terms of

TABLE 3Price-RegressionsResultsfor the Model

Ln(Si,) = ao + a,P,i + a2Size,iProduct

Toilet TissuesPaper TowelsStuffing/DressingShampooCooking/Salad OilReady to Eat CerealDog FoodDry Mix DinnersBars and SquaresCake MixCat FoodFrozen EntreesGelatinSpaghetti SaucesCreme Rinse/ConditionersSoupsOther Mixes

N R2 Price51 0.44 27.40

(5.22)74 0.51 - 0.1553(- 2.68)24 0.60 - 40.34

(-0.99)70 0.58 2.625(4.03)79 0.29 2.33(1.06)196 0.55 7.248(5.40)132 0.48 21.771(5.49)

71 0.72 65.52(9.41)13 0.38a -5.167

(-0.08)149 0.07 - 44.37(-1.46)57 0.65 30.626

(5.87)191 0.30 36.51(4.37)72 0.40 33.296(5.56)65 0.55 8.047(4.29)25 0.63 1.47(2.20)182 0.81 48.57

(13.78)57 0.42 105.42(2.14)

aThe regression was not overall significant at the 0.05 level.

Size6.86 x 10-5

(0.44)- 0.0096(-5.94)- 0.0001

(-4.85)- 0.0008(-4.39)- 0.0001(-3.92)- 0.0005(-7.63)-2.09x 10-5(-6.33)-4.03 x 10-5(-3.24)- 0.0002

(-1.71)-2.48 x 10-5(-3.22)-6.65 x 10-5(-4.65)- 3.19 x 10-5

(-6.37)-8.13 x 10-5(-2.37)- 0.0003(-3.39)- 0.0006

(1.68)-7.7 x 10-5(-9.27)-2.44 x 10-5(-4.55)

I - d.1 I

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CHAKRAVARTHI NARASIMHANTABLE 4

Summaryof RegressionsAcross Brandsand SizesPrice + Size -

Number of Number of Number of Number ofModel Cases Significant Cases Cases Significant CasesI Si = a0 + a1Price/,+ a2Sizej 14 12 14 10

(0.82) (0.71) (0.82) (0.59)II Ln(S,) = ao + alLn(Price,/) + a2Ln(Size,) 12 10 16 15(0.71) (0.59) (0.94) (0.88)III S/ = ao + a,Price,, + a2Ln(Size/j) 13 13 14 11(0.76) (0.76) (0.82) (0.65)IV Ln(S) = a0 + aIPricel + a2Size, 14 13 16 14(0.82) (0.76) (0.94) (0.82)

Note. (i) Total number of product categories (number of cases)= 17.(ii) Figures in parentheses are proportion of cases out of 17.(iii) Significant cases correspond to 0.05 level of significance, one tailed test.the second order derivatives, Models II and IV imply less stringent restrictions thanModels I and III.14All the four models were estimated using the data on brands and sizes. In order toconserve space only the results from Model IV are presented in Table 3. In Table 4 thesummary of results from all the models are presented for comparison.As can be seen from Table 3, the predictions from the theory are strongly supported.Table 4 reveals that in general Models II and IV predicted better in terms of thenumber of significant coefficients than Models I and III.

6. Managerial ImplicationsIdentifying CouponUsers

The hypothesis developed in this paper makes predictions about who is more likelyto use coupons and who is less likely to use them. Those consumers for whom it is"costly" to use coupons are less likely to use them than others. Several demographicvariables (income, education, employment status, presence of children) were used asproxies to measure this cost. Since a manager is interested in targeting the couponeffort towards the users of coupons, understanding of the differential pattern of usageof coupons across consumers is valuable to the manager. Given different demographicprofiles of media vehicles, a manager can identify the more easily targetable vehicles(i.e., the media vehicles that are likely to offer greater redemption rates) based on thehypothesis developed in this paper.CouponingAcross Brands and Sizes

According to the hypothesis developed in this paper, higher-priced brands shouldcoupon at a higher level, and larger sizes should be couponed with greater cents-offvalue but at a lower savings per unit than smaller sizes. For example, the models usedto test these implications (see equation (8)) can serve as a "market model." Given theprice of its brand, a firm can use this model to predict the savings it should offer fordifferent sizes of its product. However, there are two important considerations (notdealt with in the model development) a manager must be aware of. The firstconsideration concerns uncertainty regarding product quality. In the absence ofperfect knowledge concerning a product's quality, a consumer incurs a cost for trying aproduct whose quality he is uncertain about. In other words, informational costs will

14Models I and III imply that a2S/aP2 = a2S/aPaz = 0 while Models II and IV do not.

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PRICE DISCRIMINATION THEORY OF COUPONSenter the full price paid for the product. Therefore, one would expect new brands in aproduct class to be couponed at a higher level than dictated by the market model.Next, the issue of couponing in different media was not considered in the marketmodel. If there are systematic differences in the demographic profile and consumptionpattern (of the product) of consumers across the different media, the manager has todecide and make a judgmental revision on the cents-off values for coupons in differentmedia. This issue is further addressed below.Couponing n Different Media

Assume for simplicity that consumers can be grouped into two segments: Elasticand Inelastic. Assume further that the elastic segment buys only with coupons and theinelastic segment buys without a coupon. Let the demand by the elastic segment be Xwhich is a function of the price P and the vector of savings S = (sl, . . ., sn) where S,is the savings offered through the ith media. The marginal response of X to Si, i.e.,ax/asi can be different across media. This could arise due to differences in the reachof the media vehicles, the demographic profile of the audience in the vehicle, etc. Atthe optimum, the firm should equate the net marginal return (i.e., the incrementalcontribution minus the marginal cost of coupon) across the different media. If weassume that the couponing cost is a fixed cost then at the optimum:

ax (P- Co- Si)= a(P - co- S) forall i -j (9)where C0 is the marginal cost of the product, assumed constant. While it is straightfor-ward to characterize the optimum solution through first order conditions, use of thismodel as a managerial tool is fraught with several difficulties. First, it may beprohibitively costly for a firm to measure the demand functions. Second, adjusting theprice and savings could be so costly (a factor not considered in the above model) thatthe firm has to adopt simplifying procedures. Third, the manager may be faced with aconstraint limiting the amount he can spend on coupons. Thus, while (9) may serve asa descriptive model of firm behavior, it is a far cry from an operational model. To usethe underlying criteria (i.e., equating the marginal returns across media) the followingrule is suggested. Suppose the firm can obtain data on the distribution of coupons indifferent media (this should be a straightforwardtask) and can obtain the change indemand due to couponing. Then it is possible to estimate the response function acrossmedia as:

AX = f(Si,) (10)where AX is the change in the quantity demanded, Si the savings and DAs a vector ofdemographic variables for the ith medium or segment. Relevant demographic variableswould be the wage rate of consumers, education, employment, status of the femalehead of the household, etc. The manager can simply rank the media in terms of theirresponsiveness due to couponing and decide on the savings to be offered. One way toestimate (10) would be to use a controlled drop of couponing in different matchedsegments.Frequency of Couponing

If the price discrimination hypothesis is valid, then the suggestion would be that theperiodicity of couponing should equal the interpurchase time of the heavy users ofcoupons. When alternative vehicles are available (magazines and newspapers), one canstagger the coupon drop over time in order to reach as many consumers as possible.In summary, the theory has implications for some key managerial issues and certainsuggested guidelines for others. However, extensions of the basic model are necessary

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CHAKRAVARTHI NARASIMHANalong with estimation with data on distribution and redemption in order to formulatespecific strategies on some of the issues of relevance to managers.

7. Conclusionand Directions for Further ResearchIn this paper an important price cutting mechanism, viz., cents-off coupons, wasstudied. Based on a price theoretic model, consumers' decision to use coupons wasanalyzed. It was found that the data strongly supported the fundamental implicationthat the users of coupons are more price elastic than nonusers of coupons. However,the proxy variables used to describe the profile of coupon users provided only partialsupport. The data also strongly supported the implications that higher priced brands ina product class will coupon at greater savings relative to lower priced brands and thatlarger sizes will be couponed at a lower savings per unit of the product bought thansmaller sizes. Future research should proceed along the following directions.(i) Theory Testing: Further research is needed to discriminate this hypothesis fromthe frequently mentioned competing hypothesis, viz., the trial-repeatpurchase. Basedon a model of the firm, this hypothesis should be developed and implications shouldbe derived. One could then test one theory against another based on availableevidence.(ii) Model of Coupon:A restrictive assumption made in the theoretical developmentwas that there is only one couponed product. In reality, this assumption does not hold,and a consumer simultaneously decides on the coupon usage in different productcategories. This aspect can be modeled by extending the model described in ?4.(iii) Model of the Firm: We considered one firm and one couponed product. When

there are many brands, each possibly enjoying some localized monopoly power butstill form substitutes of one another, the equilibrium amount of couponing and therelationship between the cents-off given and say, the price of the brand would be ofinterest. Alternatively, one could think of coupons as devices the firms use in arandomizing strategy faced with an elastic and inelastic segment.(iv) EmpiricalTesting: In testing the intensity of coupon usage across consumers, thedependent variable CUPUNT is a truncated dependent variable, since it takes on thevalue of zero for those who did not use coupons. Alternative econometric procedureslike Tobit analysis can be used to model the relationship as in (7). One could alsomodel this as a two-step process where the first step is deciding whether or not to usecoupons and in the second step deciding how much to use them if the consumerdecides to use coupons at all.15

Acknowledgement. This paper is part of my Ph.D. thesis submitted to the University of Rochester. I amgrateful to the members of my thesis committee: Marshall Freimer, Martin Geisel, Ronald Schmidt and, inparticular, Subrata Sen for their constructive criticisms. I have also benefitted from the comments of mycolleagues at Chicago, especially Peter Pashigian. The reviewers of this paper made several excellentsuggestions and I thank them for this. I alone remain responsible for the remaining errors. Finally, I wouldlike to thank NPD Research, Inc. for providing me with the data for empirical analysis.

15Thispaper was received October 1982 and has been with the author for 2 revisions.

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c narsimhan

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