A PRICE DISCRIMINATION THEORY OF COUPONS

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

           A PRICE DISCRIMINATION THEORY OF COUPONS
                                         CHAKRAVARTHINARASIMHAN
                                                     Universityof Chicago
          The objective of this paper is to analyze the consumer's decision in electing to use cents-off
        coupons distributed by manufacturers of consumer products. Arguing that the decision to use
        coupons is based on the tradeoff between costs of using coupons and the savings obtained, it is
        shown 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 users
        of coupons are more price elastic than nonusers of coupons and that the opportunity cost of
        time 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. Introduction
   A cefrts-off coupon promises the consumer a reduced price on the next purchase of
a specified product. The practice of offering a reduced price through such instruments
is prevalent in the consumer goods industries, more noticeably in the frequently
purchased nondurable products and service markets. Examples of such categories
include: grocery products, meals in restaurants, hair cutting services, laundry and
cleaning services, photographic supplies, film processing, etc. Cents-off coupons are
distributed in the newspapers, magazines, by mail, in/on packages. The number.of
coupons have grown by more than 500% in the last decade and the average face value
has doubled in the same period. Thus, coupons are an important promotional
mechanism.
   There are many interesting research issues in the study of cents-off coupons. The
more important ones are:
   (i) Why do manufacturers offer such coupons? Why not reduce the price of the
product at the retail outlet?
   (ii) Who are the more intense users of coupons if not all consumers? Which
demographic 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 evaluate
the profitability of couponing, how to determine the cents off value, what tradeoffs
exist between distributing coupons in different media, etc.
   In this paper, we argue that one reason why a firm will offer coupons is to price
discriminate between the more elastic and less elastic demanders. Hypotheses concern-
ing the difference between users and nonusers of coupons in terms of observable
demographic variables will be offered. And finally, hypotheses consistent with the
                                                                 128
                                                                                            0732-2399/84/0302/0128$01.25
                                   Copyright ? 1984, The Institute of Management Sciences/Operations       Research Society of America

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PRICE DISCRIMINATION THEORY OF COUPONS                                                           129

model developed in this paper will be offered to explain systematic differences in
cents-off values offered by different brands in a product category and different sizes
within a brand. The rest of the paper is organized as follows. In ?2, past literature in
couponing 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 the
consumer model; ?5 contains the empirical tests of the implications derived from the
consumer model. ?6 outlines managerial implications from the theory and ?7 con-
cludes the paper with a summary and directions for further work.

                                             2.    Background
    Past research in marketing on coupons and their effects on consumers is rather
 scanty. Nielson (1965) discusses the market research aspects of coupons and argues
 that this could be a prime factor for the manufacturers to distribute coupons. Ward
 and Davis (1978) argue that coupons influence consumers through their redemptive
 value and their informational value (i.e., informing the consumers of the existence of
 the product). They construct a regression model with consumption as the dependent
 variable and price, income, savings given through coupons, and a host of demographic
 variables as independent variables. They break down the increase in consumption into
 two parts: a price effect and an informational effect. From the empirical estimates of
 the 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 encourage
 switching, once the coupons are retracted, the consumers who switched did not
 repurchase at the regular price. Precisely the opposite effects were encountered for
 in/on package coupons. Teel, Williams and Bearden (1980) conducted a survey of
 female heads of household to study the characteristics of coupon users. The focus was
on characterizing the profile of coupon users who would try a new product with a
coupon. They report, based on the survey results, that coupon users have significantly
larger family sizes, larger incomes and are significantly younger than nonusers of
coupons. Bearden, Teel and Williams (1981) report the results of another survey they
did to study the relationship between the percentage price reduction and willingness to
try a new brand among female grocery shoppers. They computed the percent of people
who 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 the
profitability of couponing. Based on a decision calculus approach, the parameters of
the model are estimated.
   More recently White (1983) and Levedahl (1983) have addressed the issue of the use
of cents-off coupons. White argued that coupons can be a means to discriminate
between those consumers who comparison shop and those who do not. The proportion
of consumers who comparison shop is assumed to be exogenous to the model. She
shows that as a result of entry and exit, the relative profit positions of the different
firms in the industry are unaffected but the structure of price changes, viz., some
consumers 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 for
additional units. (This definition is different from the definition of multipart pricing in
the economics literature.) He uses the data derived from a panel supplied by NPD. For
the paper towels category, the average full price with coupon (price paid plus the value
of coupon) is significantly higher for all the national brands than the average price
paid when there was no coupon. This is consistent with the price discrimination

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130                                                                           CHAKRAVARTHI NARASIMHAN

hypothesis and not the "multipart pricing" hypothesis. He further argues that recur-
rence of coupons periodically is consistent with the price discrimination hypothesis
and 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 empirical
support to this hypothesis. Before we do this, we review some alternative explanations.
   Coupons for Gathering Market Research Data. By coding the coupons for the
media and geographic regions in which they are distributed, a manufacturer can gain
valuable insights into the price sensitivity of different consumer segments. Further, he
can learn about the pattern of redemption and plan the coupon drop more effectively
and 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 these
advertisements, 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 of
offering a price cut since the manufacturer does not incur redemption costs paid to the
retailer, cost of misredemption, etc. Further, this hypothesis cannot explain the
variation in coupon usage across consumers nor does it prove useful in predicting the
savings to be offered through coupons relative to competing brands.
   CouponsInduce Trials and Hence Repeat Purchases. Coupons represent a price cut
to consumers. The consumer incurs a cost in trying a product whose value he is
uncertain about. Therefore, if he can be compensated for this cost, at least partially, a
trial 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. Some
of these are: Using cents-off labels, small sample sizes, trade promotions, etc. This
hypothesis fails to explain why these alternative mechanisms are less efficient than
cents-off coupons for inducing trial. Further and most importantly, the hypothesis has
no prediction on the intensity of coupon usage across consumers. Note that the crucial
question here is not why a price cut is given but rather why the price cut takes a
particular form. In other words, given the cost of couponing, viz., cost for distributing
coupons, redemption cost paid to retailers, clearing houses, etc., why does a firm
choose 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 the
proposition that coupons can be used to induce trial. But unlike this hypothesis, the
price discrimination hypothesis predicts why, in a positive sense, the intensity of usage
of coupons is likely to differ across consumers. And finally, the trial-repeat purchase
hypothesis does not have predictions on the cents-off to be offered through coupons
and how the savings given should vary across brands and package sizes.
   This does not necessarily mean that the trial-repeat purchase hypothesis cannot
explain some form of couponing. In product categories where the purchaser is not the
consumer, coupons can serve as a reminder to the purchaser of the product's utility to
the 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 that
in the absence of self-evaluation of a product by the purchaser, an on/in pack coupon can influcence the
nest purchase more heavily than in other product categories. Dodson et al.'s article seems to partially
support this assertion.

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PRICE DISCRIMINATION THEORY OF COUPONS                                                                131

foods and ready to eat cereals are good examples of such a category and in/on
package coupons is a major form of couponing in these categories.

                          3.     Coupons as Price Discrimination Devices
   The basic argument in the explanation offered in this paper is that to enjoy the
savings from using coupons, the consumer incurs some cost and the decision to use
coupons 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 of
organizer, time spent in periodically organizing the coupons, etc.), cost of looking
through magazines, time spent in storing and retrieving the coupons, etc. The chief
component of this cost is the cost of time. This cost will also be affected by other
household resource variables like the education level of the housewife, the presence of
children and the manner in which the household derives its income. For example, a
housewife who is employed is bound to treat her time as more valuable than a
nonworking housewife belonging to another household with identical income and
other household resource variables.2 Similarly, the presence of children could have an
impact on the cost imputed to the time available to the housewife. In general, as time
becomes more and more of a scarce resource, the value attached to successive units is
higher.
   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. They
show that presence of children and the wife being employed have a negative impact on
the 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 using
one coupon. Let c(n) be the cost function reflecting the cost of using n coupons. Let S
be the savings obtained per coupon assumed constant. Therefore the optimal number
of units the household will buy under this simple situation can be characterized by the
following first order condition, viz.,
                                                     S = c'(n)                                        (1)
where c'(.) is the marginal cost of using one coupon. If all households in the
population face the same savings S (i.e., benefit) from coupons but differ in their cost
function then it is easy to see from (1) that different households will be exhibiting
different intensities of coupon usage.3 Those households for whom c'(n) > S for all
n > 0 choose not to use coupons. Thus, given heterogeneity in the cost of using
coupons 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 constraints
imposed by the firm.4
   Why is the firm interested in providing a price cut to those consumers with lower
costs of usage? Now suppose it can be established that the consumers with lower costs
are more price elastic than those who do not use coupons, it then follows that the firm
is selling the same product at a lower price to the more elastic consumers relative to
the segment who have higher costs (and less elastic demand). It is in this sense that
coupons behave as price discrimination devices and that such a mechanism is profit
maximizing 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 a
nonworking 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 arbitrage
does not arise. That is, the manufacturer need not take any explicit action to isolate the segments.

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132                                                                           CHAKRAVARTHI NARASIMHAN

segments is worth emphasizing here. The segments are formed on the basis of rational
self-selection and not on the basis of preferences. That is, the differences in demand
elasticities (this is rigorously established in the next section) is driven by opportunity
cost 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, firms
would 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 one
per household.) Whereas under the price discrimination hypothesis the firm does not
have an incentive to restrict such use. The recurring use of coupons seems to be
consistent with price discrimination hypothesis and inconsistent with trial-repeat
hypothesis (Levedahl 1983). Further, Dodson, Tybout and Sternthal (1978) conclude
that at least as far as media distributed coupons are concerned, cents-off coupons
undermined repeat purchases. If firms know this, it is not clear why they continue to
coupon. Secondly, if consumers are uncertain about a product, one would expect them
to use coupons on small sizes, since it involves less outlay and, consequently, firms to
restrict coupons to only small sizes (thereby restricting the use of coupons by regular
users of the product who may be buying larger sizes). We do not observe this in
practice.5
   In 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 Consumer Behavior
   In 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 product
class are derived. As detailed in the previous section, it is assumed that a consumer
trades 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-theoretic
framework.

Assumptions
  A . The consumer maximizes a well-defined utility function (for other assumptions
on the nature of this utility function see below), defined over two goods denoted as X
and L. The good X is available for purchase with coupon, and L can represent a
composite good or leisure.6
  A2. The consumer knows the price of good X with certainty and he also knows the
quality of the product. That is, we assume a world of costless information on prices
and quality.
  A3. If the consumer decides to buy X with a coupon, he uses one coupon for one
unit of the product and obtains a savings of S. This assumes that products are
available in one "size" only. While this is obviously restrictive, it simplifies the
treatment. We will return to the issue of sizes later.
  A4. The utility function U (defined over X and L) is continuous, twice-differentiable
and the Hessian of U is negative definite. That is, Uxx, ULL < 0 andUxx ULL - UXL

   5This is based on anecdoctal evidence. Further, in the empirical testing section, we will see that brands
coupon for different sizes (see Table 3).
  6This is essentially a mathematical simplification. Even though a consumer purchases a number of goods
in the economy, to study the price effects on one good, one can conveniently combine the all other goods in
one category and classify this as a composite good.

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PRICE DISCRIMINATION THEORY OF COUPONS                                                             133

> 0 where the subscripts refer to the variables with respect to which the partial
derivative of U is considered.
   A5. Both X and L are "normal" goods, i.e., as income increases holding everything
else constant, the consumer consumes more of X and L.
   Assumptions A4 and A5 are made for tractability. A5 is a strong sufficient (not
necessary) 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 time
horizon.
   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 of
consumers 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 the
labor market the consumer increases his wage income, but at a decreasing rate. This
assumption relies on the fact that the consumer is likely to exhaust more beneficial (to
him) 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 for
mathematical tractability.
   The consumer model can be represented by the following nonlinear constrained
maximization 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 using
coupons, varies across consumers holding everything else constant and (ii) how the
price elasticity of demand varies across consumers using coupons with different
intensity. That is, we are interested in the signs of dX*/aa and
                                                               arpl(X*)/aa   where
rp,(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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134                                                                        CHAKRAVARTHI NARASIMHAN

the first inequality implies that as the opportunity cost of time increases, the intensity
of coupon usage decreases. The second inequality implies that the more intense users
of coupons (those with a lower a) are more price elastic ('qp,(x) is a negative number)
than the less intense users of coupons.
Other Implications
   Couponing Across Brands. Consider a product class with a number of brands
differentiated on some set of characteristics. To simplify, let R denote a composite
characteristic on which brands are differentiated. The brands in this product class are
sold at different prices, and let P,(R) represent the market price function, which is
assumed to be well-defined continuous and twice differentiable over the relevant range
of analysis. Since different brands will be couponed at different values, let S(R)
represent the savings per coupon offered by different brands. The consumer model
under 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 function
which traces out indifference curves in the P - R plane describing the price the
consumer is willing to pay for various values of R, holding his income and utility level
constant. 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 the
relevance of the market price function, the location of consumers and producers at
various points in the characteristic spectrum, and the formulation of market segments.
Rosen also established that assuming the characteristics are normal (i.e., higher-income
consumers demand larger amounts of the characteristics), on the average higher-
income consumers will be consuming brands with higher levels of R or which are
priced 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 would
expect consumers with higher wage rates or opportunity costs of time to be located at
higher 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 average
will coupon at higher values. This effect is reinforced by the following reasoning as
well. 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 brands
with differing R sell. 0(U, R, Y) describes the price a consumer is willing to pay for
different R, holding is utility (U) and income (Y) fixed. The consumer selects the
brand Ro paying price PO.Consider two other brands R1 and R2 priced at P1 and P2
such that P2 > Pl > PO.Now the 0 function which describes the consumers' tradeoff
of R against price is a concave function of R (see Rosen 1974). Therefore, if the
higher-priced brands P, and P2 were to coupon so as to make the consumer buying Ro
to buy their brand, they have to offer a net savings of 8, and 82, respectively, at which
the consumer would be just about indifferent between Ro or switching to one of the
higher-priced brands. From Figure 1, it is clear that 82 > 86 or that the net savings

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PRICE DISCRIMINATION THEORY OF COUPONS                                                                                   135

                              p

                                                                                                       P(R)

                              p2

                              P!     .                                                    /                   e (R,U,Y)

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

                                                                         R'     R0            R1   2    R

                       FIGURE1. 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 the
same regardless of which brand's coupon the consumer uses, this would imply that the
higher-priced brand should offer higher savings through coupons than a lower-priced
brand. What drives this implication is that the 0 function is concave and the market
price function P(R) is convex.
   In Figure 1, another brand (P', R') is shown. This brand is priced lower than the
brand the consumer is currently buying; i.e., (P, Ro). It appears as though it could
offer a higher savings equal to 82, say, to make the consumer buying (PO,RO)to buy its
brand. However, given our assertion that consumers buying (P', R') on the average
have 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 present
consumers 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-priced
brands.8
   CouponingAcross Sizes. Until now it was assumed that the consumer buys one unit
through a coupon, no more or no less. However, a manufacturer may issue a coupon
for different sizes of the same product, offering different absolute discounts (15? off a
 12-oz. box and 254 off on a 24-oz. box).
   Consider one particular brand and two different sizes: L (large) and S (small). For
expositional convenience, assume the large box is twice the size of the small box. Let C
be the marginal cost for collecting and using a coupon, assumed to be constant. To
remove price effects, assume that the price per unit is the same forL and S. In other
words, if the small size sells for Ps and the large size for PL, then PL = 2Ps. Now, if
the 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 prevent
arbitrage, the net benefit from using a coupon on the large size and using two coupons
to 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 and
thus, it is only a partial equilibrium analysis. One should establish why in equilibrium the firm is interested
in offering coupons in the manner argued above by "closing" the market. This, however, is beyond the scope
of this paper.

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136                                                                           CHAKRAVARTHI          NARASIMHAN

    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 arbitrary if one treats the small
 size as a unit, (5) implies that the savings per unit on a large size box must be smaller
 than the savings per unit on a smaller size box. Note that the above result is not
 affected 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 be
 empirically 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 through
 coupons will be positively correlated
    (iv) Across different sizes of a brand, the savings per unit of the product bought will
 be inversely related to the size.

                                            5.    EmpiricalAnalysis
   In this section the implications derived from the consumer model are tested with
 diary panel data. The panel contains purchase records of about 1,000 consumers in 20
 product categories.
 1. Testing Differences in Demand Elasticities.
    A key implication of the consumer model described in ?4 was that there should be a
 systematic 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 than
 nonusers of coupons. The null hypothesis, then, is that users of coupons are more price
 elastic 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 and
 straightforward manner. A user was defined as one who made at least one purchase
 with a coupon. This is a conservative definition and would bias the test (to be
 described below) towards rejecting the null hypothesis:9

          Ln( 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 will
be lower than it would be if the null hypothesis were true. Thus, this minimizes the chances of finding a
greater elasticity for the users of coupons, making the test conservative.

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PRICE DISCRIMINATION THEORY OF COUPONS                                                                                    137

                                               TABLE I
                 Results of Regressionto Test Differences in Demand Elasticities Between
                                     Users and Nonusers of Coupons
       Product            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)
     Conditioners
   Soups                 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 cats
  respectively.

   The above functional form was used since we are primarily interested in testing
differences in demand elasticities. The coefficients in a log-log model directly yield the
estimates of elasticities of the dependent variable with respect to the independent
variable. In equation (6), FAMSIZ is included since consumption will be affected by
the number of members in a household. EDUFEM, FEMEMP and ADEFEM are
included to control for "taste" differences across households.
   The model specified by equation (6) was estimated at the product category level for
the user and nonuser segment respectively. The null hypothesis that coefficients of all
variables 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 food
and 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 extra
price term as follows: DPR, = a7[8iLn(PRICE)] where 8; takes on a value of 1 if the
ith household is a coupon user and 0 otherwise. For the four categories, where the
homogeneity test was rejected, the individual constraints were tested and only those
that 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 the
nonusers of coupons and (a, + a7) is the estimate of the price elasticity of the users of
coupons. 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 seen
from this table that the hypothesis that users of coupons are more price elastic cannot
be rejected in most of the product categories.

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138                                                                           CHAKRAVARTHI NARASIMHAN

  From Table 1 we see that in the case of the following product categories: paper
towels, hair coloring, ready to eat cereals and dog food, the null hypothesis was
rejected. 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 a
dominant force.10 But this is true in the case of cat food also in which the null
hypothesis could not be rejected. Overall, we could say that the results in general
confirm that users of coupons are more price elastic than nonusers.
2.   Testing the Intensity of Usage of CouponsAcross Consumers
   Recall from t last l   section
                          sctn    that
                                  tha X            0 (see eon
                                                     (e equation   (3))
                                                                    (   w
                                                                        where  X isi the
quantity bought using coupons and a is the wage rate to reflect the opportunity cost of
time. In testing this relationship we have to model the relationship between X* and
variables that are likely to affect the opportunity cost of time. We first discuss the
selection of variables, the regression model and finally present the results.
   Selection of Variables. The dependent variable to test the above implications is the
quantity bought using coupons. One of the independent variables selected is the total
quantity bought in this product category. The reason for this is the following: in the
theoretical development, consumption was modelled only as a function of price and
income. But households can vary in their consumption due to other factors such as the
number of members in a household and of course due to taste differences. The
households with greater consumption in the product class are more often in the market
and can consequently take advantage of the coupon offerings more easily." In fact, a
simple t test of the means of quantity bought between user and nonuser segment
revealed that the users of coupons have a significantly higher average consumption
than nonusers of coupons. The other independent variables are those that capture the
opportunity cost of time. In deciding on these variables, the following issues have to be
considered. These are (i) whether both husband and wife are employed or whether
only 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 the
intensity of coupon usage either in terms of the levels or in the responsiveness of the
household to a change in any of these variables. For example, it was argued in an
earlier section that a housewife who works is bound to treat her time as more valuable
than another with the same income from her husband. The educational level will affect
the "efficiency" of the housewife in organizing her time. The presence of children will
put additional strain on the housewife's time and will consequently be reflected on the
opportunity cost of time of the housewife. All these assumptions are consistent with
Blattberg et al.'s (1978) work on deal prone consumers.
   To carry out the test, the sample was divided into three groups as follows: (i) no
male head of the household, (ii) married couple, wife not employed and (iii) married
couple, wife employed. In selecting the independent variables the presence of children
and the educational status of the housewife are relevant for all three groups. The
employment 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 the
housewife is the only source of income. For the second group, income is not
appropriate 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 eat
cereals, dog food and cat food were 5.55 (20.31), 6.40 (25.31), and 4.69 (17.74), respectively. These were
among 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 to
take the coupons for redemption. In general, the cost of using the coupon is likely to be less the more
frequently one buys the product (higher consumption rates), since many cost components associated with
storing, retrieval, redemption of coupons, etc. are going to be less because of better organization.

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PRICE DISCRIMINATION THEORY OF COUPONS                                                                139

reasoning holds for the third group since the household income overstates the income
of the wife. For the second group, two dummy variables were selected to control for
the husband's occupation status. The reason for controlling this is because it was felt
that the husband's occupational status will have a bearing on the wife's opportunity
cost of time. For example, an executive's wife may have to allocate a portion of her
time to activities (party going, office organizations, etc.) which may be specific to her
husband's occupational status. Thus, in estimating across households with differing
occupational status of the male head of the household, controlling for this aspect is
necessary. The two dummies were labelled OCC1 and OCC2. OCC1 takes on a value 1
if the husband is a professional, proprietor, manager or farm owner. OCC2 takes on a
value I if the male head of the household has one of the following job classifications:
clerical, sales, skilled foreman, unskilled operator, private household worker, service
worker. The omitted category is retired, unemployed students, laborers and those in
military service.
   Having selected the independent variables, the next task was to select the functional
form. Since the price theoretic model does not prove useful in selecting a functional
form it was decided to choose a functional form that fits best among some commonly
used relationships. A multiplicative model is ruled out since the dependent variable
takes on a value of 0 for nonusers. A semilog form where the independent variables
were 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 retain
only those that improved the R2. This was determined by the traditional F test for
adding variables and an F value of greater than I was the critical level.12In order that
the significance levels should not be overstated, the experimentation with different
functional forms was done with one product category (toilet tissue) and the functional
form that fit the data best was used for all other product categories. The functional
form 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 no
children below 18, 0 otherwise.
  Note that in the above model, FEMEMP takes on the value 0 if the household
belongs to group (ii) (married couple, wife not unemployed), INCOME takes on the
value of 0 for groups (ii) and (iii) (both employed) and OCCI and OCC2 have
meaning only for group (ii).
  Finally, one has to ascertain whether the groups are homogeneous in their responses
to the common variables: EDUFEM, DUMCHD, FEMEMP, QTY, QTY2. The
model as given by (7) was estimated by assuming homogeneity of response for these
common variables. Where the null hypothesis of homogeneity was rejected, the
individual variables were examined and only those constraints that were appropriate
were imposed. The results of the estimation for different product categories are given
in Table 2. The coefficients of only these variables that are tested are given in the
table. The null hypothesis is that the usage is negatively affected by income and
employment hours of the female and positively influenced by the absence of children
and educational level of the housewife. Thus the null hypothesis a1,a2, a4 < 0 and
a3, 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 2
                                                                               Test of Intensity of Coupon Usage
                                                                                                   EDUFEM
     Product             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                       9.24
                                            (2.54)                (-2.18)                (2.80)b                            (1.48
Paper Towels            933 0.43             0.0001                 - 3.89 x 10-3         0.67       -                       0.31
                                            (0.57)                (-0.52)                (3.30)                             (0.21
Stuffing/Dressing       434 0.20             0.0002                 - 4.55 x 10-9         0.51       -                       0.90
                                            (0.55)                (-0.45)                (1.49)                             (1.33
Hair Coloring           205 0.12          - 8.67 x 107                 1.86 x 10-1        0.0007    0.0007    -0.0006        0.00
                                         (- 1.88)                     (1.58)             (1.83)    (1.83)    (-1.23)        (0.03
Shampoo                 845 0.18          -4.9 x 10-9                  1.43 x 108         0.98       --                      0.16
                                         (-0.97)                      (0.70)             (2.27)                             (0.18
Cooking/Salad Oil       946 0.27             0.001                  - 6.36 x 10-8         3.25       -          -            1.87
                                            (0.65)                (-1.05)                (2.04)                             (0.58
Ready to Eat Cereal 952 0.55                 0.0665                 - 2.91 x 10-7        23.3       5.01       18.29        17.26
                                            (0.76)                (-1.12)                (1.18)    (0.83)      (2.60)       (1.76
Dog Food                492 0.34             0.039                  - 1.5 x 10-5        100.67       -                     87.73
                                            (1.03)                (-1.27)                (2.83)                             (1.30
Dry Mix Dinners         648 0.23             1.6 x 104                 2.68 x 10-9     - 0.62       0.39        1.68         3.06
                                            (0.15)                    (0.09)          (-0.22)      (0.44)      (1.69)       (2.31
Bars and Squares        247 0.33             2.2 x 104              - 4.82 x 10-9         0.07       -                       1.93
                                           (0.24)                 ( - 0.16)           (-0.05)                           ( - 0.79

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Cake Mix                886 0.50              0.008                 - 1.61 x 10-7             9.50     4.11     8.39 - 10.4
                                              (1.88)                (-1.18)                   (0.89)   (1.25)   (2.29)     (0.60
 Cat Food                328 0.43              0.008                 -7.90x     10-7           8.07                  - -31.27
                                              (0.49)                (-1.40)                   (0.42)                    (-0.16)
 Frozen Entrees          715 0.18              0.005                 - 7.9 x 10-8              1.35                   - -1.76
                                              (2.31)                (-0.91)                   (0.77)                    (-0.48)
 Gelatin                 774 0.28              4.5 x 10-5            - 4.07 x 10-9             0.65                   - -0.83
                                              (0.06)                (-0.17)                   (1.41)                       (0.22
 Spaghetti Sauces        620 0.22           - 0.0003                    1.67 x 10-8            5.25     0.50     4.1        4.21
                                           (-0.14)                     (0.25)                 (1.25)   (0.32)   (2.74)     (1.59
 Creme Rinse             499 0.21              0.0002                -6.8 x 10-9               1.39              -          ((.1
   Conditioners                               (0.50)                (-0.38)                   (3.46)                       (0.17
 Soups                   959 0.17              0.0016                -4.72 x 10-8           - 1.49               -          5.39
                                              (1.27)                (-0.92)                   (1.14)                       (1.99
 Other Mixes             596 0.33              0.003                 - 5.55 10-8            - 1.05      0.32     3.34       4.63
                                              (1.65)                (-1.12)                (-0.34)     (0.40)   (2.66)     (2.08
 Hot Dogs                885 0.20              0.0037                - 9.47 x 10-8          - 0.91      0.24     2.33       2.05
                                              (2.34)                (-2.07)                (-0.33)     (0.20)   (1.69)     (1.09
  aI and III refer to the following groups respectively: Household with no malehead, household with female not e
  bFigures in parentheses are t-values.
  'A "-" means that the hypothesis of homogeneity of response across groups could not be rejected and consequ
variable. The critical value of t (for large degrees of freedom) for a one-tailed test is 1.29 at 0.10 level of significan

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142                                                                          CHAKRAVARTHI NARASIMHAN

   Discussion. Examination of Table 2 reveals that the income effect is nonlinear. In
all product categories a1 and a2 have different signs. Only in three product categories
both 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 level
seems to fall as predicted by the theoretical model. For example, this critical income
level is $16,206 for toilet tissue. But the lack of significance of the income coefficient is
somewhat disappointing. The coefficient of FEMEMP has the wrong sign in three
product categories for both groups. For group one only in the case of one product
category (hair coloring) and for group three only in one category (frozen entree). In
nine of the 19 product categories, the coefficients are significantly negative. The
coefficient of EDUFEM in general has the correct sign. Only six out of 31 estimates
have the wrong sign (none significant) and 16 are significantly positive. The coefficient
of DUMCHD has the correct sign in 20 out of 27 different estimates and 13 of them
are significantly positive.
   Looking across at the three demographic groups, the model seems to predict best for
the third group (both husband and wife employed). This is probably understandable
given the greater time constraint a working couple will face in general than other
households, ceteris paribus. Overall, one can say that the evidence presented here is
strangely 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 the
assumptions underlying the model are too restrictive to yield meaningful results. Two
assumptions are particularly restrictive. 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 is
willing to put in the effort to clip and redeem them.
   When the household faces coupons from many product categories, it is not going to
spend the same amount of effort in each category. Frequency of purchase and the
expenditure in the product category are some important determinants.13 The QTY
variable used in (7) partially captures this but it is difficult to judge how well the
variation in coupon usage across product categories is captured by this variable. Given
panel data, it is impossible to check, for example, whether condition (ii) above was
satisfied. If there had been a systematic difference in the distribution of coupons across
demographic regions (for example, due to differences in product availability across
regions), assumption (ii) above is very restrictive. Again it is hard to speculate on the
effect of this violation on the results.
3.   Testing CouponingAcross Brands and Sizes
  In this model, predictions regarding couponing across brands in a product class and
across sizes within a brand are tested. The predictions were (1) higher priced brands
should offer higher savings per unit through coupons, and (2) across sizes, the savings
per unit must be negatively correlated with the size of the package. To test these
implications, only coupons from newspapers, magazines, mail and from prior pur-
chases are considered. Since coupons used in conjunction with other deals would
reflect savings more than the actual value mentioned on the coupon, such purchases
were deleted.
  Within each product category, a model relating the savings per unit, the price per
unit 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 one
coupon purchase was made by a typical household was 6.13.

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PRICE DISCRIMINATION THEORY OF COUPONS                                                                         143

  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 the jth size of the ith brand.
For each brand and size, the price and savings obtained were averaged across
consumers yielding one observation per brand per size. The above model was esti-
mated by specifying different functional forms for "f." Specifically, the following were
chosen.
  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 (see
equation (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 the
savings per unit for one percent change in price (or the size) is constant. In terms of

                                                    TABLE 3
                                      Price-Regressions Resultsfor the Model
                                          Ln(Si,)
                                              I
                                                  = ao + a,P,i  +
                                                           - d.1 a2Size,i
                                                                       I

                    Product                   N           R2               Price                  Size
            Toilet Tissues                   51           0.44            27.40                  6.86 x 10-5
                                                                           (5.22)               (0.44)
            Paper Towels                     74           0.51           - 0.1553             - 0.0096
                                                                        (- 2.68)             (-5.94)
            Stuffing/Dressing                24           0.60          - 40.34               - 0.0001
                                                                        (-0.99)              (-4.85)
            Shampoo                          70           0.58              2.625             - 0.0008
                                                                           (4.03)            (-4.39)
            Cooking/Salad Oil                79           0.29              2.33             - 0.0001
                                                                           (1.06)           (-3.92)
            Ready to Eat Cereal             196           0.55              7.248            - 0.0005
                                                                           (5.40)           (-7.63)
            Dog Food                        132           0.48            21.771             -2.09x   10-5
                                                                           (5.49)           (-6.33)
            Dry Mix Dinners                  71           0.72            65.52              -4.03 x 10-5
                                                                           (9.41)           (-3.24)
            Bars and Squares                  13          0.38a          -5.167              - 0.0002
                                                                        (-0.08)             (-1.71)
            Cake Mix                        149           0.07          - 44.37              -2.48 x 10-5
                                                                        (-1.46)             (-3.22)
            Cat Food                         57           0.65            30.626             -6.65 x 10-5
                                                                           (5.87)           (-4.65)
            Frozen Entrees                  191           0.30            36.51              - 3.19 x 10-5
                                                                           (4.37)           (-6.37)
            Gelatin                          72           0.40            33.296             -8.13 x 10-5
                                                                           (5.56)           (-2.37)
            Spaghetti Sauces                 65           0.55              8.047            - 0.0003
                                                                           (4.29)           (-3.39)
            Creme Rinse/                     25           0.63              1.47             - 0.0006
              Conditioners                                                 (2.20)              (1.68)
            Soups                           182           0.81            48.57              -7.7 x 10-5
                                                                         (13.78)            (-9.27)
            Other Mixes                      57           0.42           105.42              -2.44 x 10-5
                                                                           (2.14)           (-4.55)

           aThe regression was not overall significant at the 0.05 level.

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144                                                                            CHAKRAVARTHI NARASIMHAN

                                                        TABLE 4
                                 Summary of RegressionsAcross Brands and Sizes
                                                                    Price +                              Size -
                                                      Number of          Number of      Number of            Number of
              Model                                     Cases         Significant Cases   Cases           Significant Cases
 I 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 than
  Models I and III.14
    All the four models were estimated using the data on brands and sizes. In order to
  conserve space only the results from Model IV are presented in Table 3. In Table 4 the
  summary 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 the
  number of significant coefficients than Models I and III.
                                         6.     Managerial Implications

  Identifying Coupon Users
     The hypothesis developed in this paper makes predictions about who is more likely
  to 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 demographic
  variables (income, education, employment status, presence of children) were used as
  proxies to measure this cost. Since a manager is interested in targeting the coupon
  effort towards the users of coupons, understanding of the differential pattern of usage
  of coupons across consumers is valuable to the manager. Given different demographic
  profiles 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 the
  hypothesis developed in this paper.

  CouponingAcross Brands and Sizes
     According to the hypothesis developed in this paper, higher-priced brands should
  coupon at a higher level, and larger sizes should be couponed with greater cents-off
  value but at a lower savings per unit than smaller sizes. For example, the models used
  to test these implications (see equation (8)) can serve as a "market model." Given the
  price of its brand, a firm can use this model to predict the savings it should offer for
  different sizes of its product. However, there are two important considerations (not
  dealt with in the model development) a manager must be aware of. The first
  consideration concerns uncertainty regarding product quality. In the absence of
  perfect knowledge concerning a product's quality, a consumer incurs a cost for trying a
  product 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 COUPONS                                                                 145

enter the full price paid for the product. Therefore, one would expect new brands in a
product 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 market
model. If there are systematic differences in the demographic profile and consumption
pattern (of the product) of consumers across the different media, the manager has to
decide and make a judgmental revision on the cents-off values for coupons in different
media. This issue is further addressed below.

Couponingin Different Media
   Assume for simplicity that consumers can be grouped into two segments: Elastic
and Inelastic. Assume further that the elastic segment buys only with coupons and the
inelastic segment buys without a coupon. Let the demand by the elastic segment be X
which 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 reach
of the media vehicles, the demographic profile of the audience in the vehicle, etc. At
the optimum, the firm should equate the net marginal return (i.e., the incremental
contribution minus the marginal cost of coupon) across the different media. If we
assume that the couponing cost is a fixed cost then at the optimum:
               ax                                         - co-                   forall      i
                     (P-     Co- Si)=           a(P                   S)                          -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 this
model as a managerial tool is fraught with several difficulties. First, it may be
prohibitively costly for a firm to measure the demand functions. Second, adjusting the
price and savings could be so costly (a factor not considered in the above model) that
the firm has to adopt simplifying procedures. Third, the manager may be faced with a
constraint limiting the amount he can spend on coupons. Thus, while (9) may serve as
a descriptive model of firm behavior, it is a far cry from an operational model. To use
the underlying criteria (i.e., equating the marginal returns across media) the following
rule is suggested. Suppose the firm can obtain data on the distribution of coupons in
different media (this should be a straightforward task) and can obtain the change in
demand due to couponing. Then it is possible to estimate the response function across
media as:
                                              AX = f(Si,)                                              (10)
where AX is the change in the quantity demanded, Si the savings and DAis a vector of
demographic variables for the ith medium or segment. Relevant demographic variables
would be the wage rate of consumers, education, employment, status of the female
head of the household, etc. The manager can simply rank the media in terms of their
responsiveness due to couponing and decide on the savings to be offered. One way to
estimate (10) would be to use a controlled drop of couponing in different matched
segments.
Frequencyof Couponing
   If the price discrimination hypothesis is valid, then the suggestion would be that the
periodicity of couponing should equal the interpurchase time of the heavy users of
coupons. When alternative vehicles are available (magazines and newspapers), one can
stagger 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 certain
suggested guidelines for others. However, extensions of the basic model are necessary

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