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To Groupon or Not to
                                               Groupon: The Profitability of
                                               Deep Discounts
                                               Benjamin Edelman
                                               Sonia Jaffe
                                               Scott Duke Kominers




                                               Working Paper
                                               11-063




Copyright © 2010 by Benjamin Edelman, Sonia Jaffe, and Scott Duke Kominers
Working papers are in draft form. This working paper is distributed for purposes of comment and
discussion only. It may not be reproduced without permission of the copyright holder. Copies of working
papers are available from the author.
To Groupon or Not to Groupon:
                 The Profitability of Deep Discounts∗
        Benjamin Edelman†                Sonia Jaffe‡           Scott Duke Kominers§
                                     December 17, 2010


                                             Abstract
           We examine the profitability and implications of online discount vouchers, a
       new marketing tool that offers consumers large discounts when they prepay for
       participating merchants’ goods and services. Within a model of repeat experience
       good purchase, we examine two mechanisms by which a discount voucher service
       can benefit affiliated merchants: price discrimination and advertising. For vouchers
       to provide successful price discrimination, the valuations of consumers who have
       access to vouchers must systematically differ from—and be lower than—those of
       consumers who do not have access to vouchers. Offering vouchers is more profitable
       for merchants which are patient or relatively unknown, and for merchants with low
       marginal costs. Extensions to our model accommodate the possibilities of multiple
       voucher purchases and merchant price re-optimization.
       Keywords: voucher discounts, Groupon, experience goods, repeat purchase.




   ∗
     The authors appreciate the helpful comments and suggestions of Peter Coles, Clayton Featherstone,
Alvin Roth, and participants in the Harvard Workshop on Research in Behavior in Games and Markets.
Kominers gratefully acknowledges the support of a National Science Foundation Graduate Research Fel-
lowship, a Yahoo! Key Scientific Challenges Program Fellowship, and a Terence M. Considine Fellowship.
   †
     Harvard Business School; bedelman@hbs.edu.
   ‡
     Department of Economics, Harvard University; sjaffe@fas.harvard.edu.
   §
     Department of Economics, Harvard University, and Harvard Business School; skominers@hbs.edu.


                                                  1
1     Introduction
A variety of web sites now sell discount vouchers for services as diverse as restaurants,
skydiving, and museum visits. To consumers, discount vouchers promise substantial
savings—often 50% or more. To merchants, discount vouchers offer opportunities for
price discrimination as well as exposure to new customers and online “buzz.” Best known
among voucher vendors is Chicago-based Groupon, a two-year-old startup already touting
a ten-digit valuation and, purportedly, recently rejecting a $6 billion acquisition offer from
Google (Surowiecki (2010)). Hundreds of websites offer discount schemes similar to that
of Groupon.1
    The rise of discount vouchers presents many intriguing questions: Who is liable if a
merchant goes bankrupt after issuing vouchers but before performing its service? What
happens if a merchant simply refuses to provide the promised service? Since vouchers
entail prepayment of funds by consumers, do buyers enjoy the consumer protections many
states provide for gift certificates (such as delayed expiration and the right to a cash
refund when value is substantially used)? Must consumers using vouchers remit tax
on merchants’ ordinary menu prices, or is tax due only on the voucher-adjusted prices
consumers actually pay? What prevents consumers from printing multiple copies of a
discount voucher and redeeming those copies repeatedly?
    To merchants considering whether to offer discount vouchers, the most important
question is the basic economics of the offer: Can providing large voucher discounts actu-
ally be profitable? Voucher discounts are worthwhile if they predominantly attract new
customers who regularly return, paying full price on future visits. But if vouchers prompt
many long-time customers to use discounts, offering vouchers could reduce profits. For
most merchants, the effects of offering vouchers lie between these extremes: vouchers bring
in some new customers, but also provide discounts to some regular customers. In this
paper, we offer a model to explore how consumer demographics and offer details interact
to shape the profitability of voucher discounts.
    We illustrate two mechanisms by which a discount voucher service can benefit affil-
iated merchants. First, discount vouchers can facilitate price discrimination, allowing
merchants to offer distinct prices to different consumer populations. In order for voucher
offers to yield profitable price discrimination, the consumers who are offered the voucher
discounts must be more price-sensitive (with regards to participating merchants’ goods or
services) than the population as a whole. Second, discount vouchers can benefit merchants
through advertising, by informing consumers of a merchant’s existence. For these adver-
tising effects to be important, a merchant must begin with sufficiently low recognition
among prospective consumers.
    The remainder of this paper is organized as follows. We review the related literature
in Section 2. We present our model of voucher discounts in Section 3, exploring price
discrimination and advertising effects. In Section 4, we extend our model to consider the
possibility of consumers purchasing multiple vouchers and of merchants adjusting prices
   1
     Seeing these many sites, several companies now offer voucher aggregation. Yipit, one such company,
tracked over 200 different discount voucher services as of December, 2010.



                                                  2
in anticipation of voucher usage. Finally, in Section 5, we discuss implications of our
results for merchants and voucher services.


2       Related Literature
The recent proliferation of voucher discount services has garnered substantial press: a
multitude of newspaper articles and blog posts, and even a short feature in The New
Yorker (Surowiecki (2010)). However, voucher discounts have received little attention in
the academic literature.
    To our knowledge, the only prior academic study of online voucher discounts is the
survey work of Dholakia (2010). In that work, Dholakia (2010) polls businesses that of-
fered Groupon discounts. Echoing sentiments expressed in the popular press,2 Dholakia
(2010) finds mixed empirical results: some business owners speak glowingly of Groupon,
while others regret their voucher promotions. Unlike the survey approach of Dholakia
(2010), we seek to understand voucher discount economics on a theoretical level. Our
results indicate that voucher discounts are naturally good fits for certain types of mer-
chants, and poor fits for others; these theoretical observations can help us interpret the
range of reactions to Groupon and similar services.
    Although there is little academic work on voucher discounts, a well-established liter-
ature explores the advertising and pricing of experience goods, i.e. goods for which some
characteristics cannot be observed prior to consumption (Nelson (1970, 1974)).
    The parsimonious framework of Bils (1989), upon which we base our model, studies
how prices of experience goods respond to shifts in demand. Bils (1989) assumes that
consumers know their conditional valuations for a firm’s goods, but do not know whether
that firm’s goods “fit” until they have tried them.3 Analyzing overlapping consumer gen-
erations, Bils (1989) measures the tradeoff between attracting more first-time consumers
and extracting surplus from returning consumers.
    Meanwhile, much of the work on experience goods concerns issues of information asym-
metry: if a merchant’s quality is unknown to consumers but known to the merchant, then
advertising (Nelson (1974); Milgrom and Roberts (1986)), introductory offers (Shapiro
(1983); Milgrom and Roberts (1986); Bagwell (1990)), or high initial pricing (Bagwell
and Riordan (1991); Judd and Riordan (1994)) can provide signals of quality. Of this lit-
erature, the closest to our subject is the work on introductory offers. Voucher discounts, a
form of discounted initial pricing, may encourage consumers to try experience goods they
otherwise would have ignored. However, we identify this effect in a setting without asym-
metric information regarding merchant quality—consumer heterogeneity, not information
asymmetries, drives our main results.4 Additionally, our work differs from the classical
    2
     For example, Overly (2010) reports on Washington merchants’ mixed reactions to the LivingSocial
voucher service.
   3
     Firms know the distribution of consumer valuations and the (common) probability of fit.
   4
     Of course, our treatment of advertising includes a very coarse informational asymmetry: some con-
sumers are simply not aware of the merchant’s existence. However, conditional upon learning of the
merchant, consumers in our model receive more information than the merchant does about their valua-



                                                  3
literature on the advertisement of experience goods, as advertising in our setting serves
the purpose of awareness, rather than signaling.5
    A substantial literature has observed that selective discounting provides opportunities
for price discrimination. In the settings of Varian (1980), Jeuland and Narasimhan (1985),
and Narasimhan (1988), for example, merchants engage in sale pricing in order to attract
larger market segments.6 Similar results have been found to motivate the use of cents-off
coupons, certificates which promise discounts on repeat (rather than initial) purchases
(Cremer (1984); Narasimhan (1984)). We bring the insights of the literature on sale-
driven price discrimination to bear on voucher discounting—a new “sale” technology. Like
the price-theoretic literature which precedes our work, we find that price discrimination
depends crucially upon the presence of significant consumer heterogeneity.
    Although our work is theoretical, perhaps most central for an empirical comparison
of our work to its antecedents is the observation that the prior theoretical literature,
including the articles discussed above, has considered only marginal pricing decisions.
The previous work on experience goods and price discrimination does not consider deep
discounts of the magnitudes now offered by voucher services.


3     Model
Offering a voucher through Groupon has two potential advantages: price discrimination
and advertising. We present a simple model in which a continuum of consumers have
the opportunity to buy products from a single firm. The consumers are drawn from two
populations, one of which can be targeted by voucher discount offers. First, in Section 3.1,
we consider the case in which all consumers are aware of the firm and vouchers serve only
to facilitate price discrimination. Then, in Section 3.2, we introduce advertising effects.
We present comparative statics in Section 3.3.
    Our model has two periods, and the firm ex ante commits to a price p for both
periods. The firm and consumers share a common discount factor δ. Following the setup
of Bils (1989), consumers share a common probability r that the firm’s product is a “fit.”
Conditional on fit, the valuation of a consumer i for the firm’s offering is vi .
    A consumer i purchases in the first period if either the single-period value, rvi − p, or
tions. This is in sharp contrast to much of the previous work on experience goods, in which merchants
can in principle exploit private quality information in order to lead consumers to purchase undesirable
(or undesirably costly) products (e.g., Shapiro (1983); Bagwell (1987)).
   5
     In the classical theory of experience goods, advertising serves a “burning money” role. Merchants with
high-quality products can afford to advertise more than those with low-quality products can, as consumers
recognize this fact in equilibrium and flock to merchants who advertise heavily (Nelson (1974); Milgrom
and Roberts (1986)). In our model, advertising instead serves to inform consumers of a merchant’s
existence; these announcements are a central feature of the service voucher vendors promise.
   6
     In other models, heterogeneity in consumer search costs (e.g., Salop and Stiglitz (1977)) or reservation
values (e.g., Sobel (1984)) motivate sales. Bergemann and V¨lim¨ki (2006) study the pricing paths of
                                                                  a a
“mass-market” and “niche” experience goods, finding that initial sales are essential in niche markets to
guarantee traffic from new buyers.




                                                     4
the expected discounted future value, rvi − p + δr(vi − p), is positive, i.e. if

                            max{rvi − p, rvi − p + δr(vi − p)} ≥ 0.

For δ > 0, there is an informational value to visiting in the first period: if a consumer
learns that the firm’s product is a fit, then the consumer knows to return. As a result, all
consumers with values at least
                                                 1 + δr
                                        v(p) ≡          p>p
                                                 r + δr
purchase in the first period.
    To consider the effects of offering discounts to a subset of consumers, we assume there
are two distinct consumer populations. Proportion λ of consumers have valuations drawn
from a distribution with cumulative distribution function G, while proportion 1 − λ have
valuations drawn from a distribution with cumulative distribution function F . We denote
by V ≡ supp(F ) ∪ supp(G) the set of possible consumer valuations. We assume that
G(v) ≥ F (v) for all v ∈ V , i.e. that the valuations of consumers in the G population are
systematically lower than those of consumers in the F population.
    The firm faces demand

                             λ(1 − G(v(p))) + (1 − λ)(1 − F (v(p)))

in the first period, and fraction r of those consumers return in the second period. The
firm maximizes profits π given by

               π(p) ≡ (1 + δr)(λ(1 − G(v(p))) + (1 − λ)(1 − F (v(p))))(p − c),

where c is the firm’s marginal cost. The first-order condition of the firm’s optimization
problem is
                                              1 + δr ∗
   λ(1 − G(v ∗ )) + (1 − λ)(1 − F (v ∗ )) −          ((p − c)(λg(v ∗ ) + (1 − λ)f (v ∗ )) = 0      (1)
                                              r + δr
where p∗ is the optimal price and v ∗ ≡ v(p∗ ). We assume that the distribution of con-
sumers is such that profits are single-peaked, so that p∗ is uniquely defined.

3.1     Discount Vouchers
After setting its optimal price p∗ , the firm is given the opportunity to offer a discount
voucher.7 Only fraction γ of consumers in the G population have access to the discount
voucher system. (Consumers in the F population cannot buy vouchers.) Through the
voucher system, these consumers have the opportunity to purchase from the firm at a
discounted price αp in the first period. If α > r, then everyone who purchases in the first
period will return if the firm is a fit; the minimal valuation of consumers who purchase is
   7
    For now, we assume the firm did not consider the possibility of a voucher when setting its price. In
Section 4.2, we consider the possibility of re-optimization.

                                                  5
α + δr
                                      v (p) ≡
                                      ˜         p > v(p).
                                        r + δr
If α < r, then some consumers i with vi < p will purchase in the first period but will not
return (even if the firm is a fit). Those will be the consumers i for whom

                                rvi − αp > 0           and       vi < p.

   The voucher service retains proportion 1 − β of the voucher sales price, so the firm’s
revenue from each discount voucher is αβp∗ . Defining v ≡ v (p∗ ) and v ≡ α p∗ , we see that
                                                      ˜ ˜            ˆ r
offering discount vouchers yields the following change in profits:

  ∆π(p∗ ) =
            ((1 + rδ)(p∗ − c)(G(v ∗ ) − G(˜)) − (1 − αβ)p∗ (1 − G(˜)))
                                          v                       v         α > r,
       γλ               ∗                   ∗        ∗              ∗
                                                                                   (2)
            (p − c)(G(v ) − G(ˆ) + δr(G(v ) − G(p )) − (1 − αβ)p (1 − G(ˆ)) α < r.
                               v                                        v

    The first term of (2) represents the increased profits from the gain in consumers
G(v ∗ ) − G(˜); the second term measures profits lost by lowering the first-period price
            v
from p∗ to αβp∗ . Note that γ affects the magnitude of the change in profits, but not the
sign.8 The following result is therefore immediate.
Proposition 1. If it is profitable to offer the voucher discount to one consumer (randomly
drawn from the G population), then it is more profitable to offer the voucher discount to
all such consumers.
    When α = 1, introducing the discount voucher does not affect consumers’ purchase de-
cisions (v ∗ = v ), as consumers are offered no actual “discount.”9 Meanwhile, if consumers
               ˜
who use discount vouchers have the same distribution of valuations as other consumers
(F (v) = G(v) for all v), then the first- and second-order conditions show that the change
in profits is maximal at α = 1, so if α < 1 then vouchers are unprofitable. Conversely, if
the distributions of valuations are well behaved and G is to the left of F , then there is
some α < 1 such that offering a discounted price of αp ≥ αp can be profitable. This is
because the firm wants to offer a lower price to consumers from the G population; setting
α < 1 brings the firm’s price to the G population closer to the optimal price for that
population.
    We formalize these observations in the following proposition.
Proposition 2. If F (v) = G(v) for all v and min{α, β} < 1, then the introduction of a
discount voucher yields a decrease in profit. By contrast, if

                                     F (v) < G(v)            ∀v ∈ V,
   8
    By contrast, λ affects p∗ and can therefore affect the sign of ∆π(p∗ ).
   9
    If β < 1, then vouchers decrease firm profits when α = 1 because the voucher service keeps a cut
of revenue. But this case is degenerate: if—as we have assumed in this section—the only benefit of
vouchers is price discrimination, then certainly the firm will only use vouchers if they offer actual price
discrimination opportunities.

                                                   6
then there is some α < 1 such that offering a discount voucher with discounted price of
αp∗ ≥ αp∗ is profitable, so long as β is sufficiently close to 1.

   The conditions of Proposition 2 are sufficient for the result, but not necessary. Indeed,
whenever F and G are such that the firm’s optimal price for consumers from the G pop-
ulation is lower than the firm’s optimal price for the combined distribution of consumers,
there are some α, β < 1 for which the discount voucher is profitable.

3.2    Advertising Effects
In addition to offering consumers discounts, vouchers may also serve to inform consumers
about the existence and details of affiliated firms.
    We suppose that fraction κ of consumers know about a participating firm, but fraction
1 − κ do not. The uninformed consumers may have high valuations for the firm’s product
(conditional on learning about the firm), but they cannot purchase without first being
informed of the firm’s existence.
    If the probability of knowing about a firm is constant across consumers (independent
of valuations), then a firm’s profits absent an online voucher are given by πκ (p∗ ) ≡ κπ(p∗ );
the optimal price p∗ is unchanged from that defined by (1). In that case, if a firm offers
a voucher, then all consumers receiving the voucher learn of the firm’s existence. The
implied change in profits is:


  ∆πκ (p∗ ) =
                               (αβp∗ − c + δr(p∗ − c))(1 − G(˜))
                                                             v            α > r,
      κ∆π(p∗ ) + γλ(1 − κ)         ∗                       ∗          ∗
                                                                                 (3)
                               (αβp − c)(1 − G(ˆ)) + δr(p − c)(1 − G(p )) α < r.
                                                 v

    Because uninformed consumers do not purchase absent the voucher, no profits are
foregone by offering those consumers discounted pricing. Thus, so long as the discount is
not so big that losses in the first period outweigh gains in the second period, the second
term in (3) is positive. A sufficient (but not necessary) condition for this to occur is that
the firm’s per-voucher revenue is larger than its marginal cost:

                                         αβp∗ ≥ c.                                       (4)

This condition (4) is not sufficient for voucher profitability absent the advertising effect—
it does not guarantee that ∆π(p∗ ) is positive. However with advertising, as long as
condition (4) holds, vouchers are always profitable for “sufficiently unknown” firms as
there is always some κ > 0 such that the second term of (3) dominates the first.

Proposition 3. Suppose that αβp∗ ≥ c. Then, there exists some κ > 0 such that offering
                                                              ¯
vouchers is profitable whenever κ < κ.
                                   ¯

   Unlike in the pure price discrimination case, when vouchers provide advertising benefits
the effect of the difference between the distributions of valuations on the profitability of

                                             7
vouchers is ambiguous. For a fixed p∗ , the additional profits from advertising are higher
when the valuations drawn from G(v) are higher (smaller difference between distributions).
However, changing G(v) changes p∗ , so that the net effect of changing G depends on the
shapes of F and G.

3.3    Example Comparative Statics
To obtain closed-form comparative statics, we consider the case where valuations are
uniformly distributed in each population, but the population means vary:
                                                 
                     0 v < 0
                                                 0
                                                          v < −µ
             F (v) = v v ∈ [0, 1]         G(v) = v + µ v ∈ [−µ, 1 − µ]
                                                 
                       1 v > 1,                     1      v > 1 − µ.
                                                 

Here, µ parameterizes the difference between the two distributions: it measures the
amount that G(v) is “shifted to the left” relative to F (v).
   For F and G so defined, the optimal price p∗ is given by:

                                   1         (1 + δ)
                            p∗ =       c+            (1 − λµ)r .
                                   2        (1 + δr)

In this expression, (1 − λµ)r = ((1 − λ) · 1 + λ · (1 − µ))r is the weighted average of
                                                                                        1+δ
the maximal valuations of the two consumer populations. The multiplicative factor 1+δr
represents the premium consumers are willing to pay because of the information value of
purchasing in the first period.
    For simplicity, we consider the case in which β = 1 (the voucher vendor charges no fee),
α > r (the proportion of the price paid with the voucher is greater than the probability of
fit), and κ = 1 (there are no advertising effects). With these assumptions, the minimum
difference between the distributions necessary for a discount voucher to be profitable,
denoted µ, is given by

                                (1 − α)(r(1 + δ) + c(1 + δr))
                       µ=                                         .
                            (1 + δ)r(2(1 + δr(1 − λ)) − λ(1 + α))

The comparative statics of µ are intuitive.

   • Patience: The change in firm profits increases in δ, the discount factor, while µ
     decreases in δ. This is consistent with the interpretation that discount vouchers let
     a firm accept losses (decreased profits) in the short run in exchange for increased
     profits in the future, a benefit more valuable to patient firms.

   • Costs: Increased marginal costs lower the change in profits and raise the thresh-
     old for profitability. Since offering a discount voucher increases quantity sold and
     decreases per-unit price, it is more profitable for firms with lower marginal costs.



                                               8
• Population share: If many consumers come from the low-value population (i.e. if λ
      is high), then it is difficult for the voucher service to be profitable for firms. When
      λ is high, voucher users’ valuations significantly affect the base price p∗ so that, for
      a given α, price discrimination is less profitable.

    • Discounted price: Although the effect of α on the change in profits is ambiguous,
      increasing α unambiguously decreases the threshold µ. This is intuitive, as the less
      of a price decrease the voucher represents, the less heterogeneity across populations
      is required in order for the discounted voucher to be profitable.

    • Probability of fit: Like with α, the effect of a higher probability of fit r on the
      change in profits is unclear, but increasing r unambiguously lowers µ.


4     Extensions
4.1    The Possibility that Consumers Might Purchase Multiple
       Vouchers
So far we have assumed that each consumer can purchase at most one voucher, a re-
striction which lets us model the discounted price αp∗ as being available only in the first
period. However, if consumers can buy multiple discount vouchers, then they can enjoy
the discounted price in both periods.
    If all discount vouchers must be purchased in the first period (as is the case with
Groupon and similar voucher vendors), then a consumer i with valuation vi only finds it
profitable to buy a second voucher if the expected value of second-period consumption is
greater than the present voucher cost, that is, if

                                        δrvi ≥ αp∗ .

Consumers with valuations vi ∈ [ α p, rδ p] buy a discount voucher and do not return.
                                     r
                                         α
                        α
Consumers with vi ∈ [ rδ p, p] only return if they can buy two vouchers (and the firm is a
match). Consumers with vi > p return whenever the firm’s product is a match.
    The profits in the first period are the same as when consumers only purchase a single
discount voucher. However, if consumers are able to purchase multiple discount vouchers,
then some consumers who would normally return at full price instead return with a second
voucher. It follows that allowing consumers to purchase multiple discount vouchers is only
profitable if the firm seeks to offer starkly different prices to the two consumer populations.

Proposition 4. Suppose that there exist α and β such that it is profitable, relative to
the possibility of allowing each consumer only one voucher purchase, for a firm to allow
consumers to purchase two vouchers. Then, there exist α and β with α β < αβ such
that it is profitable to offer a single voucher at rates α and β , but allowing consumers to
purchase an additional voucher at those rates decreases profits.



                                             9
The profits from allowing the purchase of a second voucher are negative at α = 0, so
if they are positive for some α and β they must cross zero at intermediate values of α , β .
Since the profits from allowing the second voucher are lower than the profits from initially
offering a voucher, it will still be profitable to offer a single voucher at those intermediate
values.

4.2    The Possibility that the Firm Might Re-optimize Its Prices
If the firm can adjust its posted prices to account for the presence of discount vouchers,
then the firm will re-optimize to set a new price p∗ maximizing
                                                 ˜

         γλ(αβ p∗ − c + δr(˜∗ − c))(1 − G(˜(˜∗ )))
               ˜           p              v p
                      + (1 + δr) λ(1 − γ)(1 − G(v(p))) + (1 − λ)(1 − F (v(p))) .

Pricing at p∗ raises the profits from a discount voucher promotion and lowers the required
           ˜
minimum difference between distributions required for voucher profitability. The prospect
of adjusting prices places new importance on γ: the sign of the change in profits now
depends on γ because the proportion of consumers receiving the discounted price affects
the firm’s re-optimization.
    Even with the opportunity of price re-optimization, discount vouchers are not prof-
itable when the two populations are identical (F (v) = G(v) for all v). Under the assump-
tions of Section 3.3, for λ sufficiently large, µ is decreasing in γ. In this case the firm
would prefer to set different prices for the two consumer populations, it can do this more
effectively when more of the G consumers may acquire vouchers (i.e. when γ is large).
When γ is low, the firm is limited in the extent to which it can raise the price faced by
consumers from the F population because many G-population consumers face the same
price.


5     Discussion
5.1    Implications for Merchants
Our results offer practical advice for firms considering whether to offer discount vouchers.
Our discussion in Section 4.1 indicates that a firm might want to disallow purchase of
multiple discount vouchers. But as argued by Friedman and Resnick (2001), firms face
substantial practical difficulties in implementing this restriction. What stops consumers
from creating multiple accounts and purchasing one voucher through each such account?
    To date, it appears that few firms have adjusted prices in anticipation of many con-
sumers using discount vouchers. However, we did notice a sharp price increases at one
local restaurant that offers frequent discounts through discount voucher services. Visiting
this restaurant, our experience has been that at least half of consumers come bearing dis-
count vouchers. Vouchers have noticeably increased the restaurant’s traffic, yet at prices
(net of voucher services’ fees, even bearing in mind the price increase) that surely reduce
the restaurant’s margins. We doubt the restaurant would have enjoyed a similar traffic

                                            10
increase had it simply lowered its prices 25%; clearly vouchers play an important role in
making consumers aware of discounts. Yet with voucher services retaining as much as
half the consumer’s prepayment, heavy reliance on discount voucher marketing comes at
a significant cost.
    Firms would do well to assess whether their voucher-using customers have already
visited and previously paid full price. Firms should also measure how many voucher-
using customers later come back without vouchers. In principle, credit card systems
could track this information with little harm to customer privacy or data security. But
in practice, most firms currently lack the tools or expertise to run such analyses.

5.2     The Future of Voucher Services
Our model reveals that a discount voucher service is more likely to be profitable for af-
filiated firms, all else equal, if customers using that service have valuations substantially
different from (and in particular, below) those of other customers. But notice the difficulty
as the voucher service grows: As more consumers use vouchers, voucher-users necessarily
come to resemble average consumers, so the use of a voucher comes to convey less infor-
mation about a consumer’s valuation. Thus, as voucher services grow, their affiliates will
have to rely on voucher advertising rather than voucher price discrimination. Current
voucher services’ profits and recent growth may therefore not be good predictors of those
services’ future values.
    Meanwhile, we are struck by the large fees that leading discount voucher services cur-
rently charge to participating firms. Groupon charges 50% of voucher price: if a restaurant
offers a $20 voucher for $40 of food, Groupon retains $10—a large fee relative to Groupon’s
marginal costs of voucher provision (Groupon (2010)). As our results in Section 3.1 indi-
cate, such large fees may impede firms’ usage of discount vouchers. However, competition
among discount voucher services may drive down these fees.10,11
    Recently, Groupon has begun to unbundle some of its services. As of December, 2010,
Groupon is charging just 10% to a firm which only wants its offer to appear following
user searches, while continuing to require the 50% fee for Groupon’s traditional service of
featuring a merchant in a daily email to all consumers in a given city (Groupon (2010)).
On one view, the 10% fee might look like a bargain to firms—10% is certainly far less
than 50%. However, if Groupon’s low-priced service only gives a firm access to consumers
who already know about that firm, then it provides no advertising opportunities—only
price discrimination.




  10
     Small voucher services may charge fees as low as 10%. Yet small voucher services cannot provide
substantial advertising benefits. As a result, despite lower fees at small voucher services, many firms
prefer the larger services.
  11
     Another issue of competition in the voucher market is the possibility that a well-positioned competitor
(such as Google, Facebook, or Yelp) could develop a similar service and promote that service to its existing
users.


                                                    11
References
Bagwell, K. (1987). Introductory price as a signal of cost in a model of repeat business.
  Review of Economic Studies 54 (3), 365–384.

Bagwell, K. (1990). Informational product differentiation as a barrier to entry. Interna-
  tional Journal of Industrial Organization 8 (2), 207–223.

Bagwell, K. and M. H. Riordan (1991). High and declining prices signal product quality.
  American Economic Review 81 (1), 224–239.

Bergemann, D. and J. V¨lim¨ki (2006). Dynamic pricing of new experience goods. Journal
                       a a
  of Political Economy 114 (4), 713–743.

Bils, M. (1989). Pricing in a customer market. Quarterly Journal of Economics 104 (4),
  699–718.

Cremer, J. (1984). On the economics of repeat buying.           RAND Journal of Eco-
  nomics 15 (3), 396–403.

Dholakia, U. M. (2010). How effective are Groupon promotions for businesses? Mimeo,
 Rice University.

Friedman, E. and P. Resnick (2001). The social cost of cheap pseudonyms. Journal of
  Economics and Management Strategy 10 (2), 173–199.

Groupon (2010, December 15).      Run your own deals with Groupon stores.
  http://www.groupon.com/merchants/welcome.

Jeuland, A. P. and C. Narasimhan (1985). Dealing-temporary price cuts-by seller as a
  buyer discrimination mechanism. Journal of Business 58 (3), 295–308.

Judd, K. L. and M. H. Riordan (1994). Price and quality in a new product monopoly.
  Review of Economic Studies 61 (4), 773–789.

Milgrom, P. and J. Roberts (1986). Price and advertising signals of product quality.
 Journal of Political Economy 94 (4), 796–821.

Narasimhan, C. (1984). A price discrimination theory of coupons. Marketing Science 3 (2),
  128–147.

Narasimhan, C. (1988). Competitive promotional strategies. Journal of Business 61 (4),
  427–449.

Nelson, P. (1970). Information and consumer behavior.        Journal of Political Econ-
  omy 78 (2), 311–329.

Nelson, P. (1974). Advertising as information. Journal of Political Economy 82 (4), 729–
  754.

                                           12
Overly, S. (2010, December 6). LivingSocial deals draw mixed merchant reactions. Wash-
 ington Post.

Salop, S. and J. Stiglitz (1977). Bargains and ripoffs: A model of monopolistically com-
  petitive price dispersion. Review of Economic Studies 44 (3), 493–510.

Shapiro, C. (1983). Optimal pricing of experience goods. Bell Journal of Economics 14 (2),
  497–507.

Sobel, J. (1984). The timing of sales. Review of Economic Studies 51 (3), 353–368.

Surowiecki, J. (2010, December 20). Groupon clipping. The New Yorker , 46.

Varian, H. R. (1980). A model of sales. American Economic Review 70 (4), 651–659.




                                           13

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To Groupon Or Not

  • 1. To Groupon or Not to Groupon: The Profitability of Deep Discounts Benjamin Edelman Sonia Jaffe Scott Duke Kominers Working Paper 11-063 Copyright © 2010 by Benjamin Edelman, Sonia Jaffe, and Scott Duke Kominers Working papers are in draft form. This working paper is distributed for purposes of comment and discussion only. It may not be reproduced without permission of the copyright holder. Copies of working papers are available from the author.
  • 2. To Groupon or Not to Groupon: The Profitability of Deep Discounts∗ Benjamin Edelman† Sonia Jaffe‡ Scott Duke Kominers§ December 17, 2010 Abstract We examine the profitability and implications of online discount vouchers, a new marketing tool that offers consumers large discounts when they prepay for participating merchants’ goods and services. Within a model of repeat experience good purchase, we examine two mechanisms by which a discount voucher service can benefit affiliated merchants: price discrimination and advertising. For vouchers to provide successful price discrimination, the valuations of consumers who have access to vouchers must systematically differ from—and be lower than—those of consumers who do not have access to vouchers. Offering vouchers is more profitable for merchants which are patient or relatively unknown, and for merchants with low marginal costs. Extensions to our model accommodate the possibilities of multiple voucher purchases and merchant price re-optimization. Keywords: voucher discounts, Groupon, experience goods, repeat purchase. ∗ The authors appreciate the helpful comments and suggestions of Peter Coles, Clayton Featherstone, Alvin Roth, and participants in the Harvard Workshop on Research in Behavior in Games and Markets. Kominers gratefully acknowledges the support of a National Science Foundation Graduate Research Fel- lowship, a Yahoo! Key Scientific Challenges Program Fellowship, and a Terence M. Considine Fellowship. † Harvard Business School; bedelman@hbs.edu. ‡ Department of Economics, Harvard University; sjaffe@fas.harvard.edu. § Department of Economics, Harvard University, and Harvard Business School; skominers@hbs.edu. 1
  • 3. 1 Introduction A variety of web sites now sell discount vouchers for services as diverse as restaurants, skydiving, and museum visits. To consumers, discount vouchers promise substantial savings—often 50% or more. To merchants, discount vouchers offer opportunities for price discrimination as well as exposure to new customers and online “buzz.” Best known among voucher vendors is Chicago-based Groupon, a two-year-old startup already touting a ten-digit valuation and, purportedly, recently rejecting a $6 billion acquisition offer from Google (Surowiecki (2010)). Hundreds of websites offer discount schemes similar to that of Groupon.1 The rise of discount vouchers presents many intriguing questions: Who is liable if a merchant goes bankrupt after issuing vouchers but before performing its service? What happens if a merchant simply refuses to provide the promised service? Since vouchers entail prepayment of funds by consumers, do buyers enjoy the consumer protections many states provide for gift certificates (such as delayed expiration and the right to a cash refund when value is substantially used)? Must consumers using vouchers remit tax on merchants’ ordinary menu prices, or is tax due only on the voucher-adjusted prices consumers actually pay? What prevents consumers from printing multiple copies of a discount voucher and redeeming those copies repeatedly? To merchants considering whether to offer discount vouchers, the most important question is the basic economics of the offer: Can providing large voucher discounts actu- ally be profitable? Voucher discounts are worthwhile if they predominantly attract new customers who regularly return, paying full price on future visits. But if vouchers prompt many long-time customers to use discounts, offering vouchers could reduce profits. For most merchants, the effects of offering vouchers lie between these extremes: vouchers bring in some new customers, but also provide discounts to some regular customers. In this paper, we offer a model to explore how consumer demographics and offer details interact to shape the profitability of voucher discounts. We illustrate two mechanisms by which a discount voucher service can benefit affil- iated merchants. First, discount vouchers can facilitate price discrimination, allowing merchants to offer distinct prices to different consumer populations. In order for voucher offers to yield profitable price discrimination, the consumers who are offered the voucher discounts must be more price-sensitive (with regards to participating merchants’ goods or services) than the population as a whole. Second, discount vouchers can benefit merchants through advertising, by informing consumers of a merchant’s existence. For these adver- tising effects to be important, a merchant must begin with sufficiently low recognition among prospective consumers. The remainder of this paper is organized as follows. We review the related literature in Section 2. We present our model of voucher discounts in Section 3, exploring price discrimination and advertising effects. In Section 4, we extend our model to consider the possibility of consumers purchasing multiple vouchers and of merchants adjusting prices 1 Seeing these many sites, several companies now offer voucher aggregation. Yipit, one such company, tracked over 200 different discount voucher services as of December, 2010. 2
  • 4. in anticipation of voucher usage. Finally, in Section 5, we discuss implications of our results for merchants and voucher services. 2 Related Literature The recent proliferation of voucher discount services has garnered substantial press: a multitude of newspaper articles and blog posts, and even a short feature in The New Yorker (Surowiecki (2010)). However, voucher discounts have received little attention in the academic literature. To our knowledge, the only prior academic study of online voucher discounts is the survey work of Dholakia (2010). In that work, Dholakia (2010) polls businesses that of- fered Groupon discounts. Echoing sentiments expressed in the popular press,2 Dholakia (2010) finds mixed empirical results: some business owners speak glowingly of Groupon, while others regret their voucher promotions. Unlike the survey approach of Dholakia (2010), we seek to understand voucher discount economics on a theoretical level. Our results indicate that voucher discounts are naturally good fits for certain types of mer- chants, and poor fits for others; these theoretical observations can help us interpret the range of reactions to Groupon and similar services. Although there is little academic work on voucher discounts, a well-established liter- ature explores the advertising and pricing of experience goods, i.e. goods for which some characteristics cannot be observed prior to consumption (Nelson (1970, 1974)). The parsimonious framework of Bils (1989), upon which we base our model, studies how prices of experience goods respond to shifts in demand. Bils (1989) assumes that consumers know their conditional valuations for a firm’s goods, but do not know whether that firm’s goods “fit” until they have tried them.3 Analyzing overlapping consumer gen- erations, Bils (1989) measures the tradeoff between attracting more first-time consumers and extracting surplus from returning consumers. Meanwhile, much of the work on experience goods concerns issues of information asym- metry: if a merchant’s quality is unknown to consumers but known to the merchant, then advertising (Nelson (1974); Milgrom and Roberts (1986)), introductory offers (Shapiro (1983); Milgrom and Roberts (1986); Bagwell (1990)), or high initial pricing (Bagwell and Riordan (1991); Judd and Riordan (1994)) can provide signals of quality. Of this lit- erature, the closest to our subject is the work on introductory offers. Voucher discounts, a form of discounted initial pricing, may encourage consumers to try experience goods they otherwise would have ignored. However, we identify this effect in a setting without asym- metric information regarding merchant quality—consumer heterogeneity, not information asymmetries, drives our main results.4 Additionally, our work differs from the classical 2 For example, Overly (2010) reports on Washington merchants’ mixed reactions to the LivingSocial voucher service. 3 Firms know the distribution of consumer valuations and the (common) probability of fit. 4 Of course, our treatment of advertising includes a very coarse informational asymmetry: some con- sumers are simply not aware of the merchant’s existence. However, conditional upon learning of the merchant, consumers in our model receive more information than the merchant does about their valua- 3
  • 5. literature on the advertisement of experience goods, as advertising in our setting serves the purpose of awareness, rather than signaling.5 A substantial literature has observed that selective discounting provides opportunities for price discrimination. In the settings of Varian (1980), Jeuland and Narasimhan (1985), and Narasimhan (1988), for example, merchants engage in sale pricing in order to attract larger market segments.6 Similar results have been found to motivate the use of cents-off coupons, certificates which promise discounts on repeat (rather than initial) purchases (Cremer (1984); Narasimhan (1984)). We bring the insights of the literature on sale- driven price discrimination to bear on voucher discounting—a new “sale” technology. Like the price-theoretic literature which precedes our work, we find that price discrimination depends crucially upon the presence of significant consumer heterogeneity. Although our work is theoretical, perhaps most central for an empirical comparison of our work to its antecedents is the observation that the prior theoretical literature, including the articles discussed above, has considered only marginal pricing decisions. The previous work on experience goods and price discrimination does not consider deep discounts of the magnitudes now offered by voucher services. 3 Model Offering a voucher through Groupon has two potential advantages: price discrimination and advertising. We present a simple model in which a continuum of consumers have the opportunity to buy products from a single firm. The consumers are drawn from two populations, one of which can be targeted by voucher discount offers. First, in Section 3.1, we consider the case in which all consumers are aware of the firm and vouchers serve only to facilitate price discrimination. Then, in Section 3.2, we introduce advertising effects. We present comparative statics in Section 3.3. Our model has two periods, and the firm ex ante commits to a price p for both periods. The firm and consumers share a common discount factor δ. Following the setup of Bils (1989), consumers share a common probability r that the firm’s product is a “fit.” Conditional on fit, the valuation of a consumer i for the firm’s offering is vi . A consumer i purchases in the first period if either the single-period value, rvi − p, or tions. This is in sharp contrast to much of the previous work on experience goods, in which merchants can in principle exploit private quality information in order to lead consumers to purchase undesirable (or undesirably costly) products (e.g., Shapiro (1983); Bagwell (1987)). 5 In the classical theory of experience goods, advertising serves a “burning money” role. Merchants with high-quality products can afford to advertise more than those with low-quality products can, as consumers recognize this fact in equilibrium and flock to merchants who advertise heavily (Nelson (1974); Milgrom and Roberts (1986)). In our model, advertising instead serves to inform consumers of a merchant’s existence; these announcements are a central feature of the service voucher vendors promise. 6 In other models, heterogeneity in consumer search costs (e.g., Salop and Stiglitz (1977)) or reservation values (e.g., Sobel (1984)) motivate sales. Bergemann and V¨lim¨ki (2006) study the pricing paths of a a “mass-market” and “niche” experience goods, finding that initial sales are essential in niche markets to guarantee traffic from new buyers. 4
  • 6. the expected discounted future value, rvi − p + δr(vi − p), is positive, i.e. if max{rvi − p, rvi − p + δr(vi − p)} ≥ 0. For δ > 0, there is an informational value to visiting in the first period: if a consumer learns that the firm’s product is a fit, then the consumer knows to return. As a result, all consumers with values at least 1 + δr v(p) ≡ p>p r + δr purchase in the first period. To consider the effects of offering discounts to a subset of consumers, we assume there are two distinct consumer populations. Proportion λ of consumers have valuations drawn from a distribution with cumulative distribution function G, while proportion 1 − λ have valuations drawn from a distribution with cumulative distribution function F . We denote by V ≡ supp(F ) ∪ supp(G) the set of possible consumer valuations. We assume that G(v) ≥ F (v) for all v ∈ V , i.e. that the valuations of consumers in the G population are systematically lower than those of consumers in the F population. The firm faces demand λ(1 − G(v(p))) + (1 − λ)(1 − F (v(p))) in the first period, and fraction r of those consumers return in the second period. The firm maximizes profits π given by π(p) ≡ (1 + δr)(λ(1 − G(v(p))) + (1 − λ)(1 − F (v(p))))(p − c), where c is the firm’s marginal cost. The first-order condition of the firm’s optimization problem is 1 + δr ∗ λ(1 − G(v ∗ )) + (1 − λ)(1 − F (v ∗ )) − ((p − c)(λg(v ∗ ) + (1 − λ)f (v ∗ )) = 0 (1) r + δr where p∗ is the optimal price and v ∗ ≡ v(p∗ ). We assume that the distribution of con- sumers is such that profits are single-peaked, so that p∗ is uniquely defined. 3.1 Discount Vouchers After setting its optimal price p∗ , the firm is given the opportunity to offer a discount voucher.7 Only fraction γ of consumers in the G population have access to the discount voucher system. (Consumers in the F population cannot buy vouchers.) Through the voucher system, these consumers have the opportunity to purchase from the firm at a discounted price αp in the first period. If α > r, then everyone who purchases in the first period will return if the firm is a fit; the minimal valuation of consumers who purchase is 7 For now, we assume the firm did not consider the possibility of a voucher when setting its price. In Section 4.2, we consider the possibility of re-optimization. 5
  • 7. α + δr v (p) ≡ ˜ p > v(p). r + δr If α < r, then some consumers i with vi < p will purchase in the first period but will not return (even if the firm is a fit). Those will be the consumers i for whom rvi − αp > 0 and vi < p. The voucher service retains proportion 1 − β of the voucher sales price, so the firm’s revenue from each discount voucher is αβp∗ . Defining v ≡ v (p∗ ) and v ≡ α p∗ , we see that ˜ ˜ ˆ r offering discount vouchers yields the following change in profits: ∆π(p∗ ) = ((1 + rδ)(p∗ − c)(G(v ∗ ) − G(˜)) − (1 − αβ)p∗ (1 − G(˜))) v v α > r, γλ ∗ ∗ ∗ ∗ (2) (p − c)(G(v ) − G(ˆ) + δr(G(v ) − G(p )) − (1 − αβ)p (1 − G(ˆ)) α < r. v v The first term of (2) represents the increased profits from the gain in consumers G(v ∗ ) − G(˜); the second term measures profits lost by lowering the first-period price v from p∗ to αβp∗ . Note that γ affects the magnitude of the change in profits, but not the sign.8 The following result is therefore immediate. Proposition 1. If it is profitable to offer the voucher discount to one consumer (randomly drawn from the G population), then it is more profitable to offer the voucher discount to all such consumers. When α = 1, introducing the discount voucher does not affect consumers’ purchase de- cisions (v ∗ = v ), as consumers are offered no actual “discount.”9 Meanwhile, if consumers ˜ who use discount vouchers have the same distribution of valuations as other consumers (F (v) = G(v) for all v), then the first- and second-order conditions show that the change in profits is maximal at α = 1, so if α < 1 then vouchers are unprofitable. Conversely, if the distributions of valuations are well behaved and G is to the left of F , then there is some α < 1 such that offering a discounted price of αp ≥ αp can be profitable. This is because the firm wants to offer a lower price to consumers from the G population; setting α < 1 brings the firm’s price to the G population closer to the optimal price for that population. We formalize these observations in the following proposition. Proposition 2. If F (v) = G(v) for all v and min{α, β} < 1, then the introduction of a discount voucher yields a decrease in profit. By contrast, if F (v) < G(v) ∀v ∈ V, 8 By contrast, λ affects p∗ and can therefore affect the sign of ∆π(p∗ ). 9 If β < 1, then vouchers decrease firm profits when α = 1 because the voucher service keeps a cut of revenue. But this case is degenerate: if—as we have assumed in this section—the only benefit of vouchers is price discrimination, then certainly the firm will only use vouchers if they offer actual price discrimination opportunities. 6
  • 8. then there is some α < 1 such that offering a discount voucher with discounted price of αp∗ ≥ αp∗ is profitable, so long as β is sufficiently close to 1. The conditions of Proposition 2 are sufficient for the result, but not necessary. Indeed, whenever F and G are such that the firm’s optimal price for consumers from the G pop- ulation is lower than the firm’s optimal price for the combined distribution of consumers, there are some α, β < 1 for which the discount voucher is profitable. 3.2 Advertising Effects In addition to offering consumers discounts, vouchers may also serve to inform consumers about the existence and details of affiliated firms. We suppose that fraction κ of consumers know about a participating firm, but fraction 1 − κ do not. The uninformed consumers may have high valuations for the firm’s product (conditional on learning about the firm), but they cannot purchase without first being informed of the firm’s existence. If the probability of knowing about a firm is constant across consumers (independent of valuations), then a firm’s profits absent an online voucher are given by πκ (p∗ ) ≡ κπ(p∗ ); the optimal price p∗ is unchanged from that defined by (1). In that case, if a firm offers a voucher, then all consumers receiving the voucher learn of the firm’s existence. The implied change in profits is: ∆πκ (p∗ ) = (αβp∗ − c + δr(p∗ − c))(1 − G(˜)) v α > r, κ∆π(p∗ ) + γλ(1 − κ) ∗ ∗ ∗ (3) (αβp − c)(1 − G(ˆ)) + δr(p − c)(1 − G(p )) α < r. v Because uninformed consumers do not purchase absent the voucher, no profits are foregone by offering those consumers discounted pricing. Thus, so long as the discount is not so big that losses in the first period outweigh gains in the second period, the second term in (3) is positive. A sufficient (but not necessary) condition for this to occur is that the firm’s per-voucher revenue is larger than its marginal cost: αβp∗ ≥ c. (4) This condition (4) is not sufficient for voucher profitability absent the advertising effect— it does not guarantee that ∆π(p∗ ) is positive. However with advertising, as long as condition (4) holds, vouchers are always profitable for “sufficiently unknown” firms as there is always some κ > 0 such that the second term of (3) dominates the first. Proposition 3. Suppose that αβp∗ ≥ c. Then, there exists some κ > 0 such that offering ¯ vouchers is profitable whenever κ < κ. ¯ Unlike in the pure price discrimination case, when vouchers provide advertising benefits the effect of the difference between the distributions of valuations on the profitability of 7
  • 9. vouchers is ambiguous. For a fixed p∗ , the additional profits from advertising are higher when the valuations drawn from G(v) are higher (smaller difference between distributions). However, changing G(v) changes p∗ , so that the net effect of changing G depends on the shapes of F and G. 3.3 Example Comparative Statics To obtain closed-form comparative statics, we consider the case where valuations are uniformly distributed in each population, but the population means vary:   0 v < 0  0  v < −µ F (v) = v v ∈ [0, 1] G(v) = v + µ v ∈ [−µ, 1 − µ]   1 v > 1, 1 v > 1 − µ.   Here, µ parameterizes the difference between the two distributions: it measures the amount that G(v) is “shifted to the left” relative to F (v). For F and G so defined, the optimal price p∗ is given by: 1 (1 + δ) p∗ = c+ (1 − λµ)r . 2 (1 + δr) In this expression, (1 − λµ)r = ((1 − λ) · 1 + λ · (1 − µ))r is the weighted average of 1+δ the maximal valuations of the two consumer populations. The multiplicative factor 1+δr represents the premium consumers are willing to pay because of the information value of purchasing in the first period. For simplicity, we consider the case in which β = 1 (the voucher vendor charges no fee), α > r (the proportion of the price paid with the voucher is greater than the probability of fit), and κ = 1 (there are no advertising effects). With these assumptions, the minimum difference between the distributions necessary for a discount voucher to be profitable, denoted µ, is given by (1 − α)(r(1 + δ) + c(1 + δr)) µ= . (1 + δ)r(2(1 + δr(1 − λ)) − λ(1 + α)) The comparative statics of µ are intuitive. • Patience: The change in firm profits increases in δ, the discount factor, while µ decreases in δ. This is consistent with the interpretation that discount vouchers let a firm accept losses (decreased profits) in the short run in exchange for increased profits in the future, a benefit more valuable to patient firms. • Costs: Increased marginal costs lower the change in profits and raise the thresh- old for profitability. Since offering a discount voucher increases quantity sold and decreases per-unit price, it is more profitable for firms with lower marginal costs. 8
  • 10. • Population share: If many consumers come from the low-value population (i.e. if λ is high), then it is difficult for the voucher service to be profitable for firms. When λ is high, voucher users’ valuations significantly affect the base price p∗ so that, for a given α, price discrimination is less profitable. • Discounted price: Although the effect of α on the change in profits is ambiguous, increasing α unambiguously decreases the threshold µ. This is intuitive, as the less of a price decrease the voucher represents, the less heterogeneity across populations is required in order for the discounted voucher to be profitable. • Probability of fit: Like with α, the effect of a higher probability of fit r on the change in profits is unclear, but increasing r unambiguously lowers µ. 4 Extensions 4.1 The Possibility that Consumers Might Purchase Multiple Vouchers So far we have assumed that each consumer can purchase at most one voucher, a re- striction which lets us model the discounted price αp∗ as being available only in the first period. However, if consumers can buy multiple discount vouchers, then they can enjoy the discounted price in both periods. If all discount vouchers must be purchased in the first period (as is the case with Groupon and similar voucher vendors), then a consumer i with valuation vi only finds it profitable to buy a second voucher if the expected value of second-period consumption is greater than the present voucher cost, that is, if δrvi ≥ αp∗ . Consumers with valuations vi ∈ [ α p, rδ p] buy a discount voucher and do not return. r α α Consumers with vi ∈ [ rδ p, p] only return if they can buy two vouchers (and the firm is a match). Consumers with vi > p return whenever the firm’s product is a match. The profits in the first period are the same as when consumers only purchase a single discount voucher. However, if consumers are able to purchase multiple discount vouchers, then some consumers who would normally return at full price instead return with a second voucher. It follows that allowing consumers to purchase multiple discount vouchers is only profitable if the firm seeks to offer starkly different prices to the two consumer populations. Proposition 4. Suppose that there exist α and β such that it is profitable, relative to the possibility of allowing each consumer only one voucher purchase, for a firm to allow consumers to purchase two vouchers. Then, there exist α and β with α β < αβ such that it is profitable to offer a single voucher at rates α and β , but allowing consumers to purchase an additional voucher at those rates decreases profits. 9
  • 11. The profits from allowing the purchase of a second voucher are negative at α = 0, so if they are positive for some α and β they must cross zero at intermediate values of α , β . Since the profits from allowing the second voucher are lower than the profits from initially offering a voucher, it will still be profitable to offer a single voucher at those intermediate values. 4.2 The Possibility that the Firm Might Re-optimize Its Prices If the firm can adjust its posted prices to account for the presence of discount vouchers, then the firm will re-optimize to set a new price p∗ maximizing ˜ γλ(αβ p∗ − c + δr(˜∗ − c))(1 − G(˜(˜∗ ))) ˜ p v p + (1 + δr) λ(1 − γ)(1 − G(v(p))) + (1 − λ)(1 − F (v(p))) . Pricing at p∗ raises the profits from a discount voucher promotion and lowers the required ˜ minimum difference between distributions required for voucher profitability. The prospect of adjusting prices places new importance on γ: the sign of the change in profits now depends on γ because the proportion of consumers receiving the discounted price affects the firm’s re-optimization. Even with the opportunity of price re-optimization, discount vouchers are not prof- itable when the two populations are identical (F (v) = G(v) for all v). Under the assump- tions of Section 3.3, for λ sufficiently large, µ is decreasing in γ. In this case the firm would prefer to set different prices for the two consumer populations, it can do this more effectively when more of the G consumers may acquire vouchers (i.e. when γ is large). When γ is low, the firm is limited in the extent to which it can raise the price faced by consumers from the F population because many G-population consumers face the same price. 5 Discussion 5.1 Implications for Merchants Our results offer practical advice for firms considering whether to offer discount vouchers. Our discussion in Section 4.1 indicates that a firm might want to disallow purchase of multiple discount vouchers. But as argued by Friedman and Resnick (2001), firms face substantial practical difficulties in implementing this restriction. What stops consumers from creating multiple accounts and purchasing one voucher through each such account? To date, it appears that few firms have adjusted prices in anticipation of many con- sumers using discount vouchers. However, we did notice a sharp price increases at one local restaurant that offers frequent discounts through discount voucher services. Visiting this restaurant, our experience has been that at least half of consumers come bearing dis- count vouchers. Vouchers have noticeably increased the restaurant’s traffic, yet at prices (net of voucher services’ fees, even bearing in mind the price increase) that surely reduce the restaurant’s margins. We doubt the restaurant would have enjoyed a similar traffic 10
  • 12. increase had it simply lowered its prices 25%; clearly vouchers play an important role in making consumers aware of discounts. Yet with voucher services retaining as much as half the consumer’s prepayment, heavy reliance on discount voucher marketing comes at a significant cost. Firms would do well to assess whether their voucher-using customers have already visited and previously paid full price. Firms should also measure how many voucher- using customers later come back without vouchers. In principle, credit card systems could track this information with little harm to customer privacy or data security. But in practice, most firms currently lack the tools or expertise to run such analyses. 5.2 The Future of Voucher Services Our model reveals that a discount voucher service is more likely to be profitable for af- filiated firms, all else equal, if customers using that service have valuations substantially different from (and in particular, below) those of other customers. But notice the difficulty as the voucher service grows: As more consumers use vouchers, voucher-users necessarily come to resemble average consumers, so the use of a voucher comes to convey less infor- mation about a consumer’s valuation. Thus, as voucher services grow, their affiliates will have to rely on voucher advertising rather than voucher price discrimination. Current voucher services’ profits and recent growth may therefore not be good predictors of those services’ future values. Meanwhile, we are struck by the large fees that leading discount voucher services cur- rently charge to participating firms. Groupon charges 50% of voucher price: if a restaurant offers a $20 voucher for $40 of food, Groupon retains $10—a large fee relative to Groupon’s marginal costs of voucher provision (Groupon (2010)). As our results in Section 3.1 indi- cate, such large fees may impede firms’ usage of discount vouchers. However, competition among discount voucher services may drive down these fees.10,11 Recently, Groupon has begun to unbundle some of its services. As of December, 2010, Groupon is charging just 10% to a firm which only wants its offer to appear following user searches, while continuing to require the 50% fee for Groupon’s traditional service of featuring a merchant in a daily email to all consumers in a given city (Groupon (2010)). On one view, the 10% fee might look like a bargain to firms—10% is certainly far less than 50%. However, if Groupon’s low-priced service only gives a firm access to consumers who already know about that firm, then it provides no advertising opportunities—only price discrimination. 10 Small voucher services may charge fees as low as 10%. Yet small voucher services cannot provide substantial advertising benefits. As a result, despite lower fees at small voucher services, many firms prefer the larger services. 11 Another issue of competition in the voucher market is the possibility that a well-positioned competitor (such as Google, Facebook, or Yelp) could develop a similar service and promote that service to its existing users. 11
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