PRICE WARS TRIGGERED BY ENTRY *
Kenneth G. Elzinga
David E. Mills
Department of Economics
Rouss Hall 114
University of Virginia
Charlottesville, VA 22903
804-924-6752 (KGE)
804-924-3061 (DEM)
804-924-7659 (FAX)
International Journal of Industrial Organization, 17 (1999 179-198
* The authors thank Joseph E. Harrington, Paul Klemperer, referees, and seminar participants at
a session of the ASSA meetings, the Georgia Institute of Technology, the University of
Kentucky, and the Antitrust Division of the Department of Justice for comments on earlier
versions.
I. INTRODUCTION
Theories of price wars, like the episodes they seek to explain, are numerous and diverse.
Some theories attribute low prices to unexpected demand shocks. Others interpret price wars as
strategic temporary reversions to competitive pricing by colluding firms, or as breakdowns in
price-fixing cartels.1 Another explanation holds that price wars are low-price outcomes in
equilibria with mixed strategies.2 These theories focus on closed oligopolies; low prices are
unrelated to entry or strategic entry deterrence on the part of incumbents.
In other theories, the prices of a monopolist or dominant firm fall temporarily because of
strategic entry deterrence, limit pricing, or predation.3 In these models, deterrence typically is
successful: there is no entry. Klemperer's paper (1989) is an appealing exception. In
Klemperer's theory of price warfare, low prices are triggered by actual entry in markets where
customers of new entrants incur switching or set-up costs. To attract customers who will incur
these set-up costs, entrants in Klemperer's model offer temporary discounts from prevailing price
levels. In reaction, and to stem the loss of customers to entrants, the incumbent also offers
temporary discounts. The result is a price war. Once entrants have established a clientele, the
price war stops and all firms raise their prices.
The principal predictions of Klemperer's theory are plausible empirically. An
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incumbent's early success selling a new product attracts entry. Prices dip when entrants arrive,
then rebound once the market reacts fully to their arrival. Further, during the price war the
incumbent need not cut its price as low as entrants to hold its own. The theory's principle
departure from what generally happens in price wars is its failure to predict established
customers ever actually switching to new entrants. Klemperer's entrants reduce prices in a
market only by drawing new customers into the market; they do not succeed in winning over any
of the incumbent's existing customers. Put starkly, it is a theory based on switching costs in
which there is no switching.
The reason Klemperer's equilibrium lacks any customers who switch from the incumbent
to entrants is his model's assumption that set-up costs are identical across customers. For
switching to occur, it is necessary that customers have heterogeneous set-up costs. 4 Since set-up
or switching costs are investments in relationship-specific assets, they will be greater for some
buy-sell relationships than others. This paper extends Klemperer's model to analyze price wars
triggered by entry where buyers have heterogeneous set-up costs, and then it furnishes an
illustration of a price war in which actual events adhere to the predicted pattern.
We develop a model that focuses on the sale of a homogeneous manufactured good to
dealers who resell the good to consumers or end users.5 The good is introduced by a single
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manufacturer who has a first-mover advantage but who eventually faces competition from
entrants. Downstream distribution of the good is competitive. Dealers incur set-up costs when
they establish a relationship with a manufacturer and begin placing regular orders for the good.
For simplicity, the dealers are assumed to be identical in every respect except the size of their
set-up costs; these costs are firm-specific and are greater for some dealers than others. Since the
good is homogeneous, set-up costs restrain dealers from buying the good from more than one
manufacturer at a time.
A price war breaks out when entrants arrive. During the price war, the entrants' price is
below the incumbent's price. It is even below the entrants' costs. The low price increases sales
of the good so that new dealers are drawn into the market to distribute entrants' output. Further,
depending upon the distribution of dealer set-up costs, the price war may induce some (but not
all) of the incumbent's dealers to switch to an entrant. Once entry is complete and all the dealers
have attached themselves to a supplier, the price war ends and the price of the good increases.
In equilibria where switching occurs, there are three classes of dealers: "switchers," "nonswitchers" and "latecomers." The switchers are those with the lowest set-up costs. They buy the
product from the incumbent in the pre-entry periods but switch to an entrant during the price war.
Latecomers have the highest set-up costs of all the dealers and do not buy the good until entrants
arrive and prices fall. Non-switchers have intermediate set-up costs and buy from the incumbent
in every period.
The model is constructed to reflect conditions in the wholesale distribution of generic
cigarettes where, in 1984-85, the entry of new generic cigarette producers triggered a price war.
After presenting the model and deriving results concerning price warfare and switching, we give
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a brief account of the generic cigarette price war, and show how this episode conforms to the
model's predictions.
Our analysis applies to a broad range of markets for homogeneous manufactured goods
in which entry precipitates price wars upstream from consumers or end users of the goods.
Examples might include sales of specialized construction materials to building supply firms,
"private label" clothing sales to department stores, and heating oil sales to retail fuel distributors.
It also applies to sales of homogeneous inputs and materials (e.g. industrial chemicals), to sales
of undifferentiated intermediate products (e.g. electronic components), and to sales of many
professional services (e.g. specialized accounting or management consulting services).
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II. THE MODEL
A. ASSUMPTIONS
Consider a good that is manufactured and distributed in discrete periods t=1,2,.... In
period 1, the pioneering manufacturer (the incumbent) offers the good for sale to dealers for the
first time. The dealers resell the good to consumers. Assume the good is produced at a constant
marginal cost c with no fixed costs of production. The good cannot be stored from one period to
the next.
Consumers' (inverse) demand for the good is v(q) in every period, where v(q) is concave
and v'(q)<0. Upstream, the collective demand for the good on the part of dealers is derived from
consumers' demand by subtracting dealers' handling costs, assumed here to be zero. Thus, the
dealers' demand for the good is v(q) in every period as well.
Assume there is a continuum of potential dealers, each purchasing exactly one unit of the
good for resale or none.6 A dealer who buys a unit of the good from the incumbent incurs a onetime set-up cost when it makes its first purchase. If the dealer continues to buy the good from the
incumbent in successive periods, it does not incur this cost again. The dealer becomes "locked
in" to the incumbent up to the magnitude of this cost. The size of the set-up cost varies among
the potential dealers. By ordering dealers according to their set-up costs, assume we get a linear
function
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s(q) = s0+s1q for q3[0,Q],
where s0'0 and s1>0, and where Q is so large that there are always potential dealer entrants.
Each dealer knows the size of its own set-up costs but the manufacturer lacks this knowledge.
To exclude the uninteresting case in which demand is too meager to make any sales profitable,
we assume that
v(0) - s0 > c.
(1)
In period 2, like period 1, the incumbent has no competition in manufacturing and selling
the good to dealers. But in periods t'3, entry is free and new manufacturers arrive to compete
with the incumbent. Assume that entrants' products and costs are identical to the incumbent's. If
a dealer buys the good from an entrant, it incurs a set-up cost when it makes its first purchase.
Set-up costs for buying from entrants are the same as they were in buying from the incumbent.
They vary in size among the potential dealers, but they do not depend on the manufacturer who
supplies the good. If a dealer switches its source of the good from one manufacturer to another,
or if it drops out of the market for a period and later returns, it incurs the set-up cost again. Setup costs imply that, in equilibrium, each dealer buys the good from only one manufacturer at a
time. Like the incumbent, entrants do not know the set-up costs of particular dealers.
The incumbent and entrants choose output levels simultaneously in every period. The
firms are unable to commit to future output levels. The incumbent's output in period t is
designated qti, and the collective output of entrants in period t is designated qte, where qte=0 for
t=1,2.
In the wholesale market, where manufacturers sell the good to dealers, competition
among dealers drives each manufacturer's price to the level that gives its marginal dealer zero
æ
profit. The manufacturer receives the same price from all of its dealers (neither the incumbent
nor any entrant can price discriminate among its dealers). This price depends on whether any of
the manufacturer's sales are to new dealers. In periods when a manufacturer attracts new dealers,
its price must be low enough to absorb the set-up costs of those customers. Since the
manufacturer cannot price discriminate to absorb its new dealers' set-up costs, it must accept a
lower wholesale price from all of its dealers -- even those locked in previously. This means
different manufacturers may have different wholesale prices in some periods. In particular, as
seen below, it means that the incumbent's wholesale prices are not always the same as entrants'.
In the retail market, where dealers sell the good to consumers, competition establishes a retail
price of v(qti+qte), since total output is qti+qte.
Entrants react collectively to the incumbent's output choice in periods t'3, and are
modeled as a competitive fringe. The incumbent is the only strategic agent in the model. This
firm anticipates entrants' reactions and chooses qti in each period to maximize its discounted
profit.
B. ENTRANTS
The first step in finding an equilibrium sequence of prices and quantities in the model is
depicting the behavior of entrants in time period 3 and after. With free entry in these periods,
total output cannot be so small that selling a unit of the good to an unserved dealer would appear
profitable to an entrant. The minimum level of total output in periods t'3 is governed by a zeroprofit condition for a potential entrant.
å
To find the minimum level of total output consistent with free entry, suppose that total
output were q in every period beginning with some t'3. The retail price of the good would be
v(q) in every period t'3. With this, the most a new dealer would pay for a unit of the good is
v(q)-s(q) in period t, since it would incur a set-up cost in this period, and v(q) in subsequent
periods. At these prices, and assuming a discount factor õ between periods, where õ3(0,1), an
entrant could earn a discounted profit of
[v(q)-c](1+õ+õ2+...) - s(q).
(2)
by selling the good to a new dealer beginning in period t. Define q* to be the level of total output
where the expression in (2) equals zero:
[v(q*)-c]/(1-õ) = s(q*).
(3)
With free entry and a continuum of dealers, total output will never fall below q *. The behavior of
entrants assures that the minimum level of total output in periods t'3 is q*.
Now define q** to be the level of total output where
v(q** ) = c.
(4)
Definitions (3) and (4) imply that q**>q*. Sales beyond q** would cause retail and wholesale
prices to fall below the cost of producing the good. A wholesale price this low is unacceptable to
entrants -- even to those who have locked-in dealers. Thus, with free entry and a continuum of
dealers, the maximum level of total output in periods t'3 is q**.
The exact level of entrants' output in any period t'3 depends on their output, if any, in the
previous period and the incumbent's (simultaneously chosen) output in period t:
q*-qti
if qt-1e+qti < q*
qte = qt-1e if q* & qt-1e+qti < q**(5)
if q** & qt-1e+qti
max{q**-qti, 0}
ä
These equations indicate that if entrants have no locked-in dealers in some period t (e.g., qt-1e=0),
they produce q*-qti units in that period as long as qti<q*. Otherwise, they produce nothing. If entrants
do have some locked-in dealers in period t (qt-1e>0), then the amount they produce at t depends on
qt-1e and the incumbent's output qti. In no case do entrants ever permit total output to fall below q*
and, no matter how many locked-in dealers they have, entrants never produce so much that total
output exceeds q**.
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III. EQUILIBRIUM PRICE AND OUTPUT SEQUENCES
The incumbent chooses an output sequence to maximize its discounted profit given the
behavior of entrants, as summarized in equation (5). Since retail and wholesale prices adjust from
period to period to clear the market, equilibrium prices are derived from the output levels firms
choose. The incumbent’s profit-maximizing output sequence has several identifiable characteristics.
Consider pre-entry periods 1 and 2 first.
In periods 1 and 2, competition among potential dealers determines who will distribute the
incumbent's output. The q1i units of output the incumbent produces in period 1 are purchased by the
q1i dealers with the lowest set-up costs. The incumbent's wholesale price in this period is
p1i = v(q1i)-s(q1i),
(6)
reflecting the fact that the incumbent must absorb its dealers' set-up costs. Since the incumbent
cannot price discriminate, p1i must be low enough for its marginal distributor (q1i) to earn zero profit
in this period.7 The retail price is v(q1i) in this period.
In the second period, the incumbent's wholesale price depends on whether the firm increases
its output. If q2i & q1i, then the incumbent only sells the good to locked-in dealers in period 2. In this
case, the incumbent’s wholesale price would be higher than in period 1:
p2i = v(q2i).
(7)
If q2i > q1i, then the incumbent sells the good to some dealers in period 2 who did not buy the good
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in period 1.8 In this case, the incumbent's wholesale price would be
p2i = v(q2i)-s(q2i),
(8)
because the incumbent must absorb its new dealers' set-up costs and cannot discriminate against its
locked-in dealers. In either case, the retail price is v(q2i) in period 2.
The incumbent's output in periods 1 and 2 is positive and less than q*. We know that q1i and
q2i are positive because assumption (1) implies that some units of the good can be sold for a positive
profit in these periods no matter what happens in later periods. Similarly, we know that the
incumbent chooses q1i<q* and q2i<q* because output greater than or equal to q* would yield nonpositive discounted profit regardless of what transpires later.
New manufacturers are free to enter beginning in period 3. The following proposition9 shows
that the incumbent's best response to entrants is to produce a constant level of output in every period
t'3, where q3i is at most q2i.
Proposition 1: The incumbent's profit-maximizing output sequence has q3i & q2i and qti = q3i for all
t>3.
Since the incumbent produces less output than q* in the second period, this proposition
implies that the firm produces less output than q* in all periods t'3. To deter entry completely and
to monopolize sales indefinitely, the incumbent would have to produce at least q * units of output in
every period t'3. One implication of Proposition 1 is that, in equilibrium, the incumbent never
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adopts this output strategy. Equation (5) shows that this decision by the incumbent induces entry
in period 3.
Period 3 entrants produce q3e=q*-q3i units of the good collectively. This attracts new dealers
who buy and resell q*-q2i units of output in the market. The new dealers are those with the lowest
set-up costs among the remaining potential dealers. The entrants' market-clearing wholesale price
in period 3 is
p3e = v(q*)-s(q*),
(9)
reflecting the fact that entrants must absorb the set-up costs incurred by their dealers and enable even
the marginal dealer to earn zero profit.
Those dealers retained by the incumbent are the q3i previously locked-in customers with the
highest set-up costs. These are the easiest dealers to retain, in the face of competition from entrants,
because they can be retained with the largest possible wholesale price. This price will exceed the
entrants' entry period price by an amount just equal to the set-up cost of the marginal retained dealer:
p3i = v(q*)-s(q*)+s(q2i-q3i).
(10)
The retail price in period 3 is v(q*) for all units of the good sold.
Proposition 1 and equation (5) also depict characteristics of the output sequence in periods
4 and after. The most important characteristic is that every firm produces the same level of output
and sells only to its locked-in dealers in periods t'4. After period 3, there is no more entry. Total
output remains q*, so the market-clearing wholesale price, and the retail price, is
pti = pte = v(q*).
(11)
for all firms in the post-entry periods. With total output maintained at this level, equation (3) implies
that entrants earn zero discounted profit.
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With the depiction of prices in the entry and post-entry periods provided by equations (10)
and (11), it is possible to prove the following proposition about the incumbent’s output levels in
periods 1 and 2.
Proposition 2: The incumbent's profit-maximizing output sequence has q2i=q1i.
This proposition means it is never optimal for the incumbent to give up any of the dealers it locked
in previously while entry still is restricted. And it is never optimal for the incumbent to increase
production to attract additional dealers in period 2. The optimal course of action for the incumbent
in the pre-entry periods is to lock in a set of dealers in period 1 and then "exploit" them in period 2.
Propositions 1 and 2 and equations (6), (7), (10) and (11) provide a sufficient
characterization of the incumbent's output choices and prices to express that firm's discounted profit
as a function of q1i and q3i:
%i(q1i,q3i) = (1+õ)[v(q1i)-c]q1i - s(q1i)q1i
+ õ2[v(q*)-s(q*)+s(q1i-q3i)-c]q3i
(12)
+ [õ3/(1-õ)][v(q*)-c]q3i.
Since v(q) is decreasing and concave, and since s(q) is increasing and linear, %i is strictly concave
in q1i and q3i in the relevant output range and has a unique maximum. Let q' be the firm's optimal
value of q1i, and q& its optimal value of q3i. In equilibrium, the incumbent produces q' in the first two
periods and q& in every period thereafter, where q& &q' . Assumption (1) implies that %Ii(q',q&)>0. The
equilibrium output levels for the incumbent and the entrants are shown in TABLE 1.
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TABLE 1: EQUILIBRIUM PRICES AND QUANTITIES
t
pt i
pte
qti
qte
1
v(q' )-s(q' )
n.a.
q'
0
2
v(q' )
n.a.
q'
0
3
v(q*)-s(q*)+s(q' -q& )
v(q*)-s(q*)
q&
q*-q&
4....
v(q*)
v(q*)
q&
q*-q&
In equilibrium, active dealers are separated into (at most) three groups: "latecomers,"
"switchers," and "non-switchers." Latecomers are dealers drawn into the market in period 3 when
new manufacturers enter. None of the latecomers buys the good in the pre-entry periods, and none
buys the good from the incumbent in any period. An equilibrium always has latecomers because the
incumbent's pre-entry output q' always is less than q*. The marginal latecomer (i.e., q*) earns zero
profit in every period, but inframarginal latecomers earn positive profit in period 3 (and zero profit
in all other periods). As illustrated in FIGURE 1, latecomers have higher set-up costs than those
dealers drawn into the market by the incumbent in periods 1 and 2.
Entrants' sales may not
be limited to dealers who are latecomers. If the incumbent reduces its output in period 3, some of
its locked-in dealers cannot purchase its good. These dealers, called switchers, will buy the good
from entrants in period 3 and after. Whether there are any switchers in equilibrium depends on the
distribution of set-up costs among potential dealers.
Proposition 3: For any s1, the equilibrium output sequence has q& <q' if s0 is sufficiently small.
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If dealers’ set-up costs are sufficiently large, there will be no switchers in equilibrium; the incumbent
will set q& equal to q' and retain all its locked-in dealers in the face of entry. But if some dealers’ setup costs are small enough, some of the dealers will be switchers. 10
FIGURE 1 shows that switchers have lower set-up costs than all other dealers. They are the
class of the incumbent's locked-in customers who are easiest to lure away, i.e., the most costly
dealers for the incumbent to retain. To retain these dealers in the face of entry, the incumbent would
have to tolerate p3i falling even lower than it does in equilibrium. Switching occurs because It is
more profitable for the incumbent to cede these dealers to entrants than to cut prices enough to retain
them. Switchers earn positive profit in period 1 (because they are inside the margin of the
incumbent's first period customers) and period 3. They earn zero profit in other periods.
The remaining dealers are non-switchers. An equilibrium always has non-switchers (i.e.,
q&>0) because
lim(q3i90) 0%Ii(q',q3i)/0q3i > 0
Non-switchers have set-up costs greater than switchers but less than latecomers, as seen in FIGURE
1. All non-switchers earn positive profit in period 3, and all but the marginal non-switcher earn
positive profit in period 1. All non-switchers earn zero profits in other periods.
The marginal switcher (i.e., q' -q& ) would earn as much profit switching to an entrant in period
3 as not. Similarly, the marginal non-switcher (i.e., q' ) earns the same profit it would earn by waiting
until period 3 to buy from an entrant.
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D. PRICE WARFARE
In equilibrium, the retail price of all sales equals v(q^) in periods 1 and 2 and v(q*) in periods
3 and after, where v(q*)<v(q^) . The equilibrium wholesale prices shown in TABLE 1 are derived
by substituting q' and q& into equations (6)-(11). In period 1, the incumbent's wholesale price is s(q')
below that price in period 2 because the firm must absorb set-up costs to lock in its q' dealers.
In period 3, entrants precipitate a one-period price war in the wholesale market. In particular,
Proposition 4: In equilibrium, P3e<P3i < P2i.
During the entry period, all dealers pay a lower price for the good than the incumbent's locked-in
dealers paid in period 2. But the incumbent's dealers -- the non-switchers -- pay more than entrants'
dealers -- the latecomers and switchers. The price non-switchers pay during the price war depends
on how many dealers the incumbent chooses to retain in the face of entry. P3i is lower the more nonswitching dealers the incumbent preserves. If the incumbent prevents all switching, P3i must fall to
P3e+s0 . This price war is triggered by entry because entrant manufacturers must absorb the set-up
costs of their new dealers. In response, the incumbent acquiesces by accepting a lower price to
preserve an optimal number of non-switchers in the post-entry periods.
Another feature of the price war is that entrants' price P3e is below the cost of production
c. This is implied by the zero-profit condition for entrants and equation (3). Entrants lose money
on their sales in the entry period, but recover in the post-entry periods.
In the post-entry periods, the price war ends and wholesale prices rise as indicated in the
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following proposition.
Proposition 5: In equilibrium, P3i < Pti = Pte, for t'4.
Equilibrium values of prices and output are stationary during periods t'4. After the price war, all
dealers buy the good from the same manufacturer as during the price war, and the wholesale price
equals v(q*) for all sales. While this price is greater than P3i, it is less than the price the incumbent
received in period 2 before entrants arrived. Also, since equation (3) implies that v(q*)>c, the postentry wholesale price is greater than firms' production cost c. This allows entrants to recoup the loss
they incurred during the price war.
ìå
IV. AN ILLUSTRATION
The generic cigarette price war of 1984-85 is a fitting illustration of the theory of price wars
triggered by entry. Here events unfolded in a manner generally consistent with the predictions of
our model. In particular, entry precipitated a price war among cigarette manufacturers of the type
predicted by Propositions 4 and 5, and the incident separated dealers (wholesale distributors and
retail chain store customers of generic or discount-brand cigarettes) into switchers, non-switchers
and latecomers.
A. BACKGROUND
During the 1980s, the U.S. cigarette manufacturing industry had six major firms. 11 There had
been no notable entry or exit by firms in the industry for decades. U.S. cigarette consumption
peaked in 1981 at 638 billion units (i.e., cigarettes) and has declined steadily since; in 1993 507
billion units were consumed (Maxwell Reports, 1988, 1993). The decline is widely attributed to
falling demand provoked by health concerns and growing restrictions placed on smokers. With
domestic consumption falling, the industry has sought to expand export sales, but total sales have
fallen from previous levels. This has caused excess capacity in the industry.
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Cigarettes are strongly differentiated and all manufacturers sell multiple brands.12 The 1984
Maxwell Report identifies more than 210 brands and "styles" (distinguished e.g. by length and tar
delivery rating) sold in the U.S. by the six major firms. Until the mid-1980s, the most important
dimensions of competition among firms in the industry were flavor, tar delivery and advertising.13
Manufacturers' list prices typically were uniform (by length of cigarette) and discounts were
infrequent. During the 1980s, however, as demand declined and excess capacity emerged, firms
turned increasingly to price competition.
The smallest firm in the industry, Liggett & Myers (Liggett), was on the leading edge of
decline in unit sales. Its market share had fallen from over 20% in the 1940s to less than 3% by
1980. In 1980, Liggett began using some of its excess capacity to produce private-label generic
cigarettes for selected grocery wholesalers and tobacco distributors. Liggett sold generic cigarettes
to these dealers at wholesale discounts of 30-40% as compared to branded cigarettes, and the
discounts were transmitted downstream to consumers. Liggett's generic sales grew to such an extent
that, in spite of the continuing decline in its branded products, its share of the cigarette market
reached 6% in 1984.
In mid-1984, two other firms introduced low-priced cigarettes. R.J. Reynolds repositioned
its failing Doral brand to sell at low wholesale and retail prices, and advertised Doral accordingly.
Brown & Williamson (B&W) introduced a line of generic cigarettes and packaged them in much the
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same way as the incumbent firm Liggett had done.
These new-product introductions precipitated a price war in the generic segment of the
market. The price war was marked by a rapid sequence of price reductions by the manufacturers
beginning in mid-1984, and by a more or less simultaneous reescalation of prices at the close of
1985.14
B. THE PRICE WAR
In classifying set-up or switching costs, Klemperer (1987, 1988) emphasized that some of
these costs are transaction costs while others are learning costs. Wholesale cigarette distributors
incur both kinds of set-up costs when they begin distributing generic cigarettes, or when they switch
from one manufacturer of generic cigarettes to another. Transaction costs are incurred because
distributors must set up new stock keeping units in their distribution systems and must build up
capital in transacting with particular suppliers.15 Learning costs are incurred because the quality of
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a new product is not fully known ex ante. 16 The size of these costs varies from one distributor to
another because of economies of scale and scope, and because of differences in distributors' attitude
towards risk.
Price data assembled from the trial record in Liggett v. Brown & Williamson (1990)
demonstrate that prices during the generic cigarette episode follow the pattern predicted by our
model. The prices reported are the net prices per carton of generic cigarettes actually paid by
incumbent Liggett's and entrant B&W's largest customers (a carton contains 10 packs or 200
cigarettes).17 These transaction prices were as much as 30 percent below manufacturers' list prices
during the price war because of a plethora of customer rebates, allowances and promotional
programs.
The range of prices the incumbent firm Liggett charged the various classes of its customers
during 1984-85 is shown in FIGURE 2 by a price band. The highest price in the band was charged
to customers who bought "broker label" generic cigarettes. These accounted for about half of 1984
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sales. The lowest price in the band was charged to the "private label" customers, who were the
second largest category. Entrant B&W's prices were the same to all classes of customers.
B&W's generic cigarette program was announced in June, 1984. Its first sales and shipments
of generic cigarettes occurred the following August. The price war erupted during this period as
B&W sought to establish an introductory price level attractive to new customers and Liggett's
existing customers, and as Liggett cut its prices to keep from losing sales. By August, when B&W's
first sales actually occurred, both firms' prices were substantially below Liggett's previous prices.
Low prices prevailed until late in 1985 when the price war ended.
The midpoint of incumbent Liggett's price range before B&W's new product line appeared
was $3.61 per carton. During the price-war the midpoint fell to between $2.85 and $3.05 per carton.
B&W's prices during the price-war were in the range of $2.82 - $3.03 per carton. After the price-war
ended, the midpoint of Liggett's price range increased to $3.27 per carton and B&W's increased to
$3.26 per carton.
Contrary to the predictions of Klemperer's model, there was a great deal of switching during
the generic cigarette price war. There were, in all, about 3,500 wholesale customers and chain stores
who bought cigarettes from the six major manufacturers in 1984. Liggett sold generic cigarettes to
about 2,000 of these customers in the period before B&W and R. J. Reynolds entered the generic
segment of the industry. B&W acquired about 1500 generic cigarette customers during the price
war. Some of these were first-time generic cigarette buyers (i.e., latecomers), but others (i.e.,
switchers) changed over to B&W from Liggett. Of course, Liggett retained many of its generic
customers, and some distributors continued to spurn generic cigarettes throughout the price war and
only bought branded cigarettes.
ëê
ëé
V. CONCLUSION
The literature of economics is replete with theories of price warfare. Klemperer's innovation
was to attribute price wars triggered by entry to the presence of customer set-up or switching costs.
While Klemperer's predictions about the sequence of prices in these episodes are plausible in the
main, his theory raises an anomaly: actual switching by customers between vendors would never
occur; the price-cutting entrants are limited in their sales only to new customers.
Our model extends Klemperer's work by showing that customer heterogeneity can lead to
actual switching in price wars triggered by entry, depending on the distribution of customer set-up
costs. The context of the model is the wholesale distribution of manufactured goods where dealers
incur sunk costs to invest in relationship-specific assets when they begin distribution of a
manufacturer's goods. Events in the generic cigarette price war of 1984-85 provide an illustration
of prices and switching patterns predicted by our model. The model applies to a broader set of
circumstances, however. Its basic interactions and results can occur in any upstream market for
homogeneous goods and services in which one seller gets a head start on rivals and the buyers are
perfect competitors downstream.
ëè
APPENDIX
Proposition 1: The incumbent's profit-maximizing output sequence has q3i&q2i and qti=q3i for all t>3.
Proof: If the incumbent were to increase its output level in any period t'3, it would have to accept
a lower price from all its dealers in that period so it could absorb its new dealers' set-up costs. But
recall that the entrants' behavior, as summarized in equation (5), guarantees that qti+qte ' q* for t'3.
Thus, if the incumbent were to increase its output, it would make non-positive discounted profit on
its incremental sales and would earn less profit on sales to its previously locked-in dealers than by
keeping output constant. This implies that the incumbent's profit-maximizing output sequence has
qti & qt-1i for all t'3.
The result that qti & qt-1i for all t'3 means, of course, that q3i & q2i. Also, since q2i < q*, this
result means that q3i < q*. This, together with equation (5), implies that q3e = q*-q3i. Now consider
periods 4 and after. If the incumbent were to reduce its output level below q3i in any period t>3,
equation (5) indicates that entrants would raise qte to keep total output at the level q*. Thus, by
reducing its output, the incumbent would not raise the price at which its remaining output sells. By
cutting its output level, the incumbent would forgo profitable sales to some of its locked-in dealers
and gain nothing in return. This establishes that the incumbent's profit-maximizing output sequence
has qti=q3i for all t>3.
Proposition 2: The incumbent's profit-maximizing output sequence has q2i=q1i.
Proof: As a preliminary matter, define f(q2i) to be the incumbent's post-period 2 profit, evaluated at
ëç
t=3, assuming q2i dealers are locked in going into period 3. From Proposition 1 and from equations
(10) and (11), we know that for any q2i3(0, q*),
f(q2i) 2 max {[v(q*)-s(q*)+s(q2i-q3i)-c]q3i + [õ/(1-õ)][v(q*)-c]q3i}
0&q3i&q2i
(A1)
Substituting equation (3) (the definition of q*) into (A1) and simplifying terms yields
f(q2i) = max {[s0+s1(q2i-q3i)]q3i},
0&q3i&q2i
(A2)
or, solving,
f(q2i) =
(s0+s1q2i)2/4s1 if s0/s1<q2i and q2i3(0, q*)
(A3)
if q2 &s0/s1 and q2 3(0, q*)
i
i
s0q2
i
(A3) implies that f(·) is increasing and continuous, and that
f’(q2i) =
(s0+s1q2i)/2
if s0/s1<q2i and q2i3(0, q*)
s0
if q2 &s0/s1 and q2 3(0, q*)
(A4)
i
i
The proof is by contradiction. First suppose it is optimal for the incumbent to set q2i<q1i.
From equations (6) and (7), the incumbent’s output would sell at the wholesale price v(q 1i)-s(q1i) in
period 1 and v(q2i) in period 2. The firm’s discounted profit would be
[v(q1i)-s(q1i)-c]q1i + õ[v(q2i)-c]q2i + õ2f(q2i).
(A5)
By hypothesis, (A5) exceeds the discounted profit the firm would earn if it produced q1i in both
periods 1 and 2, namely
[v(q1i)-s(q1i)-c]q1i + õ[v(q1i)-c]q1i + õ2f(q1i).
(A6)
[v(q2i)-c]q2i + õf(q2i) > [v(q1i)-c]q1i + õf(q1i),
(A7)
If (A5) > (A6), then
or, since f(·) is an increasing function,
ëæ
[v(q2)-c]q2 > [v(q1)-c]q1.
(A8)
Further, since s(·) is an increasing function, (A8) implies that
[v(q2i)-s(q2i)-c]q2i > [v(q1i)-s(q1i)-c]q1i.
(A9)
(A9) establishes a contradiction because it shows that choosing q2i in both periods 1 and 2 is more
profitable than setting q2i<q1i. Thus, q2i ½ q1i.
Next suppose it is optimal for the incumbent to set q2i>q1i. With this output sequence,
equations (6) and (8) indicate that the incumbent's wholesale price is v(q1i)-s(q1i) in period 1 and
v(q2i)-s(q2i) in period 2. Its discounted profit is
[v(q1i)-s(q1i)-c]q1i + õ[v(q2i)-s(q2i)-c]q2i + õ2f(q2i).
(A10)
Since v(·) is decreasing and concave, and since s(·) is increasing and linear, the expression in (A10)
is strictly concave in q1i and q2i. Optimal values of q1i and q2i are found by solving, respectively
[v(q1i)-s(q1i)-c] + q1i[v’(q1i)-s’(q1i)] = 0
(A11a)
[v(q2i)-s(q2i)-c] + q2i[v’(q2i)-s’(q2i)] + õf’(q2i) = 0.
(A11b)
If first-order condition (A11a) is multiplied by q1i and first-order condition (A11b) is multiplied by
by q2i, and the two products are equated, we get
[v(q1i)-s(q1i)-c]q1i - [v(q2i)-s(q2i)-c]q2i =
q2i2[v’(q2i)-s’(q2i)] - q1i2[v’(q1i)-s’(q1i)]+õq2if’(q2i).
(A12)
Since [v(q)-s(q)-c]q is concave in q, then q2i>q1i implies
q2i2[v’(q2i)-s’(q2i)] - q1i2[v’(q1i)-s’(q1i)] < 0.
Using (A12), this inequality implies
[v(q1i)-s(q1i)-c]q1i - [v(q2i)-s(q2i)-c]q2i < õq2if’(q2i).
(A13)
Also, by hypothesis, (A10) exceeds the discounted profit the incumbent would earn if it produced
ëå
q2i in both periods 1 and 2, namely
[v(q2i)-s(q2i)-c]q2i + õ[v(q2i)-c]q2i + õ2f(q2i).
(A14)
If (A10) > (A14), then
[v(q1i)-s(q1i)-c]q1i - [v(q2i)-s(q2i)-c]q2i > õ[v(q2i)-c]q2i - õ[v(q2i)-s(q2i)-c]q2i,
or
[v(q1i)-s(q1i)-c]q1i - [v(q2i)-s(q2i)-c]q2i > õs(q2i)q2i.
(A15)
In order for both inequalities (A13) and (A15) to hold, we must have
õq2if’(q2i) > õs(q2i)q2i
or, equivalently, f’(q2i) > s0 + s1q2i. However, (A4) shows that this inequality cannot hold. This
establishes that q2i ¿ q1i.
Proposition 3: For any s1, the equilibrium output sequence has q& <q' if s0 is sufficiently small.
Proof: In solving equation (A2) above to get (A3), we find that the optimal value of q3i is less than
q2i if q2i >s0/s1. This implies that q& <q' whenever s0/s1<q' . Since s0'0 and s1>0, the ratio s0/s1 is bounded
below by zero. To show that s0/s1<q' holds for s0/s1 sufficiently small, it is enough to show that q' is
bounded above zero for all (s0, s1).
To prove that q' is bounded above zero, notice that
%i(q1i,q& ) = (1+õ)[v(q1i)-c]q1i - s(q1i)q1i + õ2f(q1i).
(A16)
Define 5(s0, s1) to be that value of q1i that maximizes the first two terms on the rhs of (A16). That
is, 5(s0, s1) is the level of output that maximizes the incumbent’s profit in periods 1 and 2, neglecting
subsequent periods. 5(s0, s1) is the value of q1i defined by the first-order condition
(1+õ)[v’(q1i)q1i + v(q1i) - c] - s0 - 2s1 q1i = 0.
ëä
Taking the total derivative of this condition with respect to q1i and s0, we get
05(s0, s1)/0s0 = [(1+õ)(v’‘(q1i)q1i + 2v’(q1i) - 2s1)]-1 < 0
(A17)
Output level 5(s^0, s^1) is unique and positive for any (s^0, s^1) because of assumption (1), because v(·)
is decreasing and concave, and because s(·) is increasing and linear. Also, by inequality (A17), 5(s0,
s^1) > 5(s^0, s^1) for any s0 < s^0. It follows that 5(s0, s^1) is bounded above zero as s0 9 0, and that this
holds for all values of s^1. Since q' > 5(s0, s1), this establishes that q' is bounded above zero for all (s0,
s1).
Proposition 4: In equilibrium, P3e<P3i<P2i .
Proof: Notice first that q* > q' -q& . Since s(·) is increasing, this inequality means that s(q*) > s(q'-q&) and
that
v(q*)-s(q*)+s(q'-q&) < v(q*).
(A18)
Now, since q^<q*, (A18) implies that
v(q*)-s(q*)+s(q' -q&) < v(q^).
This establishes that P3i<P2i. Next, to see that P3e<P3i, observe that
P3i-P3e = s(q' -q& ),
which is positive for all values of q& &q' .
Proposition 5: In equilibrium, P3i<Pti = Pte, for t'4.
Proof: We know that P3i<Pti, for t'4, from inequality (A18) above. The fact that Pti=Pte, for t'4, is
obvious from TABLE 1.
êí
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