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TESIS DE GRADO
MAGISTER EN ECONOMIA
(Illanes Orellana, Gastón)
Diciembre 2008
PONTIFICIA UNIVERSIDAD CATOLICA DE CHILE
INSTITUTO DE ECONOMIA
MAGISTER EN ECONOMÍA
Endogenous Switching Costs in a Differentiated Goods Market
Gastón Illanes Orellana
Comisión
Gert Wagner H.
Carlos Rodríguez S.
Diciembre, 2008
Abstract
This work models a situation where firms competing in prices on a differentiated
goods market in an infinitely repeated interaction have the ability to generate switching
costs for their consumers, forcing them to face a disutility of switching to a rival firm. In
equilibrium, I predict that this ability can generate higher or lower average prices than in
the no switching cost benchmark, depending on the degree of substitution to other goods
and on the cost of creating switching costs. If no substitutes are present and the cost of
creating switching costs is zero, prices will be significantly higher than the no switching
cost benchmark. However, as the cost of creating switching costs rises, prices initially fall
and then increase, dropping below the no switching cost benchmark and then converging
asymptotically towards it. In addition, as the degree of substitution to other goods rises,
prices drop to lower levels and take longer to converge from below to the no switching
benchmark. This implies that concern over switching costs generated by firms may be
unwarranted if relevant substitutes are present or if there is a cost of creating these
switching costs. However, if no such substitutes are available and the cost of creating
switching costs is low, regulatory intervention may be needed to avoid equilibria with
higher prices than the no switching cost benchmark.
Resumen1
Este trabajo modela un escenario en el que empresas que compiten en precios en
un mercado de bienes diferenciados, en el contexto de una interacción infinitamente
repetida, tienen el poder de generar costos de cambio para sus consumidores. Esto
implica que dichos consumidores enfrentan un costo de cambiarse de proveedor. En
1
Me gustaría agradecer a mi familia por su apoyo durante toda mi educación, sobre todo a mi mamá y mi
abuelo Sergio, quienes me incentivaron a ser curioso y a disfrutar aprendiendo. Gracias por haberme exigido
desde chico. También a Carolina Alfero, por su paciencia y cariño durante este proceso. Agradezco además a
los profesores de mi comisión, Gert Wagner y Carlos Rodríguez, por sus valiosos comentarios y por su gran
disposición. Sin duda, el hecho que este proceso haya sido agradable y fructífero es gracias a ellos. Además,
agradezco a mis compañeros de comisión, Úrsula Schwarzhaupt y Cristián Dagnino, por sus comentarios y su
compañerismo. Me gustaría mencionar especialmente a los profesores Raimundo Soto, Francisco Gallego,
Felipe Zurita, Salvador Valdés, y Rodrigo Cerda, quienes gentilmente respondieron mis dudas y me guiaron
en el camino. Finalmente, me gustaría agradecer a todos mis amigos que dedicaron parte de su tiempo para
aportar a este trabajo, como Pilar Alcalde, Pablo Álvarez, Luis Beltrán, Orlando Chacra, Tonino Costa, Jorge
Fantuzzi, Francisco Garrido, Fernando Luco, y Daniela Marshall. Pido disculpas si olvido a alguien. Todos los
errores contenidos en este trabajo son de mi responsabilidad.
2
equilibrio, encuentro que esta habilidad puede generar precios promedio mayores o
menores que si no hubiera costos de cambio, dependiendo del grado de sustitución a
otros bienes y del costo de crear dichos costos. Si no existen bienes sustitutos y el costo
de crear costos de cambio es cero, los precios serán mayores que si dichos costos no
existieran. Sin embargo, a medida que aumenta el costo de crear costos de cambio, los
precios inicialmente caen y luego aumentan, cayendo bajo el nivel sin costos de cambio y
luego convergiendo desde abajo hacia éste. Además, a medida que la sustitución a otros
bienes aumenta, los precios bajan a menores niveles y se demoran más en converger
desde abajo al nivel sin costos de cambio. Esto implica que la presencia de costos de
cambio endógenos puede llevar a menores precios en equilibrio si la sustitución a otros
bienes es alta o si el costo de crear dichos costos es alto. Sin embargo, si no existen
sustitutos y el costo de crear costos de cambio es bajo, la intervención regulatoria puede
ser necesaria para evitar equilibrios con precios mayores que el nivel sin costos de
cambio.
3
Index
Abstract-Resumen
Page 2
Introduction
Page 5
Overview of the Theoretical Switching Cost Literature
Page 9
Empirical Evidence
Page 12
DHR’s Model: A Formal Explanation, Results, and Intuition for
Endogenous Switching Cost Markets
Page 13
A Model for Endogenous Switching Costs
Page 19
Final Remarks
Page 24
References
Page 28
Appendix A: Figures
Page 30
Appendix B: Numerical Algorithm
Page 37
4
I. Introduction
Markets with switching costs are those where consumers face a cost if they decide
to switch providers. This implies that once consumers have bought a good or service from
a certain firm, they have made an investment that is not compatible with buying said good
or service from another. Klemperer (1995) mentions some reasons that may cause this
particular behavior to arise: i) the need for compatibility with already purchased
equipment, ii) transaction costs faced when switching providers, iii) the cost of learning
how to use new products, iv) uncertainty over the quality of untried brands, v) contractual
measures such as fines, or vi) simply psychological costs (Brehm (1956)). Clearly, there is
an important difference between switching costs that disappear after a learning process
and those which do not, since the former are only relevant the first time the consumer
switches, while the latter are always present. This study, like the entire switching cost
literature reviewed, will focus on the second type.
An important distinction to be made is that some of the previously mentioned
switching costs can be manipulated by firms, while others clearly cannot. I will refer to the
first type as endogenous switching costs, and to the second as exogenous. Therefore,
endogenous switching costs will occur whenever a firm has the ability to generate costs of
buying from a competitor for consumers who have previously purchased its goods or
services, while exogenous switching costs occur whenever said costs are not affected by
the firm´s actions.
Practical examples of this behavior abound. For example, in telecommunications
markets we may observe exogenous switching costs when number portability is not
implemented because of technological reasons, and endogenous switching costs when
consumers sign contracts that include fines for switching providers before a certain date.
For example, according to SERNAC, a Chilean government agency charged with defending
consumer’s rights, customers of different mobile phone companies in Chile have faced
fines of $85.000 pesos for early termination of services, a practice that was recently
5
declared illegal2. However, in order to avoid paying this fine, customers must either
complain to SERNAC or sue. This process is tedious, takes time, and suing is expensive, so
consumers may pay the fine or simply not switch. Fines of this nature, or the bureaucratic
hassle and cost required to stop service, and pricing structures such as lower prices for
same-network calls3, make telecommunications markets a prime example of a situation
where endogenous switching costs occur.
Furthermore, the previous arguments also contend that endogenous switching
costs may be found in markets for services that require some effort by the customer in
order to terminate services, like bank accounts, cable or satellite TV, and magazine
subscriptions. In these situations, if firms take action in order to make the quitting process
more costly, for example by requiring customers to terminate contracts at a company
office, we have a situation where endogenous switching costs are present. Nevertheless,
consumers do not have to have signed a contract or be subscribed to a service in order to
face endogenous switching costs. Adams (1978) describes the efforts undertaken by razor
manufacturer Gillete in order to produce razor heads that fit the competitions’ machines,
while ensuring that the competitions’ heads did not fit theirs. If successful, this would
have created a switching cost when switching from Gillete razor heads to other brands’.
Another example of markets where endogenous switching costs appear to have a
relevant impact are those where consumer loyalty programs, like air miles or supermarket
points, are present. Once consumers have purchased from a company that offers these
rewards, they have a greater incentive to continue purchasing from it in the future, since
this allows for the accumulation of more points and for more valuable prizes. In this
scheme, companies decide how many points are accrued from a purchase, the duration of
their validity, and what their value is. An interesting aspect of this arrangement is that
2
3
$85.000 pesos are roughly USD 130. See http://www.sernac.cl/noticias/detalle.php?id=638
This creates a network effect, which is also considered a switching cost. See Farrell and Klemperer (2007).
6
companies can change the value of the points at any time, effectively changing the level of
switching costs for their customers4.
What is the impact of endogenous switching costs on prices and competition?
What is the optimal level of switching costs? Should endogenous switching costs generate
regulatory concerns? This study aims to shed light into these questions, building a
parsimonious model that describes the main characteristics of markets with switching
costs.
The aforementioned examples shed light into one of these important main
characteristics, since the firms are not producing homogenous goods. Instead, there exists
a certain degree of differentiation, which reflects the fact that consumers´ tastes play a
role in the choice between goods. Thus, if consumers´ tastes change, they will switch
between firms only if the benefit of doing so is greater than the switching cost, which is
more likely for lower values of said cost. Therefore, in differentiated goods markets,
consumers are imperfectly locked-in to a firm, while in homogenous goods markets they
are perfectly locked in, since as long as the price difference between the incumbent firm
and the others is smaller than the switching cost, which always occurs in equilibrium,
consumers will never switch.
The object of this study is to examine differentiated goods markets where firms
have the ability to fix the level of switching costs, which implies that consumers will
choose amongst firms by looking at both price and switching cost. Its aim is to determine
whether this capacity enables firms to obtain higher profits by raising prices above the no
switching cost benchmark. In order to do so, this study introduces a model that allows
firms to choose the level of switching costs faced by customers who decide to switch.
The result of this inquiry generates the following prediction: in markets where
reasonable substitutes exist, so customers may choose not to purchase the good from a
firm in the market, but rather a similar but different good, prices will not rise dramatically
4
This is not an uncommon phenomenon. See http://dansdeals.wordpress.com/2007/06/13/cathay-pacificasia-miles-devaluation/ for an example.
7
even if firms can generate switching costs. In fact, in some relevant situations, average
prices can be lower than in the no switching cost benchmark. Whether this is the case will
depend both on the elasticity of substitution to other goods, and on the cost of creating
switching costs. However, if no reasonable substitutes exist, and the cost of creating
switching costs is low or zero, firms will raise prices, effectively locking-in consumers. An
example of a market where substitution may be strong is mobile telecommunications,
where the existence of land lines makes it feasible to substitute towards “fixed” telephone
service. In contrast, workers in Chile are required by law to hire the services of a pension
fund management firm (AFP), so that in this case no outside-the-market substitute is
available. In this scenario, this work predicts that endogenous switching costs will
probably lead to higher fees. Of course, these are just conjectures made for illustrative
purposes; whether there exists reasonable substitution to other goods in a certain market
is an empirical matter.
Before proceeding to the arguments that sustain these results, it is important to
note that this analysis assumes that firms have the power to create switching costs for
their consumers. How does this come to be? Why is it that some firms have the ability to
do this and others do not? And do all firms that are able to generate switching costs find it
optimal to do so? The following arguments aim to clarify these questions.
From the analysis of the switching cost literature and the observation of how the
previously mentioned markets work, a few regularities can be identified. First, a repeated
interaction between consumers and firms is necessary, since we are modeling the creation
of a firm-specific investment by the customer when she purchases from a firm. If the
interaction were a one-shot deal, this investment would be irrelevant. Second, it is
necessary for firms to have market power in order to generate switching costs. If a firm
competing in a perfectly competitive market were to create switching costs, consumers
would not purchase from it in order to avoid being locked-in in the future. Third, it is
plausible to think that generating switching costs has a cost5, since it requires
5
After all, there is no such thing as a free lunch.
8
implementing a scheme that will create a disutility of switching. These costs could be
fixed, like administrative costs, explaining why some firms find it optimal not to create
switching costs, or variable, reflecting that resources are necessary to create each unit of
switching costs. Finally, creating switching costs may be the way firms having market
power attempt to generate more. This author´s results predict that whether they choose
to do so or not, and to what extent, will depend on the degree of substitution to the
outside good, and on the costs incurred in order to generate switching costs.
In order to explore this situation, this work is divided into six sections: the first
section is the preceding introduction, the second section surveys the main results of the
switching cost literature, the third section reviews some empirical results for markets with
switching costs, the fourth section offers a detailed explanation of the model that serves
as a base for this investigation, the fifth section introduces the model used to examine
endogenous switching cost markets and shows its main results, and the sixth section
shows areas for future research and concludes.
II. Overview of the Theoretical Switching Cost Literature.
This section reviews the main results in the switching cost literature that should be
kept in mind as bearings for the analysis of the next sections. A good starting point is
Klemperer (1987), who models the interaction between two firms in a two-period
homogenous good market where consumers acquire a heterogeneous switching cost by
purchasing in the first period. Under these assumptions, and examining pure strategy
Nash equilibria only, this paper finds that switching costs generate two effects: on the one
hand, they make second period demand more inelastic, which raises profits, and on the
other, the existence of second period profits induces greater competition in the first
period, lowering profits. Therefore, an initial conclusion of this analysis is that switching
costs generate an ambiguous effect on profits and prices, depending on which effect is
stronger.
However, the author points out that this result is limited, because if customers are
forward looking, they will recognize that a firm with more customers in the first period will
9
have more market power in the second, and so will choose looking at the present value of
expected prices rather than only at the first period price. This will reduce the gain from
offering discounts in the first period, which means that switching costs necessarily raise
both prices and profits.
Farell and Shapiro (1988) seek to extend this analysis to an infinite period
interaction, where new consumers enter the market each period. Once again, they
examine a duopoly, but they assume that switching costs are homogenous and that all
consumers have unit demands. Also, they look for pure strategy Nash equilibria, but
looking only at Markovian strategies, which restrict players to choosing amongst strategies
that are not a function of the history of the game. In this scenario, supposing that firms
cannot price discriminate between old and new customers, and that each customer lives
only two periods, the authors find rather extreme results: each period, one firm serves all
the new customers, and the other serves all the old ones. Thus, the firm that serves all of
the old customers is able to raise its price above marginal cost, since they are locked-in,
charging said cost plus the value of the homogenous switching cost. At the same time, the
firm that serves all of the new customers can charge an infinitesimally smaller amount
than its rival and still serve all the new customers. Therefore, both firms´ prices are higher
than marginal cost, implying that that switching costs raise prices and profits.
Beggs and Klemperer (1992) strongly criticize Farell and Shapiro’s conclusions, by
pointing out that they assume myopic behavior by consumers. This is because consumers
choose between firms looking only at first period prices, without considering expectations
of future prices. Also, they point out that it is not realistic to believe that all new
consumers will be served by one firm and all old consumers by the other. In order to find
more realistic results, they build on top of Farell and Shapiro’s assumptions, adding
horizontal differentiation among firms for new customers, and an infinite switching cost
for old ones. In addition, their analysis begins with both firms at a market share steady
state, so that their model offers no explanation for what occurs in the first periods.
10
The main result of Beggs and Klemperer´s work is that prices and profits are higher
in a market with switching costs, especially if firms must commit to keeping prices fixed in
time. This is because the incentive to extract profits from the locked-in customers will
always be greater than the incentive to attract new ones if the discount rate is greater
than zero. Finally, the authors extend the result to a scenario where the market grows at
a constant rate. In this case, prices are lower than in markets without growth, but they are
still greater than in the no switching cost benchmark.
Dubé, Hitsch and Rossi (2007) challenge the main implication of the former
models, finding that switching costs do not necessarily imply higher prices and profits in
infinitely repeated games. This is because said models’ assumptions reduce the
importance of the incentive to lower prices in order to attract more customers (called the
investing motive), which boosts the relative importance of the incentive to raise them in
order to extract rents (the harvesting motive). The authors (from now on, DHR) use a
discrete choice model where two firms produce horizontally differentiated goods, and
assume imperfect lock-in, meaning that switching costs are finite and that in each period a
group of customers switches, which is an empirical regularity, as will be argued later.
Under these assumptions, the incentive to lower prices is augmented because it is now
possible for firms to poach other firms’ customers, a possibility that was not present in
previous models. This generates an interesting result: for low switching costs, the
investing motive is stronger than the harvesting motive, which implies that average prices
are lower, while for high switching costs, the opposite occurs and average prices are
higher. This implies that Beggs and Klemperer’s results are a special case of DHR’s, since
the former only look at the infinite switching cost scenario while the latter explore all
possible values. Finally, DHR show that their results are robust to customers with forward
looking behavior and to markets in an overlapping generations setting.
All the previously mentioned models assume that the switching cost faced by
consumers is exogenous, while we have argued that this need not be the case for all
switching cost markets. What happens in markets where firms decide the switching cost
level? Fudenberg and Tirole (2000) answer this question for a two period duopoly model
11
where firms may offer long term contracts to customers, which bind them to buy the
firm’s product for both periods, and where firms are able to price discriminate between
old and new customers. In essence, this generates an infinite switching cost in the second
period. However, in this context offering contracts with infinite second period switching
costs lowers both firm’s profits, so it is optimal for them to offer a higher price and a
lower penalty in case of switching. The intuition behind this result is that the ability to
price discriminate between old and new customers disappears with infinite switching
costs, because the other firm’s customers are no longer potential clients.
However, as has been previously mentioned, assuming two period competition
and the ability to price discriminate between types of consumers may lead to different
results than the relevant case, infinite period competition in situations where the firms do
not have this ability. In order to build on these contributions to obtain a result for this
scenario, Sections III and IV will focus on explaining the main assumptions of this
investigation’s endogenous switching cost model. However, before elaborating on these
issues it is important to determine what has been concluded by the empirical literature on
these markets.
III. Empirical Evidence.
Farrell and Klemperer (2006) survey the empirical evidence on this matter, and
conclude that it is less developed than the theoretical literature, mainly because switching
costs have a consumer specific component that is not directly observable, which makes
identification difficult. At the same time, they argue that to date the literature has ignored
the dynamic considerations of the issue, by assuming myopic behavior by the consumers.
A study that does not make this mistake is Viard (2005), who tests whether the
introduction of number portability in the 800-number market in the US led to a drop in
prices. Since this policy change implies a reduction in switching costs, it is possible to
identify the impact of these costs on prices. To do so, Viard builds a model of horizontal
differentiation, where consumers have tastes distributed on a line interval, and where
they maximize the present value of their expected profits. In each period, a group of
12
customers enters the market while another exits it, and the tastes of a subgroup change.
This last assumption allows for switching in equilibrium, something that is reported to
occur regularly in these markets. Solving the model for Nash equilibria in Markovian pure
strategies, he finds that switching costs may raise or lower prices, a result that is in line
with DHR’s work. Finally, by applying the model to his data, Viard finds that number
portability reduced prices in this market, meaning that in this case lower switching costs
led to lower prices.
DHR use a modification of their theoretical model and apply it to panel data for
orange juice and margarine purchases, finding low switching cost levels in these markets,
distributed mostly in a range of 15% to 60% of the product’s price. Also, they find that for
these levels of switching costs, prices are lower than in the no switching cost benchmark.
From this brief survey we can extract important conclusions: first, it is crucial to
consider expectations of future prices instead of assuming myopic behavior by the
consumers; second, it is an empirical regularity that consumers switch providers even in
equilibrium; and finally, that the revised results are in line with the idea that low switching
costs lower prices, while high switching costs raise them.
IV. DHR’s Model: A Formal Explanation, Results, and Intuition for Endogenous
Switching Cost Markets.
The basic idea of this investigation is to take the theoretical contribution of DHR,
and build on top of it a model where the firms have the ability to choose the level of
switching cost that its customers face if they decide to switch. This is interesting because
the previous literature does not shed light on what will be the impact of allowing for this
possibility on equilibrium prices: on the one hand, higher switching costs mean that higher
prices and profit levels can be sustained, but on the other, customers, at the same prices,
will prefer to avoid purchasing from firms with high switching costs, and also there may be
costs of generating switching costs. Therefore, it is unclear which incentive will prove to
be stronger. If we focus on the empirical examples that have been previously discussed, it
is not only clear that no firm chooses infinite switching costs, but also that the levels of
13
switching costs that are present in those markets are greater than zero. Therefore, it
appears that these forces balance out at a positive switching cost level. What determines
said level, and under which conditions it is greater or smaller, is a question that this study
aims to answer.
DHR’s base model consists of one consumer, who in each period faces the
following choice: he can buy from the firm he patronized last period (the firm he is “loyal”
to), buy from its competitor, which implies facing a switching cost, or simply not purchase
from either one of them, choosing instead an outside option. This implies that we can
define a state variable st that equals 1 when the consumer faces a switching cost of
purchasing from a firm other than firm 1, and 2 when the opposite occurs. The consumer
will choose the option that gives her the greater latent utility in the current period, which
is represented through the following indirect utility function:
U jt   j  p jt   1s t  j    jt
(1)
Equation 1 implies that the utility of consuming good j in period t is a function of a
product-specific intercept (δj), the price of said good, a switching cost if the consumer is
switching firms (γ), and a random utility shock which is magnified by a horizontal
differentiation parameter (λ). This random shock can produce switching even in
equilibrium, because a large enough shock to the consumer’s preferences will imply that
the utility of switching will be greater than the utility of continuing to purchase from the
same firm even if this implies facing a cost of doing so. Finally, 1[·] represents an indicator
function, which equals 1 when st is different than j, and 0 when they are equal, and st
evolves in the following fashion: if the consumer purchases from firm 1 in period t, st+1
equals 1; if he chooses firm 2, st+1 equals 2; and if he chooses the outside option, st+1
equals st, meaning that the consumer´s loyalty remains unchanged. For our two firm
scenario, if the consumer is loyal to firm 1 we can characterize the utility of purchasing
from each firm as:
14
U1t  1  p1t   1t
U 2t   2  p2 t     2t
(2a)
This is the standard formulation for discrete choice models, and it models a
situation where consumers are choosing between purchasing one unit of a good from any
of the J in-market firms, or a relevant substitute. This substitute gives utility:
U 0t   0   0t
(2b)
We shall later see that the value of the outside good utility intercept, δ0, will be
crucial in determining equilibrium prices and values. This merits a discussion on the
meaning of said intercept. Bajari and Benkard (2003) argue that this intercept can be
interpreted as the expected utility that the individual perceives if she spends all her
budget in other goods. Therefore, the discrete choice model can be interpreted as a
simplification of a standard utility maximization problem, where an individual must
choose between discrete quantities of a certain good (from now on, the discrete choice
good), and all other goods. Of course, the utility of choosing not to consume the discrete
choice good will depend on the degree of substitution in the individual’s utility function
between other goods and said good. For example, if the utility function is Leontief’s, this
utility will be zero.
Another way of portraying the outside good is to characterize it as a close but
relevantly different substitute of the discrete choice good. This is the typical formulation
in most industrial organization applications, and it implies that we can portray the
individual’s utility maximization as a two stage process. First, the consumer faces the
standard problem, and chooses whether to purchase from the discrete choice good
branch or not (See Figure 1). If she chooses to do so, she then faces the discrete choice
problem mentioned above, choosing amongst the J goods and the outside option, while if
she chooses not to do so, she spends her budget on all other goods. Under this
formulation, the discrete choice model mentioned above ignores the first stage, assuming
the consumer will always find it optimal to purchase from the discrete choice good
15
branch, and models the consumer’s choice amongst goods inside said branch. For
example, if the discrete choice good modeled is mobile phone service, this
characterization implies that the consumer first maximizes her utility by choosing from all
goods available to her, and always chooses to purchase some kind of mobile phone
service. Then, she chooses between all mobile phone companies, and the outside option
could be standard “fixed” phone service. Since this is the characterization that is most
frequently used in industrial organization, and also because it allows for a more
straightforward interpretation of results, this work will focus on the outside good as a
relevantly different substitute of the discrete choice good.
When this formulation is coupled with an assumption about the distribution of the
random utility shock, it allows for a simple way of characterizing the individual’s demand,
which is also the probability of buying each good. Specifically, if we assume that the
random utility shock is i.i.d with an Extreme Value Type I distribution, then the probability
that the consumer will choose good j is:
D j (st , pt ,  ) 
exp(U ( j , s, pt ,  ) / 
(3)
k 0 expU (k , st , pt ,  ) /  
J
This implies that st evolves following a Markov chain:
 D j ( st , pt )  D0 ( st , pt ) if st  j
Pr st 1  j st , pt   
if st  j
 D j ( st , pt )
(4)
And that firm j’s current period profits are:
 ( s t , p t )  D j ( s t , pt )( p jt  c j )
(5)
The preceding notation allows us to write the firm’s profit maximization problem
as:
 t

E
max
   j ( st ,  ( s t )) 
pj
 t 0

(6)
16
Where σ(st) is a vector containing the prices charged by all firms. Associated with
this profit maximization problem is the following Bellman equation:



V j ( s)  max  j ( s, p)     Pk ( s, p)V j (k )  P0 ( s, p)V j ( s ) 
p j 0
 k


(7)
In this formulation, p is a vector containing all firms’ prices, and Vj(s) is a value
function for firm j in state s. Therefore, conditional on the other firm’s strategies, each
firm chooses a strategy that maximizes its value function. Using this technology, it is
possible to obtain a Markov perfect equilibrium in pure strategies, such that no firm will
have an incentive to unilaterally change its price or switching cost level. However, DHR
report that it is not possible to obtain an analytical solution to this problem, so instead
they must solve for it numerically.
DHR report the results of numerically solving the previous problem for different
levels of the switching cost parameter γ using the following parameter values: δ1 = δ2 = 1,
α = -1, λ = 1, c1 = c2 = 0.5, and assuming that the customer faces a cost if she decides to
buy from firm 2 (is “loyal” to firm 1). However, when they calculate prices for every
switching cost level, they vary the outside option utility intercept (δ0) for each value of the
switching cost so that its market share is constant at the level estimated when γ = 0 and
δ0 = 0. Their reason for doing so is that as γ increases, the outside option’s share of the
market increases as well, so the “market size” (the sum of both firm’s shares) decreases.
Although their interesting result of average prices dropping and then rising as switching
costs increase is robust to this assumption, as Figure 1 shows, when this assumption is
dropped and δ0 = 0 is assumed for all switching cost levels, average prices are only lower
for switching cost levels below 1.5, rather than 4. Also, we see that while prices rise, they
stabilize around 1.9 instead of rising to infinity. This occurs in this exercise, but not in
DHR’s, because in this case as switching costs rise firm 1’s relevant competitor is no longer
firm 2, it is the outside option. Therefore, as firm 1 raises its price, two opposing effects
occur: on the one hand, Firm 1’s margin increases, but on the other, its demand
decreases. This second effect keeps prices low, because the firm starts competing with the
17
outside option, but its impact decreases as the utility obtained from the outside option
falls. Therefore, DHR’s assumption that δ0 falls as γ rises magnifies prices for high
switching cost levels. (See also Figures 2 through 6).
This analysis raises important empirical implications for switching cost markets,
since it has been shown that firms’ ability to raise prices above the no switching cost
benchmark depends crucially on the utility of the outside option. If it is similar to the
discrete choice good’s utility, then even for high switching costs prices will not be
dramatically higher, while if it is significantly lower, prices will be higher than in the no
switching cost benchmark if switching costs are high. This is intuitively appealing: high
substitution to the outside good negates firms’ ability to raise prices even if switching
costs are high, while low substitution means that firms can raise prices significantly if
switching costs are high.
What exactly is the scenario modeled by the no switching cost benchmark? Simply
put, it is the situation where γ is zero, so that while both firms are horizontally
differentiated, the consumer faces no switching cost of moving from one firm to another.
Therefore, it represents a differentiated-goods duopoly, with costless switching amongst
firms. While this scenario does not correspond to a perfectly competitive situation, since
both firms have market power, it represents a relevant benchmark for markets where
switching costs could be present, since the previous discussion argued that market power
is necessary for switching costs to arise.
DHR extend this analysis to consider the possibility of overlapping generations, and
results do not vary significantly. Also, they argue that this equilibrium is unchanged for the
symmetric two firm problem if forward looking consumer behavior is assumed, since in
this case symmetric behavior by the firms implies that both firms charge the same prices if
they hold the consumer “captive”. This implies that the consumer has no incentive to
“invest”, choosing the firm that gives him a lower current period utility in order to gain
more utility in the future, since he will be paying the same price in the next period no
matter which firm he patronizes. See DHR (2006), Appendix C, for details.
18
An interesting area for future research is the application of this model to the
Chilean pension fund system. Valdés (2005) shows that in 1997 the Superintendencia de
AFP, the regulatory body in charge of supervising this system, allowed pension fund
management companies (AFPs) to tacitly coordinate and lower the number of sellers they
hired, establishing quotas. Furthermore, they banned sellers from visiting pensioner´s
homes or workplaces in order to offer a switch from one AFP to another and to fill out the
paperwork required to do so. Instead, a consumer must now go to an office of the AFP it is
switching to and fill out the paperwork there. Valdés (2005) argues that these changes,
especially the first, allowed the AFPs to charge prices that exceed the economic cost of
providing pension fund management services, and resulted in abnormal profits in excess
of 80 million dollars. Since regulatory decrees that lower the amount of sellers and force
customers to attend a company office in order to switch are examples of an exogenous
raise in switching costs, it would be interesting to apply DHR´s model in this situation and
estimate the switching costs faced by pensioners and its effect on commissions and
profits.
Finally, the results of this section present significant intuitive guidelines for our
inquiry into the effects of endogenous switching costs on prices and profits. First, it
appears obvious that the firm that holds the consumers’ “loyalty” will have incentives to
raise its switching cost if it can do so, since its profits will rise, assuming that there are no
costs of doing so. However, it is also clear that this power may or may not generate
significantly higher prices and profits than in the no switching cost benchmark, depending
on the utility of the outside option, and on the cost of creating switching costs.
V. A Model for Endogenous Switching Costs.
We have already argued that the base DHR model captures the behavior of firms
when they are symmetrical and when only one customer, who chooses amongst firms in a
forward looking fashion, is present in the market. Therefore, the next step is to take this
framework and add the possibility of firms controlling the level of switching costs faced by
the customer. This is the strategy pursued in this section.
19
Once again, a latent utility formulation allows us to characterize the customer’s
utility as:
U jt (st  s)   j  p jt  scs1st  j    jt
(8a)
Notice that Equation 8a differs from Equation 1 in that the latent utility is
expressed conditional to s being the firm that holds the consumer’s “loyalty”, so that s will
determine the level of switching costs faced by the consumer if she purchases from any of
the other J-1 firms. That is why instead of a switching cost parameter γ, the variable scs
appears. If we assume that the consumer is loyal to Firm 1, meaning that this firm chooses
the level of switching costs she faces if she purchases from Firm 2, then we can portray
the utility of purchasing from each firm as:
U1t  1  p1t  1t
U 2t   2  p2t  sc1   2t
(8b)
If we assume that the random utility shock ε is i.i.d. and follows an Extreme Value
Type I distribution, we can express each firm’s demand (which is also the probability that
the customer chooses the firm’s good) as:
D j ( st , pt , sc st ) 
exp(U ( j , s, pt , sc jt ) / 

(9)
expU (k , s, pt , sc kt ) /  
k 0
J
The only difference between Equation 8a and DHR’s formulation is that in this case
the switching cost is a decision variable, not a parameter. This formulation allows us to
write the firms´ current period profits as:
 D j ( st , pt , sct )( p jt  c jt )  F j ( sc j )
 ( st , pt , scts ) 
D j ( st , pt , sct )( p jt  c jt ) if

if
st  j
st  j
(10)
The previous equation recognizes that the profit function of the firm that holds the
consumer´s loyalty will be different than that of the other firms, since it includes a cost
20
function of generating switching costs, Fj(scj). This implies that the firm’s maximization
problem is:


max E   t  j ( s t ,  ( s t ), sct )
pj
 t 0

sc
(11)
j
Where, as in the previous section, σ(st) is a vector containing all firm’s prices.
Associated with this profit maximization are the value functions:



V j ( s )  max  j ( s, p, sc)     Pk ( s, p, sc)V j (k )  P0 ( s, p, sc)V j ( s ) 
p j 0
 k

sc j  0 
(12)
In this case, p is a vector containing all firms’ prices, and sc is a vector that contains
all firms’ switching costs. Therefore, conditional on the other firms´ strategies, each firm
chooses a strategy that maximizes its value function. Using this technology, it is possible to
obtain a Markov perfect equilibrium in pure strategies, such that no firm will have an
incentive to unilaterally change its price or switching cost level. Note that the use of
Markov perfection as a solution concept rules out the possibility of pricing strategies that
depend on previous period’s prices, which implies that collusion between the firms is not
possible.
As in DHR, it is not possible to obtain an analytic solution to this problem. Instead,
a numerical solution must be found. Using the same parameter values as in the previous
section (δ1 = δ2 = 1, δ0 = 0, α = -1, λ = 1, c1 = c2 = 0.5), and assuming that the cost function
for generating switching costs is:
Fj (sc j )   ( sc j ) 2
(13)
Interesting results emerge. First, in equilibrium the firm that holds the consumer’s
“loyalty” (Firm 1) raises the switching cost level until the marginal cost of doing so equals
the marginal benefit obtained from being able to raise prices above the no switching cost
benchmark for its now locked-in customers. Firm 2 reacts by lowering prices in order to
21
compete, and in equilibrium average prices are lower than the no switching cost
benchmark for values of θ above 0.01 (see Figure 7). It may be surprising to find a
decreasing and then increasing pattern for average prices, as Figure 7 shows, and lower
average prices than in the no switching cost benchmark, but the reasoning is very
intuitive. If the marginal cost of creating switching costs is zero (θ = 0), Firm 1 will raise
switching costs until Firm 2 is excluded from the market, which will enable it to raise
prices significantly above the no switching cost benchmark (see Figure 8 for equilibrium
switching cost levels for different θ). However, as the marginal cost of creating switching
costs rises, Firm 1 generates lower switching costs, which mean that Firm 2 is no longer
excluded from the market. Therefore, in equilibrium, Firm 2 now has a relevant market
share (Figure 9), and since it offers a lower price, average prices drop. Also, Firm 1 must
now compete against Firm 2, so it too offers a lower price. This also implies that average
prices drop as θ rises from zero, dropping below the no switching cost benchmark at θ =
0.01, and reaching a minimum at θ = 0.05. For larger values of θ, average prices rise,
asymptotically approaching, but never surpassing, the no switching cost benchmark. They
rise because as θ increases, Firm 1 generates lower switching costs, which enable Firm 2
to charge a higher price, but they never surpass the no switching cost benchmark because
Firm 1´s price increase is always smaller than Firm 2´s price drop.
This happens because by generating switching costs of leaving firm Firm 1 and
moving to Firm 2, Firm 1 is able to lower Firm 2´s demand, but since it still competes with
the outside option, it is not able to fully capitalize on this. Instead, part of Firm 2´s lost
share goes to the outside option, and while Firm 1 raises prices, it is not able to raise them
as much as Firm 2 lowers its own. Firm 2 lowers its price because it is the only way to
compete with Firm 1 now that the customer faces a switching cost if she chooses to
purchase its product. Because of these two opposing reactions, average prices drop, but
this does not mean that in equilibrium Firm 1 does not experience a profit increase. Figure
10 plots both firm´s profits and the no switching cost benchmark profit level, showing that
in fact Firm 1 raises its profits by generating switching costs, lowering Firm 2´s profits in
the process.
22
Since part of Firm 2´s market share drop, in comparison to the no switching cost
benchmark, is captured by the outside option, it is important to evaluate what happens
when said option becomes less relevant. Figure 11 plots both firm´s prices, as well as the
no switching cost benchmark price and the average price paid by the consumer when the
outside option becomes less relevant (δ0 = -2). In this scenario, while the decreasing and
then increasing nature of average prices is still observed, prices are higher than in the no
switching cost benchmark for θ lower than 0.1, rather than 0.01 as in the previous case.
Also, while for θ higher than 0.1 average prices are lower than in the no switching cost
benchmark, the difference between both values is smaller than in the previous scenario.
These findings point to the fact that if substitution to the outside good is poorer, Firm 1
will be able to raise its prices higher in equilibrium, which will make for a higher average
price than in the no switching cost benchmark if the cost of creating switching costs is low,
and for an average price that is lower than the no switching cost benchmark for high
values of the cost of generating switching costs. Figure 12 shows both firm´s demands in
this scenario, confirming that Firm 1 is able to raise prices and still have a higher market
share, strictly because substitution to the outside good is poorer, while Figure 13 shows
both firm´s profits. In this scenario, because the outside good is a poorer alternative, both
firms have higher profits. Finally, if there is no outside good, average prices would be
higher than the no switching cost benchmark for all values of θ, asymptotically reaching
said benchmark as θ increases.
Therefore, this model predicts that in markets where a reasonable substitute
exists, average prices in situations where firms create switching costs will in fact be lower
than if no switching costs were present, while if there is no substitution to other goods,
average prices will be higher than in the no switching cost benchmark. Also, the model
predicts a decreasing and then increasing pattern for average prices as costs of generating
switching costs rise. It is important to understand that the prediction of lower average
prices does not imply that both firms charge lower prices, or that both firm´s profits drop.
By generating switching costs, Firm 1 is able to raise both its prices and its profits, and it is
Firm 2´s price drop that creates lower average prices. Table 1 shows the percentage
23
change with respect to the no switching cost benchmark for both firms´ prices, demands
and profits. It is clear that Firm 1 charges higher prices, has a higher demand, and has
higher profits than in the no switching cost benchmark, while Firm 2 charges lower prices,
has a smaller demand, and has lower profits. At the same time, this table clearly shows
that Firm 2´s drops in demand, profit and prices are not fully exploited by Firm 1, but that
as substitution to the outside good decreases, Firm 1 is able to profit more from
generating switching costs.
An interesting real-world consideration is that this model helps understand why in
many situations switching costs are very low, or non-existent, by including a fixed cost of
creating switching costs. If these fixed costs exist, it is clear that firms with high marginal
costs of creating switching costs will prefer not to generate them, since in equilibrium the
profit gain for high-θ firms may be smaller than the fixed cost.
In conclusion, it has been shown that in scenarios where firms have the ability to
raise switching costs, they will do so until the marginal benefit of creating this barrier to
switching equals the marginal cost of doing so. While this allows the firm that holds the
customer´s loyalty to raise prices above the no switching cost benchmark, raising its
profits, its rival´s reaction will be to lower prices in order to compete. Whether this leads
to lower equilibrium average prices than in the no switching cost benchmark will depend
on the degree of substitution to the outside good. If an outside good exists, and is a
relevant substitute, the model predicts that average prices will be lower than in the no
switching cost benchmark, while if there is no substitution to an outside good, average
prices will be higher than in the no switching cost benchmark.
VI. Final Remarks.
This work´s main result, that average prices in markets where firms have the ability
to generate switching costs may be higher or lower than in the no switching cost
benchmark, places emphasis on two aspects of this problem: the cost of generating
switching costs, and the degree of substitution to the outside good. It predicts high
switching costs and higher prices than in the no switching cost benchmark if firms have
24
the ability to generate switching costs at no cost and there is low substitution to the
outside good. As the cost of creating switching costs rises, average prices follow a
decreasing then increasing pattern, dropping below the no switching cost benchmark and
then converging asymptotically to this level. At the same time, as substitution increases,
average prices drop below the no switching cost benchmark for lower costs of generating
switching costs, reach their minimum at a lower level, and rise slower towards the no
switching cost benchmark. In a sense, switching costs create a gap between firm´s prices
in this model, but substitution to the outside good disciplines the firm that holds the
customers´ loyalty from raising prices significantly. Instead, the gap is generated more by
the rival firm´s price drop, so average prices fall.
These results appear to be most relevant in situations where there is competition
between two groups of firms, where one of them holds the loyalty of a significant portion
of the market. An example of this situation is competition amongst airline companies in
hubs where a dominant airline exists, as described by Lederman (2008). In these
scenarios, one company offers the largest amount of flights in and out of a particular city,
and therefore its frequent flyer programs are more attractive to individuals who regularly
use said hub. As a result, these customers face an endogenous switching cost of not
traveling with the dominant company. Lederman (2008) finds that when the dominant
company offers a frequent flyer program, its prices, net of other hub effects, rise between
3.5% and 5.2%, which is consistent with this author’s results. It would be interesting to
test whether the prediction of larger price spreads between firms as substitution to the
outside good, in this case other forms of transportation, becomes poorer. This would be
the case as the distance between cities grows, since ground transportation becomes a
worse alternative.
Another empirical application of these results could be markets where a dominant
firm is facing an entrant. In these situations, most or all of the market would presumably
be loyal to the dominant firm, so that consumers would face a switching cost of
purchasing from the entrant. Interestingly, if there is high substitution to the outside
good, these results predict that the entrant could obtain a large fraction of the market,
25
while if there is low substitution to said good, and it is relatively cheap to generate
switching costs, the dominant firm could be able to deter entry by creating barriers to
switching.
This implies that regulatory concerns over firms’ ability to preclude switching by
raising barriers may be unwarranted for cases where a strong substitute good is present,
or when the cost of generating these barriers is high. While these switching costs will
generate rents for the firms that hold consumer´s loyalty, they will not create higher
average prices in these situations. On the other hand, when substitution to other goods is
not a relevant option, or when the cost of generating switching costs is low, regulatory
concerns may be warranted. This distinction is interesting because most of the public
policy recommendations surveyed, such as Baker (2007), Stenner and Tangeras (2007),
and Xavier and Ypsilanti (2008), stress that switching costs are detrimental to competition,
raising prices, and that regulatory interventions designed to lower switching costs are
necessary.
An example of regulation of switching costs in markets where substitution to the
outside good is probably low is Fazio and Stern´s (2000) review of the Department of
Justice´s ruling on the merger of two relational database management software
companies, Bortland International and Ashton-Tate Corporation. In this case, the ruling
stated that both firms could merge, provided they opened their database standard to the
industry. Since database standards are usually purposely incompatible, so that a customer
that switches from one company to another must rebuild its database, this market
exhibits high switching costs. By requiring the merged company to open its standard,
meaning that any firm can have access to its code, compatibility was induced and
switching costs from Bortland/Ashton-Tate to other firms were lowered. In this case,
regulatory intervention was in line with the previously mentioned results, since a firm that
requires database management services probably has no outside alternative.
These results also imply that estimation of switching cost levels, measures of
substitution to other goods, and of costs of creating switching costs are crucial towards
26
determining which of the predicted outcomes is empirically relevant. Therefore, it is clear
that this model predicts that regulation should be preceded by a careful investigation, in
order to ensure that switching costs that lower average prices are not eliminated. This
appears to be an interesting topic for future research.
In summary, this author finds that in differentiated goods markets where firms do
not have the ability to price discriminate between old and new customers, if firms have
the ability to generate switching costs, so their customers face a disutility of purchasing
from a rival firm, they will raise said costs until this action´s marginal benefit equals its
marginal cost. However, this ability does not imply that prices rise dramatically; in fact, for
many relevant cases, average prices may be lower than in the no switching cost
benchmark. Whether this is the case or not depends on the degree of substitution to
other goods, so that if firms face relevant competition from outside the market, switching
costs that disincentive inside-the-market switching will not eliminate switching to other
goods, and on the cost of creating switching costs. Therefore, it has been shown that
whether endogenous switching costs will create significant price increases in
differentiated goods markets is more an empirical matter than a theoretical one.
27
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29
Appendix I – Figures and Tables
Figure 1 – Nesting Discrete Choice Models in a Standard Utility Maximization
Standard Profit Maximization
Max Ut(x1,x2,…,xn,y)
s.t. px+pyy ≤ m
y is the discrete choice good
y*=1
y*=0
Consumer chooses amongst J
providers of y, and an outside option.
Consumer distributes her budget
purchasing the other goods in her
choice ser.
y = max{U(y1),U(y2),…,U(yJ),U(y0)}
Figure 2 - Evolution of Prices as Switching Costs Rise
30
Figure 3 – Evolution of Demands (Choice Probabilities) as Switching Costs Rise
Figure 4 – Evolution of One Period Profits as Switching Costs Rise
31
Figure 5 – Evolution of Firms’ Present Value as Switching Costs Rise
Figure 6 – Firm 1´s Percentage Increase in Price, Market Share, and Profit with Respect
to the No Switching Cost Benchmark
32
Figure 7 – Firms´ Prices with Endogenous Switching Costs
Figure 8 – Equilibrium Switching Cost Levels
33
Figure 9 – Firms´ Demands (Choice Probabilities) with Endogenous Switching Costs
Figure 10 – Firms´ Profits
34
Figure 11 – Equilibrium Prices with Endogenous Switching Costs, for a Lower Level of the
Outside Good Utility Intercept
Figure 12 – Firms´ Demands (Choice Probabilities) for a Lower Level of the Outside Good
Utility Intercept
35
Figure 13 – Firms´ Expected Profits for a Lower Level of the Outside Good Utility
Intercept
Table 1 – Percentage Variations in Prices, Demands and Profits for Both Firms
δ0 = 0
% Price Change
Theta Firm 1
Firm 1
% Profit Change
% Price Change
% Demand Change
% Profit Change
Firm 2
Firm 1
Firm 2
Firm 1
Firm 2
Firm 1
Firm 2
Firm 1
Firm 2
5,33% -44,63% 22,26%
-100,00%
31,28%
-100,00%
26,15%
-54,38%
36,58%
-100,00%
82,86%
-100,00%
0,05
1,60%
-6,06%
6,98%
-29,69%
9,35%
-35,58%
15,16%
-21,57%
23,74%
-56,06%
48,05%
-68,34%
0,1
0,93%
-3,70%
4,15%
-17,46%
5,50%
-21,68%
10,03%
-15,69%
16,65%
-36,85%
31,81%
-49,69%
0,15
0,66%
-3,67%
2,95%
-12,33%
3,89%
-15,55%
7,27%
-12,03%
12,46%
-26,68%
23,06%
-38,11%
0,2
0,51%
-2,07%
2,28%
-9,53%
3,00%
-12,12%
5,64%
-9,67%
9,86%
-20,69%
17,88%
-30,62%
0,25
0,41%
-1,69%
1,86%
-7,76%
2,45%
-9,92%
4,58%
-8,05%
8,11%
-16,82%
14,53%
-25,49%
0,3
0,35%
-1,44%
1,57%
-6,54%
2,06%
-8,40%
3,85%
-6,88%
6,88%
-14,14%
12,21%
-21,80%
0,35
0,30%
-1,24%
1,36%
-5,66%
1,78%
-7,28%
3,32%
-6,00%
5,97%
-12,19%
10,52%
-19,02%
0,4
0,27%
-1,10%
1,20%
-4,98%
1,57%
-6,42%
2,91%
-5,32%
5,26%
-10,70%
9,23%
-16,86%
0,45
0,24%
-0,98%
1,07%
-4,45%
1,40%
-5,75%
2,59%
-4,78%
4,71%
-9,53%
8,22%
-15,13%
0,5
0,21%
-0,89%
0,97%
-4,02%
1,27%
-5,20%
2,33%
-4,34%
4,26%
-8,59%
7,41%
-13,73%
0
Firm 2
% Demand Change
δ0 = -2
36
Appendix B – Numerical Algorithms
For detailed information on the numerical algorithm used to solve DHR’s model,
see DHR’s Appendix E.
This work´s algorithm solves for both firm´s prices and levels of switching costs
created in two different states: when Firm 1 holds the customer´s loyalty, or state 1, and
when Firm 2 holds it, or state 2. The solution imposes symmetry, so that the price charged
by Firm 1 in state 1 (P11) is the same as the price charged by Firm 2 in state 2 (P22), and
also that the price charged by Firm 1 in state 2 (P12) equals the price charged by Firm 2 in
state 1 (P21). This is reasonable, since Firm 1 in state 1 is the same as Firm 2 in state 2,
and Firm 1 in state 2 is the same as Firm 2 in state 1. Also, it assumes that the switching
cost charged by Firm 1 in state 1 (SC11) equals the switching cost charged by Firm 2 in
state 2 (SC22).
1. Formulate an initial guess for P11, P12, P21, P22, and the switching cost charged by
Firm 1 in state 1 (SC11) and by firm 2 in state 2 (SC22). These initial guesses will be called
P110, P120, P210, P220, SC110, and SC220.
2. Maximize Equation 12 for Firm 1 with respect to P11 and SC11, substituting the initial
guesses for P12, P21, P22, and SC22. The values of P11 and SC11 obtained will be referred
to as P111 and SC111. By symmetry, let P221 =P111 and SC221 = SC111.
3. Maximize Equation 12 for Firm 2 with respect to P21, substituting P111, P221, P120,
SC221 and SC111. Call the value of P21 that maximizes this equation P211, and by
symmetry let P211 = P121.
4. Repeat steps 2 and 3. For every repetition, substitute for prices and switching costs
using the most recently obtained values from previous maximizations. Stop if the
Euclidean distance between the two most recent guesses for all prices and switching costs
is smaller than ε.
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