Download Buyer Search Costs and Endogenous Product Design

Buyer Search Costs and Endogenous Product Design
∗
Dmitri Kuksov
[email protected]
University of California, Berkeley
August, 2002
Abstract
In many cases, buyers must incur search costs to find the price of a product. This
search cost affects the behavior of consumers, and through that, it affects the profit
maximizing behavior of the firms. As search costs change, so do the competitive
marketing mix strategies of the firms. In predicting the effect of changing search
costs on the equilibrium prices and allocations, it is important to take all effects into
consideration. Through a model of buyer and seller behavior in the presence of buyer
price search costs and seller uncertainty about the demand, I consider the effects
of changing search costs on prices when product differentiation is fixed and when
it is endogenously determined in equilibrium. While keeping product differentiation
constant, lower buyer search cost for prices leads to lower equilibrium prices. At the
same time, lower search costs also lead to higher incentives for the firms to invest in
differentiating product design. The resulting higher level of product differentiation
decreases the effects of lower search costs on prices, so that lower buyer search costs
for prices may even lead to higher prices. Moreover, the overall effect of lower search
costs on social welfare may be negative, and the effect on the industry profits may
be positive. The result is especially interesting because recent technological changes,
such as the Internet shopping, may be affecting the market structure mostly through
lowering buyer (consumer) search costs.
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Introduction
Many technological changes affect the economy and the market equilibrium not only through
affecting the production and distribution costs and availability of new products and services, but also through affecting the informational structure of the market and the type
∗
A rough draft, comments welcome
1
of interaction between market agents. Namely, technological advances change the amount
and costs of information available to consumers, producers, and other market agents. Such
changes in the informational structure of the market may affect equilibrium outcomes both
directly, through their effects on buyer utility functions and seller prices, and indirectly
through affecting other market structure parameters, such as the number of the firms in
the market, vertical and horizontal contracts, and product design. In other words, the
indirect effect is through the effect on the parameters that are constant in the short term,
but, in the long run, are determined by market agents as well. Not accounting for these
indirect effects may produce misleading results. As noted by Stiglitz (1979),
“It is important to recognize that market structure is itself an endogenous
variable, a result (at least in many cases) of natural barriers to entry and
incentives to agglomerate, some of which are related in an essential way to the
cost of information.”
Search costs for price exist in many markets and in an essential way contribute to
profitability of the market environment. However, the effects of search costs on all decisions
by the firms have not been fully understood. In this paper, I consider the implications of
buyer search costs for price on the product and price decisions by the firms in the presence
of incomplete information.
To give an example, let us consider the Internet. When e-commerce was in the early
stages, most people advocated that the Internet will reduce prices, erode profits, and increase consumer surplus by making markets more efficient and competitive and bringing
market outcomes closer to the theoretically predicted (Bertrand equilibrium) outcomes.1
“...industry titans, such as Bill Gates, ..., regale the world’s leaders with the
promise of ‘friction free capitalism.’”
— The Economist, May 1997
“The result [of the Internet] is fierce price competition, dwindling product differentiation, and vanishing brand loyalty.”
— Business Week, May 1998
1
The following two quotes are reprinted from Brynjolfsson and Smith (1999).
2
The same predictions were supported in the academic literature (e.g., Wernefelt (1994),
Alba et al. (1997), Bakos (1997), Brynjolfsson and Smith (1999)). The way this argument
works is the following. When people think about what the Internet brings to the marketplace, one thing that immediately comes to mind is that the Internet reduces buyer search
costs. On-line search engines and shopbots are especially useful if one searches for digital
attributes such as the price. Therefore, buyers are better informed about prices. Now a
firm would lose a larger fraction of the demand if it raised the price, and on the other
hand, it is sufficient for a firm to undercut the competitors just by a little bit, to gain a
large market share. This leads to higher competition and lower prices. As a result, buyers
are better off. Further, price dispersion is predicted to become lower as in the absence of
frictions, the market prices should become closer to the perfectly competitive price. Social
welfare increases both due to lower deadweight monopoly loss and due to probably lower
total waste on search. The expectation that the total expenditure on search may be lower
is based on the optimal search behavior when the cost per search and the price dispersion
decrease (Stigler (1969)). Finally, if the decrease in prices is not offset by large decrease in
the fixed costs of retailing, profits decrease.
The empirical evidence is contrasting the above predictions. Price dispersion on line is
considerable (Iyer and Pazgal 2002). In fact, Smith and Brynjolfsson (1999) and Clemons,
Hitt, and Hann (2000) show that price dispersion online is larger than off line. Further,
in some categories, prices are not close to marginal costs. Some consumers comment that
they actually spend more on search on the Internet than they used to spend off-line, which
again, indirectly, supports the notion that online price dispersion is higher. The valuations
of internet stocks, though much lower now than at their peak, still do not support the idea
of complete erosion of profits in on-line competition.
Missing in the above arguments is the consideration of the endogenous effects of lower
search costs on the market structure, e.g., changes in the products offered by the firms.
Prices and price competition have been studied, but this is not a complete picture. The
complete picture includes effects of search costs on all decisions by the firms. One needs to
examine the situation in more detail. It is important to have a good understanding of the
process through which search costs affect the market in its entirety: products and prices
alike. The model in this paper shows, in particular, how the consideration of the effects of
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lower search costs on prices and products reconciles the fact that consumer search costs for
price may decrease with the observation that the price dispersion increases and investors
expect high profits in the electronic marketplace.
Through explicit modelling, I consider how the interaction between incomplete seller
information about the demand and buyer search costs for price results in an equilibrium
intermediate between Bertrand and monopolistic pricing equilibrium, where the equilibrium
price smoothly increases with search cost.
I further use this framework to analyze the effect of changing search costs on the equilibrium pricing, profits, and the welfare related variables with and without endogenous
changes in the products being offered. I find that not accounting for endogeneity of product
development may lead not only to quantitative, but also qualitative (directional) mistakes
in the analysis of the effect of the level of search costs on price, profits, consumer surplus,
and social welfare.
I find that, in general, product differentiation increases as search costs decrease. This
result is consistent with the common belief that search costs and product differentiation are
substitutes, or, in other words, with the statement that search costs to some extent play a
role of product differentiation. Moreover, if product differentiation is endogenously determined by sellers through either cooperative or individual investment, then depending on
the cost of the product development, the endogenous investment in product differentiation
may more than counteract the increase in competition due to lower search cost for price.
Further, especially if the product differentiation efforts do not increase the valuation of the
products by the consumers, the resulting change of social welfare due to lower search costs
may actually be negative. It is even possible that when search costs decrease, all agents
become worse off.
Search costs and product differentiation decreases competition between firms. In that,
the two concepts appear similar. However, they are fundamentally different in their nature and the mechanism by which they affect the market. First, search costs are related
to the lack of information, whereas differentiation is related to the preferences of agents
involved. That is, search costs are about the availability of information, and differentiation
is about the preferences based on the information present. Second, if the search costs are
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the same for each agent, the population may be homogeneous in the presence of search
costs. Contrary to this, if agents preferences are the same, there is no differentiation;
i.e., differentiation requires differences in preferences, whereas search costs do not require
any differences between agents. In particular, I consider the situation where search costs
do not vary with the individual. Theoretical literature considered different dimensions of
differentiation as substitutes (Iyer(2002)) as well as interaction of asymmetric information and differentiation (Villas-Boas and Schmidt-Mohr (1999)). This paper examines the
connection between search costs and endogenous product differentiation.
Stiglitz (1987) provides an example of the different effects that search costs and differentiation produce on the market equilibrium: with differentiated market, higher number of
firms result in higher competition, whereas in the presence of search costs, higher number
of firms may result in lower competition. Therefore, in order to understand the impact of
search costs on the market outcome, it is important to carefully model the effect of the
search costs.
The results of this paper have important managerial implications, since they help to
predict the competitive environment on-line or anywhere where a change in buyer search
costs is expected, and therefore help the firm to better develop its business strategy. For
example, firms that consider entering a particular industry that is in the process of technological change need to estimate the changes to the industry structure. Also, a social
planner needs to take all the implications into account when deciding which technological
changes to support or hinder.
The rest of the paper is structured as follows. The next section presents the intuition
for the model of how search costs affect the equilibrium prices and product differentiation
that I will use in this paper. Next, in Section 3, I present the formal model, followed by
examples of a business environment (Section 4) where the assumptions of the model are
likely to be well matched by reality. Then, I solve the model with and without product
differentiation (Sections 5 and 6). In Section 7, I endogenize product differentiation by
introducing the cost of product development, which allows us to consider the changes
in model predictions that considering product differentiation as endogenous could bring
(Section 7.3). This is followed by a discussion of the model extensions in Section 8, and
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some preliminary empirical evidence in Section 9 that confirms that when search costs
decrease, product differentiation tends to increase. Section 9 also contains an empirical
test of increasing dependence of differentiation on search costs. The product differentiation
time series data across different categories is obtained utilizing the Consumer Reports.
Section 10 concludes.
2
Effect of Search Costs and Differentiation on Competitive Equilibrium Prices
In order to consider the effects of changing search costs on firm’s decisions, one first needs
to understand how search costs affect the market equilibrium. The general idea is that
consumer search and awareness of competitor prices does not allow a firm to raise its price
much above the market price.
In a monopoly setting, a firm sells the product to a given consumer as far as the
consumer’s expected utility from the product is above the price charged. In a competitive
setting, a consumer buys from the firm if two conditions are satisfied: first, as in the
monopoly case, consumer expected utility has to be higher than the price, and second,
consumer should not view further search for a better price justified by the chances of
getting a better deal put together with the cost associated with the search.
From the firm’s perspective, in a monopoly setting, the price is restricted by consumer
valuations, and in a competitive setting, the price is additionally restricted by the expected
distribution of competitor prices in relation to the buyer search costs, which I will further
call the search constraint.
If a firm has complete information about the costs and valuations of consumers and
firms, then it can predict competitor prices. In reality however, a firm may not know what
the competitor prices are because it does not know, for example, the assumptions the other
firms make about the demand. Therefore, if there is a possibility that another firm thinks
that the optimal price is lower, every firm may worry that its consumers may leave to the
other firm.
Product differentiation decreases competition because if products are differentiated,
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offering a lower price is not enough to switch consumers from one firm to another, since
consumers must be reimbursed for the adjustment to fit as well. Now a consumer will search
for a better price when the benefit of a possibly lower price is high enough in relation to
both search costs and the lower fit (I assume that consumers know their fit to products
better than the prices since prices are changed more often than physical attributes of the
products). Therefore, with high differentiation, search becomes a smaller constraint. This
leads to higher prices, and the effect may propagate recursively. The intuition is that not
only each firm itself fears less of the competitor’s possible lower price, but also each firm
expects the competitor to charge a higher price for the same reason.
Lynch and Ariely (2000) has shown in an experiment that, in a competitive setting,
there is benefit of accenting product attribute information, which can be argued to be
differentiating between products by providing information that is different across products.
But just noting that product differentiation is beneficial in the competitive environment
does not answer the question whether firms should invest more in product differentiation
when the search costs are falling. One needs to know not only whether there is a benefit
of differentiation, but also whether the benefit increases when search costs are lower. The
above consideration allows to make predictions in this direction as well. I argued that
product differentiation leads to ability of the firms to charge higher prices. Since lower
search costs lead to lower competitive prices and the profit function is concave due to
downward sloping demand, the benefit of the increase in prices is higher when the original
price level is lower, i.e., when the search costs are lower.
In the next sections, I introduce a formal model of competition in the presence of search
costs and possible differentiation. The formal model allows one to see exactly how the above
intuition applies, and allows one to speculate on the relative size of the effects involved, so
that one can hypothesize on the balancing effects of lower search costs in the presence of
endogenous product differentiation on profits and consumer and social welfare.
3
The model
Consider a market consisting of two sellers selling a homogeneous or differentiated good to
a number of buyers. Each buyer knows her valuation of the product. The valuation can
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also be interpreted as the expected valuation in the case the valuation is uncertain and the
consumer has no means of finding the exact valuation, or in the case when the cost of finding
the exact valuation is prohibitive. The fact that consumers may know their valuation of
the product, but not the price comes from the reality that prices can be (and are) changed
frequently, whereas product design that affects the valuation can not be changed too fast.
For a discussion of search for multiple attributes of the products in an online environment
see Lal and Sarvary (1999). This model could also be applied to situations where search for
product valuation information precedes search for price. If search for valuation (consumer
fit) and search for price are bundled (as in Bakos (1997)), the results may be subject to
distributional assumptions (see Fath and Sarvary (2001)).
Buyers have a single unit demand, all buyers and sellers are risk neutral, and each buyer
knows one price to start with.2 The cost s of finding the second price is the same for each
consumer. A buyer has search cost associated with finding the price at any of the sellers,
and can not buy the product at a seller without incurring the search cost associated with
that seller. The later assumption reflects the idea that buyers may not be able to buy
without incurring the cost of finding the price since they have to agree to pay the price
to complete the transaction, or, explained alternatively, the search for the price includes
the search for location. Also, no transaction can be complete before the price is known,
and hence the cost of obtaining the price can not be more than the cost of making the
transaction.
The sellers have equal and constant marginal cost of the product, which is normalized
to 0.3 Sellers are uncertain about buyer valuations. This uncertainty can be interpreted in
different ways. One can think of one buyer market when one buyer comes to the seller and
the seller has to name the price based on what it can see about the buyer. Alternatively,
one can think of a market with many consumers and with the aggregate demand function
is not perfectly known to the firm. The demand function is known to sellers up to a certain
2
The rationality of at least one search, resulting in one price being known, can be explained, for example,
by a downward sloping buyer demand, so that the purchase of the optimal amount (further known as the
unit of the good) at the linear monopoly price leaves the buyer with enough surplus to cover the search
cost. It can also be that at least one price quote is discovered during the time the buyer is looking for the
product related information.
3
The key results would not change if the marginal cost is allowed to be variable.
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Segment 1
Firm 1
Segment 2
t
V = V or V
or
Firm 2
Figure 1: Consumer preference space.
seller specific error. A part of the information that the sellers use, can be commonly
known to both sellers, but sellers can also differ in the type or amount of information
about the demand they privately receive, or in the way they handle the information. Some
imperfect information about the way different retailers use the knowledge they possess can
be modelled as a form of incomplete information. For example, if a retailer does not use
certain types of information for decision making, it behaves as if it doesn’t receive that
kind of information.
I model this informational structure by assuming that the buyer valuation is based on
one valuation parameter V representing the general valuation level. Individual consumers
have valuations that depend on V and their individual fit to the particular product. Sellers
have a common prior on V , which I assume for simplicity to be either high V or low V
with equal probability. Further, each seller j has individual data or beliefs of demand,
represented by the signal xj of buyer valuation parameter V . For simplicity, I assume that
the signal x given the valuation parameter V can either provide the seller with the exact
valuation, or be completely non-informative with equal probability. In the first case, I
denote the signal by the valuation level, i.e. I write x = V , in the second case, I denote
the signal by the empty set: x = ∅. Signals are independent across firms. Summarizing,
(
V, Prob. 1/2,
(x|V ) =
∅, Prob. 1/2.
I model the distribution of consumer preferences through a distribution of consumer
ideal points, where the individual valuation depends on the distance of the consumer ideal
point from the position of the product (as in the perceptual map). To simplify matters, I
assume that given the valuation parameter V , there are two equal consumer segments at a
distance t from each other. Namely, one values the product at V , the other at V +t (product
is located at one of the ideal points), the total consumer mass is normalized to one. The
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time
Prior,
design
Nature draws
V and s
xj
price
buyer dec.
profits
Figure 2: Timing.
structure of consumer heterogeneity is generalized in the Appendix, where I consider the
case of uniformly distributed preferences (as in Hotelling model). The full possible space
of consumer ideal points is represented by Figure 1.
Product design (or positioning) decision by a firm is the decision of the choice of the
position of the product in the space of the consumer ideal points (product space) subject to
production (cost) constraints. The simplest form of the product design problem is whether
to position the product at one or the other ideal point depending on the positioning of the
competitive product and the cost of design.4
The degree of uncertainty a seller has is represented by the difference between the
possible values of the demand parameter V that can exist given the firm’s knowledge, i.e.
by δ = V − V .
Finally, timing of the game is as follows (see Fig. 2). Initially, sellers have the common
prior on buyer valuations. The number of buyers and sellers is also common knowledge.
If endogenous product design is considered, then the next step is sellers (simultaneous)
decision on the product design. Then both sellers and buyers learn the decisions of sellers
on product differentiation (so that buyers know their valuation of each product, and sellers
have the common prior on buyers valuations of each product). Next, sellers receive the
individual signals xj of demand (private knowledge to seller j, but there is common knowledge on distribution of xj ’s), and simultaneously set prices for their products. Finally,
buyers decide whether to search and which product to buy (if any). The buyers decision on
purchase define the final buyer (consumer) surplus and seller (profit) payoffs of the game.
4
One can also consider the case when a firm’s differentiation efforts result in increasing consumer
heterogeneity, i.e. when firms are located at 0 or 1, but the value of the parameter of heterogeneity t
increases. Advertising campaign explaining the differences between the products may act as such product
differentiated effort. The implications of such a model are similar.
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The assumption that the firms decision on the product design precedes the decision
on prices and also precedes the signals xj is realistic due to long time necessary to design
products and implement the design in practice.
To simplify calculations, assume that the uncertainty and consumer heterogeneity is
not too large, so that a monopoly would serve buyers of all possible valuations. Without
this assumption, the monopoly price may not be an increasing function of the expected
demand.
4
Examples of the marketplace
4.1
Business to Business markets
Let us consider an example where the above model directly applies. Consider a B2B market
with several producers and N industrial buyers, such as, for example, the market of airplane
engines. In such a market, the price is subject to individual negotiations, i.e. sellers have
the ability to discriminate between buyers.
Assume that the marginal cost is constant in the possible demand range, so that the
supply is not limited and therefore, buyers are not competing for products, but rather
sellers are competing for each buyer. Then the market is equivalent to N separate markets
with several sellers and one buyer. The price is normally set after a one-on-one negotiations
of a buyer and a seller.
When the final price is set by the seller, the seller is uncertain about the private valuation
of the buyer. The negotiations can be thought of as the process from which the seller
extracts the signal xj of the buyer valuation. Naturally, the buyer knows its valuation, and
seller needs to use its best guess of buyer’s valuation to offer the price. During negotiations,
by suggesting high prices, the seller may try to elicit the buyer valuation, and the buyer
may try to respond in such a way that seller thinks the buyer is of low valuation. In any
case, since the negotiations do not oblige neither buyer nor seller to commit, they can
only be used by the seller as information for the final offer. The information obtain in the
negotiations is used by the seller who makes the final “take it or leave it” offer. Hence, all
the negotiations reduce to the signal xj of buyer valuation that the seller receives.
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As it takes negotiations to find out the price of a seller, and the price depends on the
signal xj that the seller receives during these negotiations, sellers can not find out the price
the other sellers will set with certainty. In this example, the search cost is the cost of
negotiating with the seller to obtain the best offer.
4.2
Retail Markets
In a retail setting, stores differentiate from each other through a variety of factors such as
store interior design, convenience, vertical contracts and reputation to sell a particular set
of products at attractive prices, product assortment and the choice of brands, freshness
(groceries), etc.
This differentiation through product and physical store design are obvious examples.
Other strategies, such as vertical contracts and switching costs, can also be considered as
creating differentiation between stores. When retailers enter into different vertical contracts
with manufactures, the contracts and resulting cost structure forces retailers to behave in a
particular an predictable way that is observed by consumers and therefore retailers become
differentiated. Switching costs contribute to the creation of segments of loyal consumers
that may have systematic differences across stores, and again, lead to different and predictable pricing strategies pursued by the firms. Differentiation may also be created by using different strategy in making product information accessible to consumers. Zettelmeyer
(2002) considers firms differentiating in that dimension in the online environment. Firms
may also provide different product return policies. A larger variability of return policies on
the Internet (Wood (2001)) is consistent with the predictions of this section.
One might think that one store may check the other store’s prices, and therefore get
a better idea of whether its prices are being undercut. However, in a typical supermarket
grocery shopping context, the decision of consumers whether to search often depends on
their expectations of store prices on a bundle of goods, a bundle, contents of which may not
even be known to the seller. Therefore, it is difficult for a store to observe if the other store
is undercutting its prices. Furthermore, if there are other costs that consumers absorb (like
ease of highway access, parking, check-out lines, etc.), it may not be clear which retailer is
cheaper from a consumer point of view.
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Segment 1
Firm 1
Segment 2
t
V = V or V
Firm 2
Figure 3: The case of homogeneous goods.
5
The Model with Homogeneous Goods
I start with considering the model without product differentiation, followed with the model
with exogenously set differentiation. The comparative statics between the two cases with
defined timing and cost of product design will allow me to endogenize the product design.
If both firms are located at the same point, we have a model with homogeneous goods
(see Figure 3).
Proposition 1. There is a unique symmetric equilibrium in the above model with homogeneous goods. In the equilibrium, consumers do not search, and the price is determined by
the following rule:
(
V
p(x) =
min{V + 2s, V }
if x = V or x = ∅,
otherwise.
Proof. Existence. The above stated price rule is an equilibrium one because: if x = V , then
the valuations are V and V + t, and by assumption of the model, firm prefers to receive
demand of 1/2 with price V (from a random half of the buyers) to demand 1/4 with price
V + t (from a random half of the buyers of higher valuation), which is the highest demand
it can hope for at the price above V due to buyer valuations. At the same time, there
is nothing to be gained by reducing price, since buyers do not search. The same analysis
shows that p(∅) = V is optimal.
If x = V , the firm knows that consumer valuations are V and V + t. However, there
is 1/2 chance that the other firm has ∅ signal, and hence sets price V . Let p be the price
charged by the firm (after receiving signal x = V ). Then a consumer has to decide whether
to search for a better price. Since the other price is V with probability of (at least) 1/2,
the benefit of search for the buyer is at least
1
(p − V ).
2
13
The buyer compares the benefit of search with the cost of search s, and searches if and
only if the benefit of search outweighs the cost of search. This means that if the firm sets
price above V + 2s, buyers will search. If buyers search, the demand is 0, as they find a
better price (the price of the other firm is either V or V + t according to the equilibrium
strategy). Therefore, price can not exceed V + 2s. Also, due to consumer valuations, price
above V is suboptimal as it results in no profit. At the price of min{V + 2s, V } or below,
consumers do not search and buy. Hence there is no reason for the firm to reduce the price
below min{V + 2s, V }.
Lastly, it is optimal for consumers not to search as far as the price does not exceed
V + 2s. Hence the above is an equilibrium price strategy.
Uniqueness. To see that the above equilibrium price is the unique symmetric equilibrium
price strategy, note the following.
1) Lowest offered price can not be below V . This is due to the fact that if the firm
charges an ε < s above the lowest possible price offered in an equilibrium, consumers will
not search. If this price is below V , consumers will buy. Hence a firm that is considering
to offer the minimal price below V is better off if it raises the price by ε < s, and hence no
firm charges below V .
2) The price is set so that consumers do not search. If one consumer finds it optimal to
search, then all do. If consumers search, there is at least 1/2 chance that they leave. By
assumptions, a firm will not forego 1/2 demand for the maximal increase of price from V
to V .
3) If x = V or x = ∅, the firm sets p = V . The firm does not offer a higher price due to
consumer valuations, since the demand has the same shape as monopoly due to no search
by consumers and consumers do not search if p ≤ V by 2).
4) If x = V , the price is determined uniquely by the “no-search condition” x ≤ V + 2s
and valuation V of half of the consumers.
The following proposition summarizes the properties of the equilibrium price.
Proposition 2. In the above model with homogeneous goods, if 2s ≤ V − V ,
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1. The expected equilibrium prices and profits are smoothly increasing in s
2. If s increases above a certain level, prices become monopolistic.
3. As s decreases to 0, prices approach the price under the lowest possible belief on
consumer valuation.
4. Equilibrium price dispersion increases in s.
5. The aggregate (over possible valuations) buyer surplus is smoothly decreasing in s.
6. Social welfare does not increase in s.5
Proof. The expected (before the signal x is known) equilibrium price is
s
1
3
Ep = V + (V + 2s) = V + ,
2
4
4
and the average across a priori possible consumer valuations buyer surplus is
V − V − 2s
1
1 1
1
EBS = · 0 +
· 0 + (V − V − 2s) =
.
2
2 2
2
4
The first two claims of the proposition immediately follow from the above formulas.
Social welfare in this model does not change with s, as price only affects the allocation
of surplus.
The equilibrium price dispersion is 0 in the case of low valuation (since signals are x = V
or x = ∅) and possibly 2s in the case of high valuation. The a-priori expected variance
of price dispersion is (2s)2 /4 = s2 , which increases in s. Prices become monopolistic as s
becomes higher than V − V . The last claim follows since when s & 0, the highest possible
price V + 2s approaches the lowest possible price V .
5
If the first search is free, then there is no impact of s on the social welfare, since prices in this model
only affect the division of the surplus as even the monopoly price is such that all buyers buy. In a more
general model with a possibility of some deadweight monopoly loss, social welfare would increase when
prices decrease. This situation occurs when the model is extended to heterogeneous buyers, which will be
considered in the next section. Also, if the first search is costly, then lower search costs would imply lower
waste on search and therefore, higher social welfare.
15
Segment 1
Segment 2
t
V = V or V
Firm 1
Firm 2
Figure 4: Differentiated goods product preference space.
It can also be noted from the proof of the equilibrium that the equilibrium price schedule
in Proposition 1 remains an equilibrium price schedule if the number of sellers in the market
is not restricted to two. Also note that the predictions of the model are consistent with
general beliefs about the effects of search costs on the equilibrium prices, profits, and buyer
surplus.
The statements 1-3 of Proposition 2 indicate how Diamond paradox can be resolved if
sellers don’t have complete information about the demand. Kuksov (2002) shows how even
a small amount of private uncertainty can resolve Diamond paradox if common knowledge
is lacking. Empirical evidence in support of statement 4 of the above proposition in the
online environment is conflicting (see Brynjolfsson and Smith (2000)). We will see in
section 7 that if product differentiation is endogenous, there are conditions under which
price dispersion decreases as search costs increase. We will also see that statements 4 and
5 may not hold if product design is endogenous.
6
Differentiated Products
I model differentiated products by assuming that one firm’s product is located at the ideal
point of one segment of consumers and the product of the other firm at the ideal point of
the other segment. In this case, the product/consumer space can be represented by the
following diagram (Figure 4).
In this model of differentiation, one consumer segment values one product at V or V
and the other product at V + t and V + t respectively, and the other consumer segment
values the first product at V + t or V + t and the other at V or V respectively. Therefore,
a price differential of t is required for a given segment to consider the products as perfect
alternatives.
16
Another form of differentiation one may consider is positioning of the product closer to
the ideal points of consumers in a certain valuation case, i.e. moving the position of the
product in the horizontal dimension of the above figure. Also, one can think of informative
advertising or general product level research that shows comparative benefits of different
products (as in pharmaceutic products) as changing the distance between the ideal points
of different segments, i.e. increasing the value of t in the above figure. Both approaches
lead to conceptually same conclusions as related to the effects of endogenous vs. exogenous
product differentiation discussed below.
The case of “partial” differentiation, where a firm moves its product a part of the
way from the ideal point of one segment to the ideal point of the other segment requires
consideration of asymmetric equilibria but leads to conceptually same conclusions.
6.1
Solution of the Model with Differentiated Products
Proposition 3. There is a unique symmetric equilibrium in the above model with differentiated products. In the equilibrium, consumers do not search, and the price is determined
by the following rule:
(
V +t
p(x) =
min{V + 2t + 2s, V + t}
if x = V or x = ∅,
otherwise.
Proof. The proof of this proposition follows the same proof as that of Proposition 1. Note
two differences: the first is the minimal level of prices is raised to V + t. This is due to the
fact that consumers search at the best fitting location first. This is the equilibrium behavior
in any symmetric equilibrium since the expected (by consumers) price distribution at both
stores is the same, and hence the better fitting firm provides a higher (by t) expected
surplus.
Secondly, in order to ensure no search by consumers in the case of high valuation (signal
x = V ), it is enough to make a price differential of at most t + 2s (in contrast with the
no differentiation case, where a price differential for no search had to be 2s). This is
obtained as follows. In the case of differentiated products, a buyer compares the net utility
of purchasing at the firm 1 with the possible net utility of a purchase at the firm 2 and
the search cost s. Let Vj be the valuation of a buyer at the firm j. As in the case of no
17
differentiation, if firm 1 received a signal x = V , there is probability 1/2 that the other
firm received signal ∅ and sets price V + t. Also, the valuation of the buyer of the other
product is t less than valuation of the product of firm 1 (as was noted before, buyers first
search at the firm that provides better fit). Therefore the expected benefit of search is
1
1
((V2 − V − t) − (V1 − p)) = (p − 2t − V ).
2
2
In order that buyers would not search in the equilibrium, it is sufficient to set price such
that the benefit of search above is no more than s. Hence, consumers don’t search in the
equilibrium if the price is as high as V + 2t + 2s, which is t + 2s higher than the other
possible price (p(∅)).
In this model, the assumption that once the price is known by the consumer, the
consumer can search at a different firm at a cost of s and then return to the first firm at a
zero cost becomes important for the equilibrium price formula. However, if the consumer is
required to pay additional s to return, the results will be conceptually the same, since the
only difference would be that min{V +2t+2s, V +t} is substituted by min{V +2t+3s, V +t}
in the above formula for p(V ).
Note that irrespective of consumer search, the prices are raised by t due to a better fit.
The better fit leads to an increased social welfare, which is fully extracted by the firms.
6.2
Exogenously Differentiated Products: Results
The implications of the model with (exogenously) differentiated products are similar to
the implications of the model with homogeneous goods. Namely, we can formulate the
following proposition.
Proposition 4. In the above model with differentiated products, if 2s ≤ V − V − t,
1. The expected equilibrium prices and profits are smoothly increasing in s.
2. The aggregate (over possible valuations) buyer surplus is smoothly decreasing in s.
3. Social welfare does not increase in s.
18
4. Equilibrium price dispersion increases in s and t.
5. If s increases above a certain level, prices become monopolistic.
6. As s decreases to 0, prices approach the price under the lowest possible belief on
consumer valuation.
Proof. The proof follows from the formula for the equilibrium price rule just as in Proposition 2.
Note that if t > V − V (i.e. differentiation is higher than uncertainty about the valuation), then the prices do not depend on search costs and are as if firms would collude.
7
Endogenous Product Differentiation
To model endogenous product differentiation, we have to allow firms to develop the products
at a certain stage, and specify the possible product space and costs of positioning products
at different locations in the product space.
7.1
The Model of Endogenous Product Design
I model endogenous product design as follows. At the beginning, a generic product (in this
case, generic just means a product that has already been developed and neither firm has
proprietary rights on it) is available for both sellers for future sales. This product is located
at the ideal point of one of the consumer segments. However, there is also an option to
design another product that is located at the ideal point of the other segment.
At the point the design decision must be made, both firms have the common prior on
the buyer valuation parameter V . Either firm has the option to invest and develop the
other product at a cost C.6 After the decision on developing the product is made by the
firms, both the firms and buyers learn about the existence and valuation of the new product
6
One can also consider an incumbent firm selling the generic product, and an entrant deciding whether
to design a modification of the product or sell the generic product. The drawback of this approach is that
one may argue that the incumbent is identified in buyer minds and hence an asymmetrical equilibrium
may result.
19
(if it was designed). Then the firms simultaneously receive the signals xj of buyer valuation
parameter V , and then, simultaneously decide on the prices.
The assumption that the signal of consumer valuation x comes after the decision to
design the product is due to time required for implementing the design and variability of
consumer valuations. If product design would follow the signals of valuation, firms could
use product design to convey information about their beliefs on consumer valuation to the
other firm. The nature of the uncertainty of consumer valuation that is modelled here
assumes faster changing beliefs. After the prices are set, buyer decisions follow, and profits
realize.
To see if a firm would invest in developing the product, one needs to compare the
expected benefit of differentiation to the individual firm to the cost of differentiation C.
7.2
The Benefit of Differentiation
Comparing the expected equilibrium price with and without product differentiation, we see
that the expected benefit of differentiation is t/2 in case x = V or x = ∅, and

t
if 2s > δ,
1 
B(t, s, x) = · 2t + δ − 2s if 2s ∈ (δ − t, δ),
2 

2t
if 2s < δ − t,
where δ = V − V , x = V . This means that the expected (before receiving signal x) benefit
of differentiation is


if 2s > δ,
t/2
EB(t, s) = t/2 + (δ − 2s)/8 if 2s ∈ (δ − t, δ),


5t/8
if 2s < δ − t.
(1)
Thus we have the following proposition.
Proposition 5. The expected benefit of differentiation in the above model is positive and
non-increasing function of the search cost s.
In particular, the expected benefit of differentiation monotonously increases when s
decreases when 2s ∈ (δ − t, δ).
20
Proposition 5 can be restated as saying that buyer price search cost and product differentiation are substitutes. The result that the benefit of differentiation may increase and
does not decrease when s decreases means that for a range of the cost of differentiation
parameter C, lower s implies higher equilibrium product differentiation. This fact leads to
important implications that are discussed in the following subsection.
7.3
Endogenous Product Design: Results
The decision of a seller on whether to differentiate the product will, obviously, depend on
the cost of differentiation. Suppose it costs C to design the differentiated product. Then a
seller will be willing to design the product if and only if C < EB(t, s). Therefore, we have
the following result
Proposition 6. A seller is more likely to invest in product design if search cost s is smaller.
In other words, a seller is willing to pay larger fixed cost to design the differentiated product
if search costs are smaller.
Proof. Since expected benefit of differentiation EB(t, s) is decreasing in s (see formula (1)
or Proposition 5), product differentiation may only increase when s decreases. To see under
which conditions on s and C it happens, note that in order for product differentiation to
become equilibrium outcome from not an equilibrium outcome, s should change from a
level s1 such that C > EB(t, s1 ) to a level s2 such that C < EB(t, s2 ). For this, one must
have C ∈ (t/2, 5t/8), s1 > 2t − 4C + δ/2, and s2 < 2t − 4C + δ/2.
The above proposition implies that in an economy with a number of industries or when
many possibilities of differentiation exist, a decrease in buyer search costs for price in any
range, may result in higher product differentiation as more and more products become
differentiated.
Let us now turn our attention to the effect of search cost s on equilibrium prices.
Proposition 7. A decrease in search cost s has a direct effect of decreasing prices, and
indirect effect of increasing prices through an increase in product differentiation. The resulting change in the equilibrium price can be either positive or negative.
21
Proof. The direct effect of search cost s on prices (keeping product differentiation constant)
was discussed above (Proposition 4). The indirect effect is as follows. When s decreases,
product differentiation increases, and the increase in product differentiation leads to higher
prices. To see that this increase may more than offset the decrease in prices due to lower
search costs, it suffices to consider the case when search costs are just above and below
the level sufficient to induce product differentiation. Without the endogenous decision on
product design, the equilibrium price with slightly lower search costs would be slightly
lower. However, due to jump from not differentiated products to differentiated products,
prices may increase by t + min{t, δ − 2s}.
To see exact conditions for increasing prices, consider C ∈ (t/2, 5t/8) and s changing
from s1 > 2t − 4C + δ/2 to s2 < 2t − 4C + δ/2 (the conditions for equilibrium to change
from a no differentiated to differentiated one). In this case, the equilibrium price changes
from
to
(
V
if x = V or x = ∅,
p(x, s1 ) =
min{V + 2s1 , V } otherwise,
(
V +t
if x = V or x = ∅,
p(x, s2 ) =
min{V + 2t + 2s2 , V + t} otherwise.
The prices for the lower level of s are higher for all values of the signal x if ∆s = s1 −s2 < t.
The above proposition suggests that the effect of search costs on prices may be different
depending on the difficulty of product differentiation in a particular industry. One can
expect that prices may increase as search costs decrease in an industry where a small change
in the incentive to differentiate prompts firms to substantially increase differentiation. One
could hypothesize that flower arrangement or apparel may be examples of such industries.
The possibility of the paradoxical effect of lower search cost s on the equilibrium prices
is not only due to better product fit, but also due to lower competition, as is demonstrated
by the following counterintuitive possibilities for both seller profits and buyer surplus.
Proposition 8. As s decreases, buyer’s surplus may decrease, and equilibrium industry
profits may increase. Furthermore, social welfare may decrease.
22
Proof. As was stated in the previous proposition, as s decreases, prices may increase. An
increase in prices decreases buyer’s surplus. The effect of prices on buyer surplus is partially
mitigated by improved fit. However, it is easy to see that in the differentiated products
equilibrium, each buyer is no better than in the non-differentiated products equilibrium,
and some buyers are strictly worse off.
To see the possibility of increasing profits, note that if the decision on product differentiation is not cooperative, then the amount of differentiation is likely to be industry
suboptimal, since differentiation by one seller has a positive externality for the other. In
particular, in the current model, if the benefit of differentiation for one seller is EB(t, s),
then (since the sellers are symmetric), the benefit of differentiation for both sellers together
is 2EB(t, s). Hence, as the search costs decrease, the individual firm decision to design a
differentiated product may trigger a more optimal for the industry product differentiation,
and hence, increase industry-wide profits (as opposed to the equilibrium with higher search
costs).
Further, social welfare may decrease as search costs decrease since the benefit from better fit of t/2 for an average consumer (benefit of t for half of consumers) with differentiation
may be less than the cost of undertaken differentiation, which can be as high as 5t/8.
The condition for a decrease in social welfare is exactly when equilibrium changes from
a no differentiated to a differentiated one, because in that case C > t/2 is spend on
differentiation and social benefit of differentiation is t/2. Hence, if the differentiation is
caused by competition (i.e., when differentiation would not be an equilibrium outcome when
s is extremely high, but is an equilibrium outcome with a given s), social welfare decreases.
In other words, product differentiation caused by competition is socially suboptimal.
The intuition of this result is that when a certain action of one firm (in this case,
differentiation) has positive externality on other firms, an exogenous incentive urging firms
to take that action may make all firms strictly better off.
Besides the effect on the level of prices, decreasing search costs may have a counterintuitive effect on the price dispersion as well as the following proposition shows
Proposition 9. As search cost s decreases, price dispersion may increase
23
Proof. Indeed, without product differentiation, one can expect prices different by at most
2s. With product differentiation, prices can be different by t + 2s. If t is greater than the
change in 2s, and the change in s causes differentiation, price dispersion increases.
Among results of this section, the last proposition has been, perhaps, most widely
empirically documented in the Internet context (Brynjolfsson and Smith (2000), etc.).
In this model as it is, it is impossible that when search costs decrease, all agents would
be worse off since if the price increases then either the firm who did not invest in product
differentiation is better off (in the equilibrium with endogenous product design at most
1 firm invests in the development of the product at 1), or some buyers are better off (if
product differentiation does not change). However, it is possible that average industry
profits decrease (due to cost of differentiation that more than offsets higher profits from
lower prices), and all buyers are worse off (due to higher prices). To obtain the result that
all agents may be worse off, one can consider two markets each of which have the two firms
as competitors and in one, one firm bears the costs of product design whereas in the other
market the other firm bears the costs of product design. Also, one can consider a more
general structure of product design possibilities, where the product can be differentiated
over two independent dimensions.
In the following section, I discuss some of the extensions of this model to argue for the
robustness of the results.
8
Extensions and Future Research
The model was restricted to the case of no search for information about individual product
valuation. This situation may be interpreted as either product attributes (except for price)
being known to the buyer, or being impossible to find through search, in which case the
product valuation represent the buyer expectation of the true valuation. Such a model can
be applicable for products whose attributes are well known prior to the decision to purchase, or products that only have known and experience attributes (no search attributes).
It can also be understood as a part of a more general framework, where search for other
24
information occurs before search for price, where search for other information occurs simultaneous with the first search for price (the approach I took), or as a benchmark for models
with more extensive list of possible information searches (as a limiting case when the search
cost for other information either tends to zero or to infinity). The framework could be,
generally stating, a random utility model with buyer cost for obtaining price information
on the demand side, and uncertain (incomplete) information about demand in Bertrand
competition on the supply side, with endogenous level of investment in product design.
Some assumptions in the model may be considered too restrictive. This section further
attempts to consider analytical assumptions of the model and discuss the expected changes
to the model predictions if one relaxes some of these assumptions.
First, it was assumed that the signal of demand (buyer valuations) that a seller gets
is dichotomous. One may want to see what would happen under different assumptions on
the distribution of the demand signal error term. For example, what would happen if the
signal error is smoothly distributed. It turns out that generalizations of the error structure
complicates analytical tractability of the model. However, if the signal error is smoothly
distributed, then the intuition behind the main results remains: the uncertainty about
the competitor prices does not allow a firm to raise prices higher than certain amount
above possible prices at the competing sellers; product differentiation allows a firm to
be less concerned about competition, and the benefit of higher possible price is higher
when the general level of prices is lower (i.e. when search costs are lower). At the same
time, the equilibrium may then involve a possibility of search in the equilibrium at any
signal/valuation level, which may lead to mixed strategy equilibria (i.e. a seller expects
search with certain probability). The slope of price depending on the signal will decrease
as the signal increases.
Further, the model assumes that the cost of search is the same across consumers. Again,
if we have a distribution in s among buyers, there may be search in the equilibrium, and a
mixed strategy equilibrium may be the only one. In such a setting, one can expect that in
the equilibrium with product differentiation more consumers will search. Therefore, lower
search costs may, through higher differentiation, induce higher total search expenditure by
some consumers.
25
The problem of buyer search for the first price can be solved in several ways. The
rationality of the first search can be explained, for example, by the fact that at first, the
buyer is searching not only for price, but for product quality information as well, and hence,
due to large uncertainty about the utility prior to the first search, the first search cost is
justified for all buyers in the market. In the case of such behavior, the equilibrium price
provides an expected surplus for buyers and hence, the at front expenditure on search for
quality is justified. Alternatively, each buyer may have a downward slopping demand for
the product, and sellers may not be able to force a minimum purchase requirement (for
instance, because of having to follow linear pricing), and hence they know that they have
positive net utility of buying the product even under the monopoly price. Also, one can
consider buyer heterogeneous in search costs s (with no lower bound on possible s), so that
given expected prices closer to monopolistic, less buyers search, but some still do. Finally,
one can consider search costs depending on the valuation, so that the smaller the valuation
gets, the smaller the search costs are.
In general, buyers may use the price quotes they know to update the expected distribution of the other prices in the market if the seller signals are correlated (given V ) or
if the aggregate demand is unknown to the consumer, i.e. when signals given the buyer i
knowledge (xj | {Vij }j=1,2 ) are correlated. This may lead to an additional incentive for a
seller to set a higher price (since higher price seen by a buyer may imply that the buyer
will expect higher prices in the market, therefore may reduce the expected by the buyer
benefit of search, and hence, reduce the probability that the buyer that receives the price
quote from this seller will search and so, increase demand). However, in the model, buyer
knowledge of their own valuation, the fact that buyers are homogeneous and independence
of retailer signals means that buyers know the valuation of all buyers, and since there is
also no correlation between seller signal error term, the price at one seller does not bring
any information to the buyer about the price at the other seller.
The case of product differentiation that is unknown to buyers may also be of interest.
The incentives of the firm to introduce features about which buyers are not sure prior
to search are ambiguous: on one hand uncertainty about the valuation may attract more
buyers (since they may expect higher possible surplus, and the downside is limited for them
as they are not required to buy), on the other hand, if buyers expect wider distribution of
26
their possible valuation at the other stores, buyers may have more incentive to continue
search at other stores.
One can consider a continuous consumer space instead of the two segment population
that was considered in the model. A case of Hotelling distribution of consumer preferences (a line segment with linear transportation costs) is considered in the appendix. The
implications remain the same.
Finally, one may consider what happens under a wider range of a-priori possible signals
as in [9]. It turns out that with the lack of common knowledge all effects are magnified.
The next subsection provides intuition for what happens when the common knowledge on
the distribution of x is lacking, i.e. when each firm is not sure of what other firms may
know, and has to infer what signals other firms may have from its own signal of demand.
8.1
Lack of Common Knowledge
One potential drawback of the model of search used is that the price given the low signal
of consumer valuation (x = V ) is at the monopoly level. This means that no matter how
small the search costs are, the prices are at least as high as the monopoly price given the
lower estimate of demand. If the uncertainty of a firm about the market demand δ = V −V
is not very large, then the prices are close to the monopoly prices. The fact that one often
observes prices well below the range of “common sense” valuations may be explained by
the fact that usually, no matter how low a firm believes the demand is, the firm allows
the possibility that another firm has even lower estimate of demand. This lack of common
knowledge about possible beliefs the firms in the marketplace have increases the effect of
both search costs and differentiation on prices and profits.
To see how the lack of common knowledge affects the equilibrium, consider the following
structure of firms’ signals of demand.7 Assume that the true valuation of buyers can be in
S = {V , V + δ, . . . , V + Kδ = V }. Also, assume that the signal x tells the firm that the
buyer valuation is Ṽ or Ṽ − δ, where Ṽ ∈ S ∪ {V + (K + 1)δ}. If note that if Ṽ = V then
putting together the signal and the prior, the firm knows the true valuation. The same is
true for Ṽ = V + (K + 1)δ. Hence for K = 1, the model simplifies to the original one.
7
For a more detailed treatment of the lack of common knowledge, see [9].
27
Now, if a firm receives signal Ṽ = V + kδ, as far as k > 1, it doesn’t know whether
the other firm received a lower signal, and thinks that the other firm may have received a
lower signal with probability 1/4. However, it knows that no firm received a signal with
Ṽ < V + (k − 1)δ. Therefore, in the case of homogeneous products, to ensure no search
(for sufficiently small s), it has to set price 2s larger than the price that is set by a firm
after receiving signal with Ṽ = V + (k − 1)δ. In the case of differentiated products, the
price increase could be as high as 2s + t. The intuition for this is exactly same as in the
proof of Proposition 3.
Recursively following the same argument for k = 2, 3, . . . , we obtain that the price at
the signal with Ṽ = V +kδ can be V +2s(k −1) in the case of homogeneous goods, and V +
t+(2s+t)(k −1) in the case of differentiated goods. Therefore, the benefit of differentiation
to the firm increases as a multiple of k. In other words, if with a lack of common knowledge
about the distribution of x, even small search costs and small uncertainty that each firm
has about the demand may have large in magnitude effects on prices and profits.
9
Empirical Evidence
The following are just a few situations which may be interpreted as supporting the proposed
theory.
Shopping malls vs. supermarkets.
Shopping malls and supermarkets are real life examples of two environments that differ
in search costs between stores. Supermarkets are far from each other, whereas shops within
a shopping mall are close together. If one wouldn’t know what actually happens, one could
think that since search costs between supermarkets are higher than between shops in a
shopping mall, markups and prices at a supermarket should be higher.
In reality, stores in a shopping mall are often very specialized and very differentiated
from each other, just as predicted by the model. For example, if there are two bakeries at
a shopping mall, one could imagine they sell different products: maybe one sells bagels,
and the other sells croissants. The result is that the competition within a shopping mall is
28
not very high, and one is not surprised to see prices at the shopping malls that are higher
than the prices at supermarkets.
Product differentiation may be increasing in a category when it is introduced
online. One of the predictions of this paper is that in an environment with lower search
costs for price, one should expect, ceteris paribus, higher efforts of the firms (sellers) in
the marketplace to differentiate their products (or themselves) from the products of the
competitors.
To test this prediction, one needs some measure of the product differentiation efforts
by the firms under different buyer price search costs. It is difficult to empirically estimate
buyer price search costs. It is also difficult to compare the firm’s efforts to differentiate its
products from the competitor products across different product categories, both because
these efforts are unobserved and because it may be easier to differentiate products in some
categories than others.
To deal with the unobservability of the firm’s efforts to differentiate its products, one
may notice that higher efforts to differentiate products should result, ceteris paribus, in a
more uniform distribution of products across the product space. To deal with the different
costs of product differentiation in different categories, one may consider the same product
category across time or geographical location.
The search costs are also not observed, and therefore one must look for proxies for
them, i.e. for variables that indicate whether search costs are higher or lower in one market
relative to another. In today’s market environment, the existence of the online marketplace,
arguably, provides such a proxy, since the more the buyers use the internet for shopping,
the easier it is for them to compare prices (since it has been noted that price search on the
internet is easier due to existence of internet search engines and shopbots). Accordingly,
one may hypothesize that a share of on-line sales in a category may be a proxy for search
costs (the higher the share, the lower the average search costs).
To obtain the data on product differentiation and search costs, I have used product
ratings across different attributes and years from Consumer Reports Buying Guides and
press releases of major internet companies.
I have the data on product differentiation across time in twelve product categories
29
constructed from product attribute ratings in the Buyer Report Buying Guides (years
1995-2001) as follows. Buyer Reports provide ratings of the brands in a category across
different characteristics within each year. The distance between the raitings (as points in
n-dimensional space, where n is the number of characteristics rated) provides a measure
of how differentiated the products are in the attribute space. An average value of differentiation is a measure of how much the firms want to differentiate. This measure is further
normalized so that it would not predictably depend on the number of the brands or the
number of attributes rated in a particular year. The resulting number provides a measure
on how much the manufacturers tried to move their products away from the competitor
products in the product space, and is the dependent variable. Hence, we have a panel
(category and time) variable of product differentiation within a category (j) in each year
(t) defined by the following formula:
B
X
1
1
DIFFjt =
B(B − 1) b,b0 =1 K − 1
K
X
!
(ajtbk − ajtb0 k )2
,
k=1
where ajtk is the value of ranked attribute k of brand b in category j at time t; B is the
number of brands in the category at the given time, and K is the number of product j
attributes rated at the given time.
The categories were selected as satisfying the condition that the brands in the category
are rated on several characteristics (attributes) on the scale from 1 to 5 (poor to excellent)
in 1999, in at least one year before 1999, and at least one year after 1999.
The time at which each category was introduced for on-line sales can be used as a
proxy for search costs, since it should be positively correlated with the share of online
sales. It turns out that Amazon.com introduced different categories for online sales at
different times (years). Other internet shops8 introduced most categories simultaneously,
or almost so. The data on the dates of introduction of categories on Amazon.com was
obtained from Amazon.com press releases (Jan. 1997 through May 2001, Amazon.com
launched a total of 12 stores, including books, music, home improvement, kitchen, camera,
wireless, baby items, etc), and was used to construct the “online penetration” explanatory
variable correlated with the consumer search costs. This variable is equals to 1 if and only
8
Such as Yahoo!shopping, Buy.com, and DealTime.
30
if the category is sold at Amazon.com in the given year, and therefore is also category and
time specific. The hypothesis tested is that of positive correlation between the dependent
variable DIFF and the online penetration variable ONLINEjt .
Note, that as an industry matures, one can expect systematic changes in the number
and distribution of the products offered. Therefore, to reduce the effect of the time trend
in product differentiation, I use the trend variable TRENDt = t with category specific
coefficient. This variables can also account for any time trends in the way categories
were rated in the consumer reports. Further, due to differences in production, usage, and
ratings across different categories, one may expect differences in product differentiation
across categories. Therefore, a category specific dummy variable must be used as well. The
econometrical model equation is thus
DIFFjt = αj + βj TRENDt + γj ONLINEjt + εjt ,
where the error term εjt represents shifts in product differentiation not accounted for by
the explanatory variables, and is assumed to be uncorrelated with the ONLINE variable.
I further estimate the coefficients of the above equation for each category through OLS.
The hypothesis is that βj > 0, i.e. that when the category is sold online, the product
differentiation is higher.
A number of systematic changes in the marketplace may contaminate the data. One
would not expect the correlation to always hold in finite samples also because the measures
of product differentiation efforts and search costs are indirect, which introduces additional
error in variables and reduces the statistical significance of the test coefficient.
The results of the OLS regressions are the following: the coefficient with ONLINE
variable has the expected sign (positive) in 11 out of 12 categories.
In the joint regression (with γ common for all categories) of the differentiation index
on the online variable and brand specific constants and trends, the coefficient with online
variable is 0.10187 (0.04766). The coefficient is large in the absolute value (the average
differentiation index is 0.48), and statistically significant at 2% level. The data, therefore,
provides some support for the hypothesis suggested.
31
10
Conclusion
Changes in one parameter of a market environment may lead to complex changes in all of
the firm decisions. As a result, comparative statics that attempt to examine the effect of
a change in one parameter by changing only that parameter and holding other parameters constant (the “ceteris paribus consideration”), may be ill-suited for predicting market
outcomes.
In this paper, I considered the interconnection of buyer search costs and firm decisions
on product design. I have shown that when product (store) design is considered endogenous,
lower buyer search costs may lead to higher differentiation. This prediction seems to be
consistent with observed market behavior. Furthermore, the model in this paper shows that
the indirect effect of lower search costs on the equilibrium price through increasing level
of differentiation may outweigh the direct effect of lower search costs, and so, when buyer
search cost for price reduces, equilibrium prices need not decrease. Therefore, considering
the effect of a change in buyer search costs on price competition alone may lead to erroneous
conclusions.
In the model developed, when product design is exogenous, lower buyer search costs for
price, ceteris paribus, imply higher competition, lower prices, lower profits, higher buyer
surplus and social welfare. At the same time, when product design is endogenous and is
determined by the seller as to maximize the expected own profit, lower buyer search cost
for price may lead to lower competition, higher prices, higher average profits, lower buyer
surplus and social welfare. Hence, carefully considering all the implications of reducing
buyer search costs is important both for businesses that are trying to assess the expected
future profitability of a particular industry, and for public policy makers accessing the social
desirability of technological changes that affect buyer search costs.
32
Appendix: Continuous Distribution of Buyers.
Here I consider aggregate uncertainty in markets with continuously distributed tastes. Consumer preferences are distributed uniformly on the unit segment with “transportation” cost
of having product away from the consumer location linear in the distance (with coefficient
of proportionality t) a la Hotelling. Further, firms have aggregate uncertainty, which means
that the valuation parameter V may be unknown to the firms. The prior distribution on
V is that it is drawn from a subset V of a real line. Each firm further receives a signal x
of V that tells the firm how likely it is that V attains various values of V. A particular
x a firm receives remains private knowledge to that firm. Firms then simultaneously set
price (p = p(x)). Consumers know the locations of firms (valuation of the products offered
by the firms) but have to incur a search cost to find the price beyond the first price that
they receive at zero cost. When firms are able to change the location, they have to do that
before receiving the signal x of the valuation parameter V (due to the long time required to
redesign the product). Consumers know their valuation, and therefore know the parameter
V.
I will assume in the following models that t is large compared to 2s for simplification
of graphical display of the regions, i.e. that the search cost for price is small relative to the
amplitude of valuations of consumers.
Case 2s > δ leads to monopoly pricing regardless of differentiation, and hence is not
interesting. Cases 4s ≥ δ and 4s < δ lead to prices being lower than monopoly for a smaller
and larger set of V respectively. I will first consider 4s < δ, which is a more difficult case,
and make notes on what would change in the other case along the way. V remains a
parameter on which the results of the model (the way search costs enter the equilibrium
prices and profits) will depend.
Model with no Product Differentiation
Consider an undifferentiated market with products of both firms located at 0 of the
Hotelling line segment. In order to consider the competitive behavior of firms, we first
need to consider what would a monopoly do in this situation (alternatively, one can think
of the monopoly case as the case when search costs are so high that the firms are not
concerned about the competition, since the decrease in demand is then just a scaling parameter).
If x = V , then the monopoly price is
(
V /2
if V ≤ 2t,
pm
0 (V , V ) =
V − t if V > 2t,
(V in pm
0 stands for the lower range of the prior, V for the signal x, the subscript 0 stands
for the no-differentiation case, and upper-script m stands for monopoly).
33
If x = ∅, then monopoly price is still piecewise linear, but has more points where the
slope changes: price is EV /2(V + V )/4 until the consumer at 1 buys in the case V = V
but gets 0 surplus. Then price increases with the slope 1 as a function of V as to keep
the consumer at 1 marginal in the case V = V until the firm finds it optimal to go for the
consumers that are marginal in case of V = V . Then the price increases with the slope
1/2 again until the consumer at 1 becomes marginal in the case V = V . Then the price
increases with slope 1, so that all consumers buy, with consumer at 1 buying just barely if
V = V . Solving the conditions above, one finds that the formula for the monopoly price
when x = ∅ as a function of V is (0 denotes no differentiation case):

V /2 + δ/4



V − t − δ
pm
0 (V , ∅) =

V /2 + t/2



V −t
if
if
if
if
V
V
V
V
< 2t − 3δ/2,
∈ [2t − 3δ/2, 3t − 2δ],
∈ [3t − 2δ, 3t],
> 3t.
Consider now the competitive equilibrium. Since given the valuation, there are two
equally probable signals x, in a pure strategy equilibrium, consumers search if they see a
price more than 2s higher than the price given the lower signal. Note that if one consumer
finds it beneficial to search, all do, and vice versa. If consumers search, they don’t come
back since they find a price that is at least as good. Therefore, if consumers search, the
firm loses all the demand. Therefore, firms set the price so that consumers do not search.
It follows that if x = V , the price pe0 (V , V ) is the monopoly price pm
0 (V , V ); if x = ∅,
e
the equilibrium price p0 (V , ∅) is the minimum of the monopoly price pm
0 (V , ∅) and the
no-search constraint pe0 (V , V ) + 2s, and if x = V , the equilibrium price pm
0 (V , V ) is again
m
the minimum of the monopoly price p0 (V , V ) and the no-search constraint pe0 (V , ∅) + 2s.
Model with Product Differentiation
Now consider the case when one firm is located at 0, and the other at 1 (restricting ourselves
to the case of two firms).
Since product fit is known, consumers closer to one of the location obtain the price of
that location first. Again, I first consider the collusive case, when each firm sells only to
the consumers that are closer to it. I will still use the upper-script m for the collusive case
as for the monopoly case before, but will use subscript d for differentiation.
The collusive price given signal x = V or x = ∅ is derived as before. The only difference
is that the consumer population is on the segment of length 1/2 instead of 1. One obtains
(
V /2
if V < t,
pm
d (V , V ) =
V − t/2 otherwise,
34
and

V /2 + δ/4



V − t/2 − δ
pm
d (V , ∅) =
V /2 + t/4



V − t/2
if
if
if
if
V
V
V
V
< t − 3δ/2,
∈ [t − 3δ/2, 3t/2 − 2δ],
∈ [3t/2 − 2δ, 3t/2],
> 3t/2.
Just as before, the collusive price is the equilibrium price if the search cost is too high
(so that the difference in the monopoly prices is never more than 2s; this happens when
2s ≥ δ).
When 2s < δ, if the firms set the collusive prices above, some consumers will search.
However, only consumers close to 1/2 will search, since the difference in the fit makes it not
optimal for the rest to switch even if they find price which is lower by δ. Therefore, a firm
may see it optimal to set the price such that some consumers search, and the equilibrium
price derivation is somewhat more complicated than in the no-differentiation case.
Again, when the signal is x = V , the price is monopolistic: ped (V , V ) = pm
d (V , V ) (the
firm is not afraid that consumers will search as they can not hope to find a lower price, and
no consumers from the other side can buy, since the price is above the valuation for them).
If the signal is x = ∅, consumers do not search out (search when they see price p(∅)):
they only can search if they hope that the other price is lower, i.e. set by a firm that has
x = V . That is only possible if actual V is V , but then the price offered by the other firm
is above their valuation due to lower fit. However, the demand is increased over a certain
range of V since some consumers from the competitor side search if V = V and other
x = V . This leads to the following equilibrium price (to find it one solves the simultaneous
equations with equilibrium price given x = V ):


V /2 + δ/4
if V < t − 3δ/2,





V − t/2 − δ
if V ∈ [t − 3δ/2, 3t/2 − 2δ],





if V ∈ [3t/2 − 2δ, 3t/2 − 2δ + 4s],
V /2 + t/4
m
pd (V , ∅) = 3V /5 + t/10 + δ/5 − 2s/5 if V ∈ [3t/2 − 2δ + 4s, V0 ],



3V /7 + 5t/14 − 2s/7
if V ∈ [V0 , 3t/2 − 4s],





V /2 + t/4
if V ∈ [3t/2 − 4s, 3t/2],



V − t/2
if V > 3t/2,
where V0 = 3t/2 − 7δ/6 + 2s/3. The fourth and the fifth segment are the segments at which
the price is above the collusive price due to expected increase of demand due to consumers
that are closer to the other firm.
Now, consider a firm having the signal x = V . Assume 4s < δ. Then the following is
35
an equilibrium price:


V /2





V − t/2
e
pd (V , V ) = V /7 + 11t/14 + 4s/7



V /2 + t/4 + 2s



V − t/2 + 2s
if
if
if
if
if
V
V
V
V
V
< t − δ,
∈ [t − δ, V0 ],
∈ [V0 , 3t/2 − 4s],
∈ [3t/2 − 4s, 3t/2],
> 3t/2.
Note that some consumers search when V = V , V is in the third segment above, and they
see the higher price (p = ped (V , V )). Namely, the consumers that are at most
ped (V , V ) − ped (V , ∅) − 2s
3t − 2v − 8s
=
.
2t
8
At the beginning of the range of V , that’s 2/5(δ − 4s) consumers, at the end the amount
decreases to 0. Also, some consumers search at the end of the second range on V . The
equilibrium and collusive prices are plotted in Figure 10
Proof. To prove that the above is an equilibrium, note that in the first range of V in the
formula above, consumers don’t search. Therefore, the monopoly price is optimal.
In the second range, some consumers may search (towards the end of the range), but the
increase in demand due to lower search is at most ∆p/2t/2, where 2t in the denominator is
because of the fit adjustment, and additional 2 for probability 1/2 that the other price is
lower (that the other firm received signal x = ∅). Hence (arithmetics using the previously
derived ped (V , ∅) shows), it is suboptimal for the firm to reduce price. It is also suboptimal to
increase price, as then some consumers will not buy due to valuation (the price is collusive).
In the third range, the marginal benefit of reducing price due to additional demand
(which is linear in ∆p) is exactly equal to the cost of losing ∆p on each consumer in the
expected demand (which is increasing as p decreases). At higher end of the third range,
the price is lowered so that it is only 2s above the other possible lower price of ped (V , ∅).
In the range 4 and 5, the price is bounded by the no-search condition, i.e. ped (V , ∅) +
2s.
If 4s > δ than the third region does not exist, and consumers never search.
The symmetric equilibrium is unique.
Price Dispersion
Price dispersion in the above models is given by the intersection of the vertical line V = V0
with the graphs of equilibrium prices given the signal. In the no-differentiation case, the
price distribution between firm with signals V and ∅; and ∅ and V are either 0 or 2s. In the
36
37
δ /2
δ
t/2
t
p(V), p(V), p(0)
t−3 δ /2
t−δ
V0
3t/2−2 δ+4s
t 3t/2−2 δ
3t/2−4s
3t/2
V
Prices without product differentiation
in this range.
The equilibrium price in the model with uniformly distributed consumer preferences.
Blue line is the competitive price with high signal, green line −− with no signal,
brown line −− with low signal. Black lines are collusive prices.
differentiated case, price dispersion on some range is larger and does not depend on s, and
is 2s or 0 for high V . Hence, price dispersion in a given market (given V and whether V or
V is the true one) can be expected either higher or lower in differentiated case depending
on the value of V .
Benefit of Differentiation
Since for smaller V , differentiated equilibrium is monopolistic, and prices in non-differentiated
market reduce from the monopolistic as s decreases, benefit of differentiation increases as
s decreases. For larger values of V (namely, for V > 3t), benefit of differentiation is independent of s: benefit from differentiation is t/4 per firm that comes from having products
with better fit, and benefit of higher search costs is s/4 per firm (both benefits are for the
firms).
Consumer Surplus
Consumers are worse of from differentiation for any s, since firms are able to extract all
the additional surplus, and the average consumer becomes closer to the marginal in the
differentiated case. However, when V < 3t, the higher the search cost, the less consumers
stand to lose due to differentiation.
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