Download Differentiated Product Oligopoly

Differentiated Product Oligopoly
Product Characteristics
• Goods characterization revisited:
– Goods are never perfect substitutes
– Distinguishing features = Product Characteristics
• Chamberlin/Lancaster approach: Model a good as a
bundle of characteristics:
• Models:
– Vertical differentiation -- quality choice
• Issues of adverse selection and moral hazard
– Horizontal differentiation -- location models
• Issues of search and information aggregation
– Multi-characteristic models
Quality and Information
• Search goods versus experience goods
– Warranty goods are pure search goods
– Incomplete or absent warranty systems together with durability of
the good  experience good
• Moral Hazard
• Adverse Selection
• We examine some simple models of these two phenomena
(known collectively as asymmetric information).
Asymmetric Information
• Monopoly firm with quality dimension choice.
– Quality choice s=0,1. Quality s=0 is low quality, while s=1 is high
quality. Quality is costly: cost of low quality c0=0, while high quality
cost c1>0.
– Buyers value goods of different quality differently. Specifically, we
assume U=s-p, where s is the quality level and p is the price paid.
Obviously, if s=0, then the buyer is not willing to pay anything for the
good. We also assume that >c1 so that the provision of quality is socially
useful.
– Buyers are not informed beforehand of quality.
• Equilibrium
– Firm won’t produce high quality, since it achieves a profit differential of
c1 by producing only low quality, without changing demand
– Equilibrium involves p=c0=0
Asymmetric Information
• Modify model to permit signaling.
– Some fraction  of buyers do research and become
informed about the quality of the good on the market.
These buyers will pay  if quality is high and 0 if it is
low. The remaining fraction (1- ) of buyers are
uninformed as before.
– Monopolist offers a price p in [0, ]. Informed buyers
purchase the good only if it is high quality, yielding a
profit of (p-c1).
Asymmetric Information
– Consider uninformed buyers:
• If they don’t buy, demand only from informed, monopolist produces
high quality and sells at p . In this case, uninformed should buy.
• If uninformed buy, then monopolists profit will be p-c1 if he produces
high quality, and (1-)p if he produces low quality. Hence, he will
produce high quality if
p-c1 (1-)p
or
 p  c1
Asymmetric Information
• Interpretation
– Notice that when only part of the market is informed, the
monopolist will produce high quality only if the price is
sufficiently high. This is because when the price is high, switching
to low quality will cause the monopolist to lose the high profit
margin he makes on informed buyers.
– Given this, uninformed agents can infer from the high price that
they are in fact getting the high quality good. In fact, if
  c1
then the monopolist will charge p= and produce only high quality.
Asymmetric Information
– This is an example of prices signaling quality.
– Role for buyers’ guides (or online search) in ensuring that at least
some fraction of the market is informed.
– Note role of information externality here: even a relatively small
number of informed buyers can induce the firm to produce high
quality, thus providing a free benefit to agents who are not
informed.
– Potential paradox: Endogenous decision to become informed
If buyers must choose to become informed and becoming informed is
costly, there may be incentives to “free ride” on the information
externality embodied in the price signal. But if everyone chooses not
to be come informed, the externality disappears.
Asymmetric Information
• Example: Trial Versions
– Buyers are allowed to download a more or less functional version of a
particular software application for free, sometimes limited to a trial period
(sometimes enforced or sometimes not) accompanied by so-called “nag
screens” which degrade loading times.
– The free download and evaluation provides the information the buyer
needs to ensure quality. At the end of the trial period, the buyer can
purchase the fully functional version by paying the full purchase price.
– Versioning is also used to segment a market (selling different quality
levels at different prices). We will discuss this when we examine price
discrimination.
Asymmetric Information
• Market for Lemons
– When quality is not an inherent choice, but rather a feature of the
good, we characterize the information problem as one of adverse
selection, since buyers on the market must try to distinguish
between which goods are low quality and which are high quality.
(Obviously, if differences are directly observable, no information
asymmetry exists.)
– A simple model
• Robinson Crusoe is selling a goat on Ebay. The goat will produce
milk given by a parameter s. If Robinson does not sell the goat, his
utility is 1s; otherwise, if he sells the goat for price p  1s, this is his
utility
Asymmetric Information
• Friday is bidding for goats on Ebay. If he buys a goat with
milk parameter s for a price p, his utility payoff will be 2s-p.
We assume that 2> 1, so that it is optimal for Robinson and
Friday to trade, no matter what the milk parameter turns out to
be.
• Friday’s problem, then is what to offer to pay for the goat.
Robinson has experience with the goat and hence knows s.
Friday knows only that s is randomly distributed (with uniform
distribution) with
s[0,smax].
• Note that if Robinson is willing to sell the goat at price p, the
quality s must be such that
p 1s
Asymmetric Information
• We assume next that Friday is risk-neutral, and hence evaluates
the utility of obtaining the goat as
2sa-p
Here, sa is the value of s that Friday anticipates getting.
• What milk value should Friday anticipate? Conditional on
Robinson being willing to sell, Friday can anticipate that s will
be uniformly distributed in the interval
[0,p/1].
• Under the risk-neutrality assumption, then we have
sa 
p
21
Asymmetric Information
• Note how the average quality of goats on the market is biased
downward by the decision to put the goat on the market. This
is the so-called adverse selection problem.
• Friday will buy the goat if and only if
2sa  p
• From the definition of sa, this tells us that Friday will make a
purchase only if 2  21. Clearly, if preferences are similar in
the sense that 2 is close to 1 (though larger), then there cannot
exist any price at which trade will occur.
Asymmetric Information
• Implications
– Information makes markets.
• In the moral hazard example, more informed buyers lead to
lower prices and larger markets, even in the case of a
monopoly.
• In the adverse selection example, more information about
product quality allows emergence of separate markets for
different qualities of good.
– Positive role of the internet in making better search possible.
– Potential negative role in making it easier to market faulty
products.
Price Competition
• Price Wars
– The Bertrand model of price competition
• 2 firms, homogeneous product, common marginal cost of production.
• Because each firm’s product is a perfect substitute for the other’s,
consumers always buy from the firm charging the lowest price.
Hence
 D  p  if p  i  p
1
i
Q D  p    2 D  p  if p i  p
i
0
if
p
p

Price Competition
• Equilibrium in a one-shot, non-cooperative pricing game will have
both firms charging marginal cost and making zero economic profits.
• We can show this result formally by showing that if firms charge
different prices, the one charging the higher price has an incentive to
at least match that of its rival. If both charge the same price but this
price is in excess of marginal cost, then by undercutting its rival
slightly, either firm can steal the other’s market share and increase
profit. The only price at which this incentive is no longer active is
when p=c.
• Note that in the absence of mechanisms to prevent undercutting, the
Bertrand mechanism leads to price instability and the phenomenon of
price wars.
Non-Price Competition
• Avoiding the Bertrand paradox
– With capacity constraints
• Cartel formation (Explicit collusive monopolization)
– Illegal under most domestic antitrust laws
– Can be difficult to enforce if cheating is hard to detect
• Dynamic price competition (Implicit collusion)
– Repeated game structure using mutual punishment strategies to enforce
cooperation
– Can also be difficult to enforce if cheating is hard to detect
– Without capacity constraints
• Commodity product  competitive outcome
• Product differentiation
• Monopolistic competition
Product Differentiation
• Modeling product differentiation
– Modeling product characteristics
– Characteristics space
– Spatial location models of competition
• Spatial competition
– The circular model
• Two dimensional characteristic space, with products located around a
circle.
• Example: Image processing software. One dimension of the
characteristics space specifies the number of photo versus video
formats the product can process. The second dimension specifies the
complexity and sophistication of functionality, ranging from complex
but sophisticated to easy to use but not very powerful.
Spatial Model
Spatial Model
• Consumers in the model wish to purchase one unit of product, and are
uniformly distributed around the circle (whose circumference is
normalized to 1). A consumer’s location on the circle represents her
most preferred combination of product characteristics.
• Consumer’s incur transportation costs in the amount t if they
purchase a good which is t units from their most preferred location.
The consumer’s surplus if she gets her most preferred product is s.
• There are n products located (exogenously) uniformly around the
circle. We can interpret the products as arising from the entry of new
firms (or of new brands put forward by existing firms) drawn from a
large pool of potential entrants to the market.
Spatial Model
• Each product has price pi for i=1,…,n. We illustrate this in the
diagram below.
Spatial Model
• With firms and consumers located symmetrically around the circle, it
makes sense to look for an equilibrium where every product sells for
the same price: pi=p. Since there are no barriers to entry in the model
(other than low fixed costs) we will have an equilibrium when the
number of firms is such than no firm earns a positive profit.
• Firm’s pay a fixed cost to enter in the amount f, and a marginal cost c
for each unit sold. Thus, firm i’s profit is given by
i=(pi-c)Di-f
where Di is the demand firm i is facing.
• To determine the demand firm i faces, we note that firm i will attract
customers only from the segment of the circle on either side of its
own location.
Spatial Model
• To determine demand explicitly, consider a buyer located at x(0,1/n)
(i.e. at a distance no more than 1/n from i’s location). This buyer will
be indifferent between buying from i or from i’s nearest neighbor if
pi+tx=p+t(1/n-x)
• Firm i’s demand is given from the equation above by solving for 2x
(since i attracts buyers from either side symmetrically). Note that p is
the price charged by either neighboring firm. Solving for demand
yields
p  nt  pi
Di  pi , p  
t
Spatial Model
• Firm i’s profit maximization problem is then one of choosing a price
to maximize
 p  nt  pi 
 i   pi  c 
f

t


• The taking first-order conditions with respect to the price, and then
setting pi=p (the symmetry assumption on prices), we find
pc
t
n
Spatial Model
• Interpretation:
– Mark-up over marginal cost is >0 firms have some monopoly
power in the market.
– Mark-up is decreasing in n; as more firms put similar products
on the market (filling in the circle), price approaches marginal
cost.
• Equilibrium number of firms: With no barriers to entry, firms
will enter until profit is zero:
1
t
   p  c  f  2  f  0
n
n
t
 n* 
f
and p*  c  tf .
Spatial Model
• What is the optimal number of firms?
– Don’t need to worry about consumer surplus, since each
consumer ends up purchasing one unit of her most preferred
good, and her utility is just the surplus s minus the price, plus the
transportation cost.
– The problem of computing the socially optimal number of firms,
then, reduces to simply choosing n to minimize the sum of the
aggregate fixed costs plus aggregate transportation costs:

 1 / 2 n 
min nf  t  2n  xdx 
n

0


t 

 min  nf  .
n
4n 

Spatial Model
• Taking first-order conditions and solving for n, we find
nˆ 
1
2
t
 12 n *
f
• From the perspective of an omniscient social planner, then, the
equilibrium in the location model has too many firms!
– Potential role for copyrights and trademarks as welfare enhancing
by limiting entry.
– Issues with the model:
• Location choice
• Sequential entry
• Brand proliferation
Advertising
• Role of advertising in non-price competition: two
polar views
– Advertising fosters product differentiation directly by persuading
consumers of differences in product which don’t actually exist
• Creates barriers to entry
• Enhances market power
– Advertising can communicate information to consumers about
product characteristics and quality.
• Facilitates matching of consumers with products
• Efficient use of information resources
Efficient Advertising
• A model of informative advertising
– Monopolistic competition: many firms, all producing a
homogeneous product using constant returns technology, with unit
cost $c.
– Each consumer in the market has unit demand for the product and
receives utility U=S-p if she buys a unit of the good at price p.
– Consumers are uninformed about the existence of the good or the
price charged by a firm. The firm can inform consumers using
advertising. For simplicity, we assume that ads are sent to
consumers at random. Each ad provides a characterization of the
good and a price quote.
Efficient Advertising
– With N consumers, each consumer receives an ad with probability
1/N. Consumers can thus receive no ads, one ad, or more than one
ad. If a consumer receives no ads, she makes no purchases. If she
receives one ad, she buys from the firm sending the ad as long as
the price p is less than S. If she receives several ads, she buys
from the firm advertising the lowest price, as long as this price is
less than S. (If more than one firms offers the same price,
consumers select a firm at random.)
– Let A denote the total number of ads sent by all firms in the
market. Let  be the probability that an individual consumer
receives at least one ad. Then the probability that she receives no
ads is (for large N)
A
 NA
 1
1    1    e
 N
Efficient Advertising
– If the marginal cost of sending out an ad is c’, then (assuming
constant marginal ad costs), the total cost of advertising is
 1 
c' A  cN ln 

1  
– The advertising cost per consumer is then
 1 
c ln 

1




– We assume that S>c+c’ (so trade will take place).
Efficient Advertising
– Free-entry equilibrium: firms pay no cost to enter (no fixed costs
of production).
• Let x(p) be the probability that a consumer makes a purchase at price
p (i.e. she receives no additional ads for a price lower than p).
– Note trade-off between higher price (which increases firm profit)
and lower probability of acceptance
• Zero profit condition for equilibrium: for any price, the expected
profit must be zero or new firms will enter the industry and send ads
at that price until the probability of acceptance drops sufficiently to
restore equilibrium
(p-c)x(p)-c’=0
• Note that when p=c+c’, we have x(c+c’)=1. When p=S, we have
x S  
c'
S c
Efficient Advertising
• x(S) must be equal to 1-, since the only time a consumer will buy at
price S is if she receives no other ads except the one at price S. But
this occurs with probability 1-. Hence, in equilibrium, we have
1  
c
S c
• Now, consider the social welfare problem. Since all possible prices
such that c+c’  p  S are possible in equilibrium, the only thing that
matters from a social welfare perspective is the cost of providing
advertising relative to its effectiveness in promoting trade.
– Positive effect in generating trade
– Negative effect if some consumer’s don’t receive information.
Efficient Advertising
• The central planner’s problem, then, is to choose  to
maximize
 1 
 S  c   c ln 

1  
• The first-order condition for this problem is
c
c
S c
 0 or 1   
1 
S c
• Hence, the competitive outcome is socially optimal.
Efficient Advertising
– Issues
• Failure of prices to converge in the competitive setting
– Result of the one-shot game assumption in the model
– Need to examine richer models in which prices, industry
structure, and advertising a determined simultaneously
– Special nature of assumptions on the ad probabilities
– Memory-less distribution function
– No targeting of ads at particularly consumers or consumer types
• Importance of targeting and ability to set differential prices in
ecommerce