Transcript Competition in prices - uni

Homogeneous-good markets
Price competition (Bertrand duopoly, price
cartels)
 Capacity and price competition
(Kreps/Scheinkman)
 Quantity competition (Cournot duopoly,
Stackelberg duopoly, quantity cartels)
 Capacity competition
 Innovation competition

Competition in prices

The Bertrand model as a simultaneous price
competition:
p1
p2
1
2
The Bertrand model
Market demand function X  p   d  ep
 Demand function of firm 1

 d  ep1 if p1  p2
 d  ep1
x1  
if p1  p2
 2
if p1  p2
 0
Equal costs:
 Different costs:

c1  c2  c
c1  c2
Demand function of firm 1
x1
X ( p 1)
1
2
X ( p 2)
0
p2
p1
Profit function of firm 1
1st case
1
2nd case
1
p1  p2
M
c1
M
p1
p2
p1
c1  p2  p1M
c1
p2
3rd case
1
c1  p2
p1
p1
M
p1
Bertrand paradox (equal costs)
 c, c 
is a Nash equilibrium in the Bertrand
model with equal marginal costs
  c , c  is the only equilibrium.
– c   ,

–
c   , c   
c   , c    with   
– c   , c 
 Marginal cost pricing and no profits!
–
Relaxing the assumptions

Capacity constraints
–
–
Assumption : X c   capacity
2
Is (c,c) an equilibrium?
1
 X c 
Product differentiation
 Repeated play

– c   , c   
–
is not an equilibrium in the one-shot
game,
but may be sustained as an equilibrium of
repeated game.
Exercise (discrete prices)
Assume discrete prices and monetary units
(1$, 2$,...) as well as equal marginal costs
c=10.
 Find the Bertrand-Nash equilibria.

Entry barriers
Free entry tends to drive profits down.
 Entry barriers allow established firms to
make profits without attracting competitors.
 Entry barriers
- cost advantages (marginal cost, sunk cost),
- product differentiation,
- government regulation.

Behavior of the firms
Blockaded entry: There is no threat of entry
even if established firms maximize profits.
 Deterred entry: Established firms try to
make entry unattractive to potential
competitors.
 Accommodated entry: Established firms do
not deter entry and potential competitors
become actual competitors.

Blockade or deterrence (c1  c2 )

Blockaded entry of firm 2:
1 d
and
c2  p M c1     c1 
2 e

c1 
d
e
Bertrand-Nash equilibrium:  p M c , c
1

Deterrence of firm 2:
c2  p
M
c1   1  d  c1 
2 e

and
Bertrand-Nash equilibrium:
 p c   c
L
1
2
2
  , c2

d
c1 
e
2

Blockade, deterrence and
Bertrand paradox
c2
no supply
d
e
blockade
firm 1 as a
monopolist
d
2e
deterrence
deterrence
d
2e
firm 2 as a
monopolist
blockade
d
e
duopoly,
Bertrand
paradox
c1
Price cartel
If the cost differences are zero (Bertrand
paradox) or as in the case of entry deterrence,
a cartel might be established.
 There are strong incentives to deviate from the
cartel prices.

The cartel, graphically
c2
d
e
no supply
firm 1 as a
monopolist
d
2e
firm 2 as a
monopolist
cartel
d
2e
d
e
c1
Exercise (price cartel)
Consider two firms competing in prices. The
demand function is given by
X(p)=20-2p .
Suppose that the equal and constant unit costs
are given by 6.
a) Find the optimal cartel price.
b) Calculate the maximum profit difference a
deviating firm could achieve.
Exercise (bundle)
A monopolist sells a bundle ...
x1(p1, p2)=100-p1 -p2
x2(p1, p2)=100-p2-p1
Unit costs are constant at $20.
a) Profit-maximizing prices?
b) Now assume there are two monopolists
selling the components independently.
The Microsoft case: What happened
Judge Thomas Penfield Jackson issued his
final judgment in the antitrust case against
Microsoft (Plaintiff: USA, Defendant:
Microsoft Corporation) in June 2000.
 Microsoft shall submit a proposed plan of
divestiture. The Plan shall provide for ...
[the] separation of the Operating Systems
Business from the Applications Business.

Krugman`s parable (New York
Times, April 26, 2000)


„Baron Wilhelm von Gates was the lord of two castles,
each commanding a strategic bottleneck along the
Rhine. From these castles he was able to demand money
from all the travelers who passed by. ... Eventually the
Holy Roman Emperor ... split up the Gates domain,
giving one of the castles to the baron's nephew.“
Result: „Not only did [travelers] now face the nuisance
of dealing with two different robber barons, but they
said they were paying more for each trip than they had
before.
What do you think?
Operating systems and applications are
complements, like the two castles.
 After the breakup, positive externalities
going from one castle to the other, from the
operating systems business to the
applications business, cannot be internalized
any more.
 Prices go up, but profits go down.

Most-Favored-Customer Clause
(MFC)
 A MFC
guarantees a customer the best price the
company gives to anyone.
 MFCs
are very common in business-to-business
contracts.
 They
sound like a good deal for your customers,
indeed the main effect is to shift the balance in
favor of the seller.
MFC: Example
In 1971 members of the American Congress figured that they should find a
way to lower campaign expenses. Thus, the politicians voted themselves an
MFC for television spots.
The law didn’t quite have the desired effect. Knowing that, in an election
year, politicians are going to purchase significant chunks of airtime, the
networks want to get as much as they can for these spots. So with an election
coming up, how will a network respond when a commercial customer comes
to negotiate the rate for an ad spot? It will be very though on price. Giving a
concession is extremely costly, since any discount must be extended to all the
politicians buying spots. The network would likely end up losing more from
the lower price paid by all politicians than it would gain from getting some
extra business.
One result of the law was that the networks ended up making more money
than before.
MFC: the seller’s perspective
Pros
1. Makes you a thouger negotiator.
(“I’d love to give you a better price, but I can’t afford to.”)
2. Reduces your customers’ incentive to bargain.
(The customer is guaranteed that no one else can get a better price, even if he
does no negotiating at all.)
Cons
1. Makes it easier for a rival to target one of your
customers.
2. Makes it harder for you to target one of your rival’s
customers.
MFC: the customer’s perspective
Pros
1. Allows you to benefit from any better deal subsequently
offered to other customers.
2. Ensures you that you’re not at a cost disadvantage relative
to rivals.
3. Eliminates the risk of looking bad if other customers strike
better deals.
Cons
1. When others have MFCs, it’s harder for you to get a
“special” deal.
Meet-the-Competition Clauses
(MCC)

An MCC is a contractual arrangement
between company and customer that gives the
company an option to retain the customer’s
business by meeting any rival bids.

An MCC doesn’t force you to meet the
competition. It simply rewards you, if you do
so, with the assurance of the customer’s
continued business.

MCCs are most often found in commodity
business.
MCC: Example
In January 1994 the Miami Dolphins football team was sold for $138
million to H.W. Huizenga. A pretty good buy - almost a steal.
When Dolphins owner J. Robbie died in 1990, the team was passed to
his nine children. Following the death of their father, the Robbies sold
Huizenga a 15 percent stake together with a right of first refusal (the
buyer’s counterpart to an MCC) on any future sale. Thus, the Robbie
children couldn’t sell the team without first giving Huizenga an
opportunity to match the best offer.
Put yourself in the shoes of a prospective bidder. You invest time, effort
and money lining up financing. Will you be able to outbid Huizenga?
Doubtful. If it make sense for you to acquire the team at a certain price,
it will make sense for Huizenga, too. The best offer was the $138million bid that Huizenga matched when he bought the team.
What should the Robbie children have done?
MCC: Pros and Cons
Pros
1. Reduces the incentive for competitors to bid.
(You can undercut any rival bid as far as it’s a good deal.)
2. Takes the guesswork out of bidding - you know what
you have to beat.
3. Lets you decide whether to keep the customer.
Cons
1. Allows competitors to bid without having to deliver.
(Your rival can make a low bid, fully expecting that you will match and lowers
your profit without having to put himself on the line.)
MCC: Imitation
 Far
from being undermined by imitation, an
MCC is actually enhanced by it.
 If
other producers also put in MCCs they will be
allowed to push prices up some more and will
have even more to lose from starting a share war.
Take-or-pay contracts
 A take-or-pay
contract is a rule structering
negotiations between companies and their
suppliers. With this kind of contract, you either
take the product from the supplier or you pay a
“penality”.
 Take-or-pay contracts are often seen in
agreements to purchase commodity inputs,
electricity and cable programming, where
suppliers face large fixed costs relative to
variable costs.
Take or pay: Pros and Cons
Pros
1. Reduces risk to your supplier, in return for which you
can ask to pay less.
2. Reduces a rival’s incentive to come after your
customers by making retaliation a near certainty.
(You would require a replacement for the lost customer in order to avoid
penalities.)
Cons
1. Increases severity of price war if deterrence fails.
(You are forced to retaliate, and that in turn could trigger a sequence of tit-fortat responses that escalate into a price war.)
Mass-Market Rules
 Mass
consumer markets are very different. Seller
don’t negotiate, hence buyers can’t negotiate.
 Suppliers get to name the price of the item they
are selling. If the customer wants the product, he
has to pay the price.
 Take it or leave it.
MFCs in mass consumer markets
 At
first glance, there would be nothing to gain by
imposing an MFC.
 But, in fact, there is still a reason to consider an
MFC.
 Though customers my be unable to negotiate, they
can postpone buying. They may do just that if
they are not convinced that you will hold firm to
your price.
 Granting MFCs helps you get out of this trap.
MFC: Example
In 1990 Chrysler used a variant of MFC to change the game of selling cars.
The way car buyers played the game is that they would wait for end-of-year
rebates, and, by waiting, leave the dealers with large inventories, which
would then force the manufacturer to offer these rebates.
Chrysler wanted to convince customers that there would be no gain from
waiting. What Chrysler did was promise people who bought a car in January
that if it offered a larger rebate later in the year, it would go back to them
and make up the difference.
Chrysler’s guarantee had two effects. Customers had no incentive to wait, so
end-year inventories were smaller and end-of-year rebates weren’t as
necessary. Moreover, Chrysler was now less tempted to offer rebates to clear
out whatever end-year inventory did remain.
MCCs in mass consumer markets
 MCC
do not make sense in mass consumer marekts
because you cannot force consumers to buy from
you.
 A minimum-price guarantee is not the same as an
MCC. Consumers don’t have to give you the option
to match.
Targeted Rebates
 You
may charge low prices, but that might attract
your rivals’ customers away, and then your rivals
will respond by lowering their prices. You are
where you started, except prices are lower all
around.
 So what you would really like to do is to charge a
low price to your own customer without threatening
your rivals’ customer bases.
 If you do that, your rivals wouldn’t have to
respond.
Targeted Rebates: Example
In response to flat demand and increased competition, General Motors changed
the game in 1992. They teamed up with a bank and launched a credit card.
Cardholders would earn credit equal to 5 percent of their charge volume, which
could be applied to the purchase of a new GM car.
The GM card rollout was the most successful ever in the credit-card-business.
How did it work? GM found a way to direct a rebate to its natural customer base
and at the same time raised its list price. A competitor could go up with its prices
without getting in danger of losing any of its natural customer base. Now GM
could raise its price again without losing any of its customer base. The rebate
program creates a win-win pricing dynamic between them.
The key to effectiveness of the rebate program is that the rebates are targeted. It
works only if the people who get rebates on GM cars are predominantly
prospective GM buyers.
Targeted Rebates: Pros and Cons
Pros
1. Allows you to charge your own customers low prices
without threatening your rival’s customer base.
2. Encourages customers - even price shoppers - to
become loyal.
3. Creates synergies with credit-card partners.
Cons
1. In rewarding loyalty in cash rather than kind, doesn’t
raise your added value.
2. Is ineffective on small-ticket items.
Targeted Rebates: Imitation
Five months later Ford joined forces with Citibank to offer a credit card and in
1994 Volkswagen launched a credit-card rebate program.
Does all this imitation put a dent in the GM program? Not necessarily. If GM was
hoping to use its program to take market share from Ford and others, then
imitation was indeed bad news.
But imitation also helps GM. As more card programs appear, car manufactures are
less tempted to cut price, because low prices are no longer as effective in
attracting customers. People who have built up credits in someone else’s program
won’t readily switch. Moreover, if a carmaker now raises price, it won’t lose as
many customers as before.
Another positive effect: It becomes more important for car buyers to choose sides.
Minimum-price guarantees
Minimum-price guarantees assure the
consumers the lowest price charged by any
one firm.
 If firm 1 offers a minimum-price guarantee,
its actual price will be equal to the
minimum of the prices charged by the two
firms:

p1act  min p1, p2 
Minimum-price guarantees,
graphically
1
M
1st case
p1
M
c1
1
1
 p2
M
p1
M
p2
p1
2nd case
c1  p2  p1M
c1
p2
p1
M
p1
3rd case
Firm 1 offers a minimumprice guarantee.
c1  p2
p1
Minimum-price guarantees firm 2’s profit function
2
1st case
2
p2 M  p1
c2  pc11p2Mp 1

p2
M
1 M

2
1 M

2
p2
c2
2
2nd case
M
p1
p2
c2
p1
p2
M
p2
3rd case
c1 
p1 
p2
M
1 M

2
Firm 1 offers a minimumprice guarantee.
c2  p1
p2
M
p2
Two-stage model
minimum-price
guarantee by
firm 1
minimum-price
guarantee by
firm 2
p1
p2
1
2
Four possibilities
Neither firm 1 nor firm 2 offers a minimumprice guarantee:
Bertrand paradox
 Only firm 1 offers a minimum-price
guarantee.
 Only firm 2 offers a minimum-price
guarantee.
 Both firms offer a minimum-price
guarantee.

Unilateral minimum-price guarantee
 c , c  is a Nash equilibrium.
  c , c  is the only equilibrium.

–
–
c   ,, , c   
c   , c   
c   , c    with   
– c   , c    with   
– c   , c , c, c   
–

Uniliteral minimum-price guarantees result in
the Bertrand paradox.
Bilateral minimum-price guarantee
 c , c  is a Nash equilibrium.
  c , c  isn’t the only equilibrium.

– p
– p
– p
M
M
–


, c    withc    p
, c    withc    p
M
, pM ?
c   , c    with c  
M
?
M
?
 pM ?
Are there any dominant strategies ?
Minimum-price guarantee
Payoff matrix
st
(1
level)
firm 2
with
minimumprice
guarantee
firm 1
with
minimumprice
guarantee
without
minimumprice
guarantee
without
minimum-price
guarantee
1 M 1 M 
  ,  
2
2

(0, 0)
(0, 0)
(0, 0)
The game in extensive form
p1
p2
A player’s
strategy:
p2
1. decision for
or against a
guarantee
g
g
p1
ng
F1
g
p1
ng
F2
p2
ng
F1
p2
p1
F2
2. decision on
prices in all 4
possible
situations
Equilibria in extensive form games

A strategy is of the following form:
g / ng, g, g , g, ng, ng, g , ng, ng

Which of these strategy combinations are
equilibria?
–
–
–
((g,pM,c,c,c),(g,pM,c,c,c)) ?
((g,pM,c,c,c),(g,pM, pM ,c,c)) ?
((ng,c,c,c,c),(ng,c,c,c,c)) ?
Executive summary I



Homogeneity leads to an aggressive price war
suppressing profits.
In case of equal costs, zero profits (the Bertrand
paradox) result. In case of unequal costs, the cost
leader will prevail.
Ways out of the Bertrand paradox:
–
–
–
Capacity constraints
Repeated play
Product differentiation
Executive summary II
Minimum-price guarantees




reduce consumers’ uncertainty about fair
prices,
make a price above unit cost a dominant
strategy,
discourage entry,
may accomplish the monopoly outcome if
given by both firms.