Transcript Monopoly

Profit Maximization
• What is the goal of the firm?
–
–
–
–
Expand, expand, expand: Amazon.
Earnings growth: GE.
Produce the highest possible quality: this class.
Many other goals: happy customers, happy
workers, good reputation, etc.
• It is to maximize profits: that is, present
value of all current and future profits (also
known as net present value NPV).
Profit Maximization
• The environment is competitive: no one firm can
influence the price.
• We can write profit maximization of a competitive
firm in terms of a cost function (cost of producing
y units of output)
Maxy p*y-c(y)
• What is the FOC?
• What is profits and choice of y if c(y)=y2?
• With general c(y), when would a firm shut down?
When average cost is always above p.
Past, Present and Future
• What happens if some decisions are already
made in the past?
• Remember one can’t change the past.
• Euro-tunnel: spend billions to build it.
Does this mean that prices have to be higher
for tickets?
• Similar for Airwave Auctions, Iridium and
many other cases.
Monopoly
• Standard Profit Maximization is
max r(y)-c(y).
• With Monopoly this is Max p(y)y-c(y) (the
difference to competition is price now
depends upon output).
• Maximization implies Marginal
Revenue=Marginal Cost.
Example (from tutorial)
• We had quantity Q=15-p. While we were choosing
prices. This is equivalent (in the monopoly case)
to choosing quantity.
• r(y)= y*p(y) where p(y)=15-y. Marginal revenue
was 15-2y.
• We had constant marginal cost of 3. Thus,
c(y)=3*y.
• Profit=y*(15-y)-3*y
• What is the choice of y? What does this imply
about p?
Example
• Price is p(y)=120-2y, this implies marginal
revenue is 120-4y.
• Total cost is c(y)=y2. This implies marginal cost is
2y.
• What is the monopoly’s choice of y (mr=mc)?
• What is the competitive equilibrium y (price=mc)?
• Why is a monopoly inefficient? Someone values a
good above its marginal cost.
• In a diagram, what is the welfare loss?
Why Monopolies?
• What causes monopolies?
– a legal fiat; e.g. US Postal Service
– a patent or trade secret; e.g. a new drug
– sole ownership of a resource; e.g. a toll
highway
– formation of a cartel/collusion; e.g. OPEC
– large economies of scale; e.g. local utility
companies.
Patents
• A patent is a monopoly right granted to an
inventor. It lasts about 17 years.
• For the government: there is a trade-off between
– loss due to monopoly rights.
– incentive to innovate.
• For the company
– Must decide between patent and trade secret.
– Minus side of patent is that it expires and is no longer
secret (competitors can perhaps go around it).
– Minus side of trade secret is that there is no legal
protection, but lasts forever. For example, Coca Cola.
– Strategy – protective, delay or shelve? License
(temporarily remove competition).
Natural Monopoly
• When is a monopoly natural such as in certain
public utilities?
• C(y)=1+y2. P(y)=3-y.
• Notice the c entails a fixed cost of 1.
• Where does p=mc (mc is 2y)?
• What is profits at this point for a single firm that
meets the whole demand?
• What happens when another firm enters? They
can’t charge a price close to competitive
equilibrium and survive.
• monopoly (mr=3-2y)? Y=3/4. If two firms try to
split this output, they still lose money.
• Government should allow a monopoly but force a
price cap.
Bertrand (1883) price competition.
• Both firms choose prices simultaneously and have
constant marginal cost c.
• Firm one chooses p1. Firm two chooses p2.
• Consumers buy from the lowest price firm. (If
p1=p2, each firm gets half the consumers.)
• An equilibrium is a choice of prices p1 and p2
such that
– firm 1 wouldn’t want to change his price given p2.
– firm 2 wouldn’t want to change her price given p1.
Bertrand Equilibrium
• Take firm 1’s decision if p2 is strictly bigger than
c:
– If he sets p1>p2, then he earns 0.
– If he sets p1=p2, then he earns 1/2*D(p2)*(p2-c).
– If he sets p1 such that c<p1<p2 he earns D(p1)*(p1-c).
• For a large enough p1<p2, we have:
– D(p1)*(p1-c)>1/2*D(p2)*(p2-c).
• Each has incentive to slightly undercut the other.
• Equilibrium is that both firms charge p1=p2=c.
• Not so famous Kaplan & Wettstein (2000) paper shows
that there may be other equilibria with positive profits if
there aren’t restrictions on D(p).
Bertrand Game
Marginal cost= £3, Demand is 15-p.
The Bertrand competition can be written as a game.
Firm B
£9
£8.50
35.75
18
£9
18
0
Firm A
17.88
0
£8.50
17.88
35.75
For any price> £3, there is this incentive to undercut.
Similar to the prisoners’ dilemma.
Cooperation in Bertrand Comp.
• A Case: The New York Post v. the New
York Daily News
• January 1994 40¢
40¢
• February 1994 50¢
40¢
• March 1994 25¢ (in Staten Island) 40¢
• July 1994
50¢
50¢
What happened?
• Until Feb 1994 both papers were sold at 40¢.
• Then the Post raised its price to 50¢ but the News
held to 40¢ (since it was used to being the first
mover).
• So in March the Post dropped its Staten Island
price to 25¢ but kept its price elsewhere at 50¢,
• until News raised its price to 50¢ in July, having
lost market share in Staten Island to the Post. No
longer leader.
• So both were now priced at 50¢ everywhere in
NYC.
Anti-competitive practices.
• In the 80’s, Crazy Eddie said that he will beat any
price since he is insane.
• Today, many companies have price-beating and
price-matching policies.
• They seem very much in favor of competition:
consumers are able to get the lower price.
• In fact, they are not. By having such a policy a
stores avoid loosing customers and thus are able to
charge a high initial price (yet another paper by this Kaplan guy).
Price-Matching Policy Game
Marginal cost= £3, Demand is 15-p. If both firms have
price-matching policies, they split the demand at the
lower price.
Firm B
£9
£8.50
17.88
18
£9
18
17.88
Firm A
17.88
17.88
£8.50
17.88
17.88
The monopoly price is now an equilibrium!
Oligopoly
• A monopoly is when there is only one firm.
• An oligopoly is when there is a limited
number of firms where each firm’s
decisions influence the profits of the other
firms.
• We can model the competition between the
firms’ price and quantity, simultaneously or
sequentially.
Quantity competition (Cournot 1838)
• Profit1=p(q1+q2)q1-c(q1)
• Profit2= p(q1+q2)q2-c(q2)
• Firm 1 chooses quantity q1 while firm 2 chooses
quantity q2.
• Say these are chosen simultaneously. An
equilibrium is where
– Firm 1’s choice of q1 is optimal given q2.
– Firm 2’s choice of q2 is optimal given q1.
• This is a Nash equilibrium!
– Take FOCs and solve simultaneous equations.
– Can also use intersection of reaction curves.
Cournot Simplified
• We can write the Cournot Duopoly in terms
of our Normal Form game (boxes).
• Take D(p)=4-p and c(q)=q.
• Price is then p=4-q1-q2.
• The quantity chosen are either S=3/4, M=1,
L=3/2.
• The payoff to player 1 is (3-q1-q2)q1
• The payoff to player 2 is (3-q1-q2)q2
Cournot Duopoly: Normal Form Game
Profit1=(3-q1-q2)q1 and Profit 2=(3-q1-q2)q2
S=3/4
M=1
L=3/2
9/8
9/8
5/4
S=3/4
9/8
15/16
9/16
15/16
1
3/4
M=1
5/4
1
1/2
1/2
9/16
0
L=3/2
9/8
3/4
0
Cournot
• What is the Nash equilibrium of the game?
• What is the highest joint payoffs? This is
the collusive outcome.
• Notice that a monopolist would set mr=4-2q
equal to mc=1.
• What is the Bertrand equilibrium (p=mc)?
Quantity competition
(Stackelberg 1934)
• Firm 1 chooses quantity q1. AFTERWARDS,
firm 2 chooses quantity q2.
• An equilibrium now is where
– Firm 2’s choice of q2 is optimal given q1.
– Firm 1’s choice of q1 is optimal given firm 2’s reaction.
• This is the same as subgame perfection.
• We can now write the game in a tree form.
Stackelberg Game.
L
M
S
B
L
(0,0)
(.75,.5)
(1.13,.56)
M
AA
M
B
B
S
L
S
(.56,1.13)
M
B
B
S
(.5,.75)
L
(.94,1.25)
(1.13,1.13)
(1,1)
(1.25,.94)
Stackelberg game
• How would you solve for the subgameperfect equilibrium?
• As before, start at the last nodes and see
what the follower firm B is doing.
Stackelberg Game.
L
M
S
B
L
(0,0)
(.75,.5)
(1.13,.56)
M
AA
M
B
B
S
L
S
(.56,1.13)
M
B
B
S
(.5,.75)
L
(.94,1.25)
(1.13,1.13)
(1,1)
(1.25,.94)
Stackelberg Game
• Now see which of these branches have the
highest payoff for the leader firm (A).
• The branches that lead to this is the
equilibrium.
Stackelberg Game.
L
M
S
B
L
(0,0)
(.75,.5)
(1.13,.56)
M
AA
M
B
B
S
L
S
(.56,1.13)
M
B
B
S
(.5,.75)
L
(.94,1.25)
(1.13,1.13)
(1,1)
(1.25,.94)
Stackelberg Game Results
• We find that the leader chooses a large quantity
which crowds out the follower.
• Collusion would have them both choosing a small
output.
• Perhaps, leader would like to demonstrate
collusion but can’t trust the follower.
• Firms want to be the market leader since there is
an advantage.
• One way could be to commit to strategy ahead of
time.
– An example of this is strategic delegation.
– Choose a lunatic CEO that just wants to expand the
business.