Monopoly

1
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).

2
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 py-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.

3
Past, Present and Future

• What happens if some decisions are already made
  in the past?
• Remember one cant 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.

4
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 RevenueMarginal
  Cost.

5
Example (from tutorial)

• We had quantity Q15-p. While we were choosing
  prices. This is equivalent (in the monopoly case)
  to choosing quantity.
• r(y) yp(y) where p(y)15-y. Marginal revenue
  was 15-2y.
• We had constant marginal cost of 3. Thus,
  c(y)3y.
• Profity(15-y)-3y
• What is the choice of y? What does this imply
  about p?

6
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 monopolys choice of y (mrmc)?
• What is the competitive equilibrium y (pricemc)?
• Why is a monopoly inefficient? Someone values a
  good above its marginal cost.
• In a diagram, what is the welfare loss?

7
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.

8
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).

9
Natural Monopoly

• When is a monopoly natural such as in certain
  public utilities?
• C(y)1y2. P(y)3-y.
• Notice the c entails a fixed cost of 1.
• Where does pmc (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 cant
  charge a price close to competitive equilibrium
  and survive.
• monopoly (mr3-2y)? Y3/4. If two firms try to
  split this output, they still lose money.
• Government should allow a monopoly but force a
  price cap.

10
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
  p1p2, each firm gets half the consumers.)
• An equilibrium is a choice of prices p1 and p2
  such that
• firm 1 wouldnt want to change his price given
  p2.
• firm 2 wouldnt want to change her price given p1.

11
Bertrand Equilibrium

• Take firm 1s decision if p2 is strictly bigger
  than c
• If he sets p1gtp2, then he earns 0.
• If he sets p1p2, then he earns 1/2D(p2)(p2-c).
• If he sets p1 such that cltp1ltp2 he earns
  D(p1)(p1-c).
• For a large enough p1ltp2, we have
• D(p1)(p1-c)gt1/2D(p2)(p2-c).
• Each has incentive to slightly undercut the
  other.
• Equilibrium is that both firms charge p1p2c.
• Not so famous Kaplan Wettstein (2000) paper
  shows that there may be other equilibria with
  positive profits if there arent restrictions on
  D(p).

12
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 pricegt 3, there is this incentive to
undercut. Similar to the prisoners dilemma.
13
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

14
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.

15
Anti-competitive practices.

• In the 80s, 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).

16
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!
17
Oligopoly

• A monopoly is when there is only one firm.
• An oligopoly is when there is a limited number of
  firms where each firms decisions influence the
  profits of the other firms.
• We can model the competition between the firms
  price and quantity, simultaneously or
  sequentially.

18
Quantity competition (Cournot 1838)

• Profit1p(q1q2)q1-c(q1)
• Profit2 p(q1q2)q2-c(q2)
• Firm 1 chooses quantity q1 while firm 2 chooses
  quantity q2.
• Say these are chosen simultaneously. An
  equilibrium is where
• Firm 1s choice of q1 is optimal given q2.
• Firm 2s 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.

19
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 p4-q1-q2.
• The quantity chosen are either S3/4, M1, L3/2.
• The payoff to player 1 is (3-q1-q2)q1
• The payoff to player 2 is (3-q1-q2)q2

20
Cournot Duopoly Normal Form Game Profit1(3-q1-q
2)q1 and Profit 2(3-q1-q2)q2
S3/4
M1
L3/2
9/8
9/8
5/4
S3/4
9/8
15/16
9/16
15/16
1
3/4
M1
5/4
1
1/2
1/2
9/16
0
L3/2
9/8
3/4
0
21
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 mr4-2q equal
  to mc1.
• What is the Bertrand equilibrium (pmc)?

22
Quantity competition (Stackelberg 1934)

• Firm 1 chooses quantity q1. AFTERWARDS, firm 2
  chooses quantity q2.
• An equilibrium now is where
• Firm 2s choice of q2 is optimal given q1.
• Firm 1s choice of q1 is optimal given firm 2s
  reaction.
• This is the same as subgame perfection.
• We can now write the game in a tree form.

23
Stackelberg Game.
(0,0)
L
M
(.75,.5)
B
S
L
(1.13,.56)
(.5,.75)
L
M
A
M
A
B
B
(1,1)
S
(1.25,.94)
L
(.56,1.13)
S
M
B
B
(.94,1.25)
(1.13,1.13)
S
24
Stackelberg game

• How would you solve for the subgame-perfect
  equilibrium?
• As before, start at the last nodes and see what
  the follower firm B is doing.

25
Stackelberg Game.
(0,0)
L
M
(.75,.5)
B
S
L
(1.13,.56)
(.5,.75)
L
M
A
M
A
B
B
(1,1)
S
(1.25,.94)
L
(.56,1.13)
S
M
B
B
(.94,1.25)
(1.13,1.13)
S
26
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.

27
Stackelberg Game.
(0,0)
L
M
(.75,.5)
B
S
L
(1.13,.56)
(.5,.75)
L
M
A
M
A
B
B
(1,1)
S
(1.25,.94)
L
(.56,1.13)
S
M
B
B
(.94,1.25)
(1.13,1.13)
S
28
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 cant 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.