Monopoly

1
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).
• FOC yields p(y)p(y)yc(y). This is also
  Marginal RevenueMarginal Cost.
• This equals p(y)(1-1/e)c(y) remember
  e(dy/dp)(p/y)
• Notice there is a problem unless egt1.

2
Example

• Price is p(y)120-2y
• Cost is c(y)y2
• Profit is p(y)y-c(y) what is choice of y?
• What is the competitive equilibrium y?
• Why is a monopoly inefficient?
• In a diagram, what is the welfare loss?

3
Rule of thumb prices

• Many shops use a rule of thumb to determine
  prices.
• Clothing stores may set price double their costs.
• Restaurants set menu prices roughly 4 times
  costs.
• Can this ever be optimal?
• If qAp? what is elasticity?
• What is price if marginal cost is constant?

4
Why Monopolies?

• What causes monopolies?
• a legal fiat e.g. US Postal Service
• a patent 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.

5
Patents

• A patent is a monopoly right granted to an
  inventor. It lasts about 17 years.
• There is a trade-off between
• loss due to monopoly rights
• incentive to innovate.

6
Natural Monopoly

• When is a monopoly natural such as in certain
  public utilities?
• C(y)1y2. P(y)3-y.
• Where does pmc?
• What is profits at this point for one firm?
• What happens when another firm enters?

7
Taxes

• What happens to the monopolys choice under a
  profit tax?
• What happens under a quantity tax?
• This shifts up the supply/marginal cost curve.
• The monopolist chooses where MRMC so the
  quantity is reduced.
• Consequently, welfare is lower.

8
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 sequentially.

9
Quantity competition (Cournot 1838)

• ?1p(q1q2)q1-c(q1)
• ?2 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.
• If D(p)4-p and c(q)q, what the equilibrium
  quantities and prices.
• Take FOCs and solve simultaneous equations.
• Can also use intersection of reaction curves.

10
Quantity competition (Stackelberg 1934)

• ?1p(q1q2)q1-c(q1)
• ?2 p(q1q2)q2-c(q2)
• 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 q2(q1).
• That is, firm 1 takes into account the reaction
  of firm 2 to his decision.

11
Stackelberg solution

• If D(p)4-p and c(q)q, what the equilibrium
  quantities and prices.
• Must first solve for firm 2s decision given q1.
• Maxq2 (4-q1-q2)-1q2
• Must then use this solution to solve for firm 1s
  decision given q2(q1) (this is a function!)
• Maxq1 4-q1-q2(q1)-1q1

12
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.

13
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).

14
Collusion

• If firms get together to set prices or limit
  quantities what would they choose.
• D(p)4-p and c(q)q.
• Quantity Maxq1,q2 (4-q1-q2-1)(q1q2).
• Price Maxp (p-1)(4-p)
• This is the monopoly price and quantity! Show all
  4 possibilities (Cournot, Bertrand, Collusion,
  Stackelberg) on the q1, q2 graph?

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).