Download Chapter 12

Chapter 12 - Monopoly
Goals:
1. The sources of monopoly power
2. The monopolist’s problem
3. Seeking more surplus
Part 1: Price Discrimination
Part 2: Bundling Goods.
Sources of Monopoly Power.
Exclusive control over crucial inputs.
 Economies of scale with a downward
sloping LAC  natural monopolies
 Network economies
 Patents temporary monopoly rights
 Licensing by governments or other
institutions

The Monopolist’s Problem.

The monopolist’s problem
◦ Objective of the monopolist : maximize
profits.
◦ Temporary assumption: the monopolist
charges a single price.
◦ In general:
Max (Q) = TR(Q) – TC(Q)=P(Q)*Q - TC(Q)
 MR(Q) = MC(Q).
Note that MR(Q) = ( P/ Q)*Q + P(Q) ≠ P
 optimum Q* and P*
Monopolist’s Problem
The Monopolist’s Problem

Example:
◦ A monopolist faces a demand for its product
given by: P=15 – 1/2Q. Its total cost takes the
following form: TC 5 Q 2
◦ Find the monopolist’s profit maximizing price
and quantity. How much economic profit the
monopolist earn?
Seeking more surplus: Price
Discrimination.
So far, monopolist charges a single price
to the entire market.
 What if the monopolist can charge
multiple prices?

◦ First-degree price discrimination
◦ Second-degree price discrimination.
◦ Third-degree price discrimination.
 Degree = ability to identify consumers.
Price Discrimination.

Third Degree Price Discrimination:
◦ Low ability to distinguish consumers.
◦ Consumers are divided in groups/markets.
◦ Charge different prices across
groups/markets.
◦ For each group, it is still a single price.
Price Discrimination

Third Degree Price
MR Discrimination.
MC 0
Q
1
◦ Exercise: A monopolist
two market segments
MR MC faces
0
Q
each with a well
defined demand function.
5 Q
◦ Demand in market 1 is P = 10 – Q1
◦ Demand in market 2 is P = 20 – Q2
Total Cost = 5 Q 2
1
2
2
2
 If the monopolist exercises his monopoly power to price
discriminate in the two market, what are the prices and
quantity he charges in each market? What is his profit?
 If the monopolist cannot price discriminate, what is the
market price and quantity? What is his profit in this case?
Price Discrimination

Third Degree Price Discrimination – Steps to
solve the monopolist’s problem.
Max = TR – TC
where TR = TR1 + TR2 and Q= Q1 + Q2
◦ First order conditions:
Q1
Q2
MR1 MC
0
MR2 MC
0
◦ Solve for Q1 and Q2.
◦
Substitute into the demand function to get P1 and P2.
Price Discrimination.

Third Degree Price Discrimination.
Price Discrimination.

Second Degree Price Discrimination.
◦ Charge small number of different prices in
one group/market (quantity discount)
Price Discrimination

Second Degree Price Discrimination.
◦ Exercise (Hurdle Model of Price Disc.)
2
 A monopolist has the total cost curve as: TC= 5 Q
 He sets two price PH and PL . To be eligible to buy at
PL, buyer needs to present a coupon cut from a
local newspaper (hurdle).
 Suppose the demand curve is: P = 20 – Q.
 What are the profit maximizing values of PH and PL . What is
the resulting economic profit?
 A new law prevent the monopolist to price discriminate.
What is his profit under this law?
 Are buyers better or worse off under this new law?
Price Discrimination

Second Degree Price Discrimination - Hurdle
Model of Price Disc.
◦ The monopolist charges two prices PL and PH
associated with quantity purchased QL and QH :
Max = TR – TC
where TR = PHQH + PLQL , Q= QL + QH
and PH = a + bQH ; PL = a + b(QL + QH)
◦ First order conditions:
QL
QH
MRL
MRH
MC
MC
0
0
◦ Solve for QL and QH.
◦
Substitute into the demand function to get PL and PH.
Price Discrimination.

First-degree price discrimination:
◦ Charge different price for each different unit
purchased.
Price Discrimination.

Practical application – Two part Tariff.
◦ Necessary conditions:
 Individual demand curves are all known
 No arbitrage opportunity.
◦ Method:
 Total amount (= tariff) the consumer pays for q units is
 T(q) = F + p*q
 F: fixed fee, p: per-unit charge
 Result: Charge consumer p=MC and F equal to the
would-be consumer surplus when p=MC.
 Hence F is different for each consumer.
 Special case: if consumers are identical F is equal across
consumers.
Price Discrimination

First Degree Price Discrimination – 2 part
tariff.
◦ Exercise: Consider the monopolist presented
in the previous exercise with demand curve
given by P=120 – Q and the MC =2Q.
◦ If the monopolist is allowed and is able to first
price discriminate, using the two part tariff
method to identify his fixed fee and the per
unit price and quantity associated with that
price.
◦ What happen to the DWL?
Other pricing method: Sell in
Bundle.

Example: Sell Word and Excel separately
or sell the bundle called Microsoft office.
Two types of consumers, A and B. A’s
valuations are 120 for Word and 80 for
Excel. B’s valuations are opposite: 80 for
Word and 120 for Excel. MC=0.
 Microsoft can sell all programs separately for
2*80+2*80=$320
 Microsoft can also sell two times MS Office
Suite for 2*200=$400