Imperfect Competition: Monopoly
New Topic: Monopoly
Q: What is a monopoly?
A monopoly is a firm that faces a downward sloping demand, and has a choice about
what price to charge – an increase in price doesn’t send most or all of the customers
away to rivals.
A Monopolistic Market consists of a single seller facing many buyers.
Monopoly
Q: What are examples of monopolies?
There few pure monopolies in the world
- US postal mail faces competition from fed-ex, or even emails
- Microsoft faces competition from apple or linux
- But there is one producer of aircraft carriers.
But many firms have some market power- can increase prices above marginal costs for
a long period of time, without driving away consumers.
Monopoly
Q: Why do monopolies arise?
Three reasons:
1. Government provision- for example patents, copyright laws, rights for satellite
communication in certain countries, taxi permits
2. Large Economies of Scale – average cost of a single firm serving the entire market is
lower than two firms. Happens when there are large fixed costs. For example:
telephone lines, electricity generation (before the 80s)
3. Control of an essential input that cannot be replicated- For example, Coca-cola’s
recipe, Google’s algorithm
Monopoly
Q: Why do monopolies arise?
Definition: A market is a natural monopoly if the total cost incurred by a single
firm producing output is less than the combined total cost of two or more firms
producing this same level of output among them.
Examples- Happens when there are high fixed costs. Electricity plants, Satelitte
companies,
Monopoly
Q: Why do monopolies arise?
Definition: Entry barriers are Factors that allow an incumbent firm to earn
positive economic profits while making it unprofitable for newcomers to
enter the industry.
1.Structural Barriers to Entry – occur when incumbent firms have cost
or demand advantages that would make it unattractive for a new firm
to enter the industry (Example- Ebay or Facebook)
2.Legal Barriers to Entry – exist when an incumbent firm is legally
protected against competition (Example- Patent laws)
3.Strategic Barriers to Entry – result when an incumbent firm takes
explicit steps to deter entry (Example- Polaroid's price war with Kodak
when Kodak entered the instant photography market in the 70s).
Monopoly
The monopoly’s problem:
The monopoly faces a downward sloping demand curve and chooses both prices and
quantity to maximize profits. Note, that the monopoly is constrained by consumer’s
demand, if it charges a high price consumers will buy less.
We let that the monopoly choose quantity q, and the demand determines the price
p(q). The problem is to choose q to maximize
 (q)  TR(q)  TC(q)  pq  TC(q)
Monopoly’s Problem
A graphical analysis of the change in revenue:
P(Q) 12  Q
By increasing quantity
from 2 units to 5 units,
the monopolist reduces
the price from $10 to $7.
The revenue gained is
area III, the revenue lost
is area I
The slope of the demand
curve determines the
optimal quantity and price
Monopoly’s Problem
The monopoly faces a demand curve and choose quantity to maximize
profit.
Total revenue TR(q)  p(q)q
The profit:  (q)  TR(q)  TC(q)  p(q)q  TC(q)
First order conditions:
The Marginal revenue is

 p(qm )  qm p(qm )  c(qm )  0
q
MR(q) 
And the optimality condition is
dTR(q)
 p(q)  qp(q)
dq
MR(q)  mc(q)
Marginal Revenue
Example suppose demand is p(q)=12-q
What is the change in revenue when the firm moves from producing 2
units to 3 units? From 3 units to 4 units? And from 4 units to 5 units?
dTR(q)
The Marginal revenue is MR(q) 
 p(q)  qp(q)
dq
Is the rate at which revenue changes with output
Marginal Revenue
The marginal revenue MR(q)  dTR(q)  p(q)  qp(q)
dq
p
Key property:
The marginal revenue lays below the
demand curve:
MR(q)  p(q)
D
q
MR
Monopoly
A graphical analysis of the monopoly's problem
Key point:
p
MC
The monopoly produces a
quantity such that marginal
costs equals marginal revenue.
pm
MR(q)  mc(q)
D
qm
q
qc
MR
But the price Pm is given by the
demand curve. It is higher than
the competitive price.
Monopoly
Example:
Suppose demand and marginal costs are linear:
p(q)  a  bq
mc(q)  cq
constants. What is the monopolist optimal quantity and price?
TR(q )  qp (q )
MR(q )  p (q )  qp ' (q )  a  bq  bq  a  2bq
mc(q )  MR(q )
cq  a  2bq
q
a
c  2b
p  a  b(
a
)
c  2b
Where a,b,c>0 are
Monopoly
Relationship between the monopoly's price and the competitive
market price.
p
The monopoly charges a higher
price, and produces less units
than the competitive outcome.
MC
Dead
Weight
Loss
pm
What is the social cost of the
monopolist?
pc
D
qm
q
qc
MR
Monopoly
Elasticity and marginal revenue:
The elasticity of demand:  q , p
The marginal revenue:
q( p) p

p q
p(q)
q p
 p(1 
)
q
p q
1
MR(q)  p(1 
)
MR(q)  p  q
 q, p
At the monopolist’s optimum:
MR(qm )  mc(qm )
or
p (qm )(1 
1
 q, p
)  mc(qm )
p (qm )  mc(qm )
1

p ( qm )
 q, p
Monopoly
Relationship between the monopoly's price and the competitive
market price.
p(qm )  mc(qm )
1
p ( qm )

 q, p
Key Property:
p
MC
Dead
Weight
Loss
pm
The “distance’ from the competitive
price is negatively related with the
elasticity of demand.
pc
The more elastic (= “flatter”) is the
demand curve, the smaller is the
difference between the market and the
monopoly price.
D
qm
q
qc
MR
The more inelastic (= “steeper) is the
demand curve, the larger is the
difference.
Monopoly
Relationship between the monopoly's price and the competitive
market price. p(qm )  mc(qm )
1

p ( qm )
p
 q, p
MC
Dead
Weight
Loss
pm
pc
Definition:
D
qm
q
qc
MR
1

The “Lerner index” is
 q, p
Is used to measure monopoly power of
a firm. It is the percent markup of price
above marginal costs
Monopoly
Note
A monopolist does not have a supply curve ,the monopolist picks a
preferred point on the demand curve. The quantity supplied is
determined by demand.
One could also think of the monopolist choosing price to maximize
profits subject to the constraint that output is determined by the
demand curve.
Types of Monopolies
Definition: A cartel is a group of firms that collusively determine the price and output in
a market. In other words, a cartel acts as a single monopoly firm that maximizes total
industry profit.
Example- OPEC