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 is one producer of aircraft carriers, but 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 many firms have some market power- can increase prices above marginal costs for
a long period of time, without driving away consumers.
Monopoly’s problem
3
Example: A monopolist faces demand given by p(q) 12  q
There are no variable costs and all fixed costs are sunk. How many units should the
monopoly produce and what price should it charge?
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
4
The monopoly faces a downward sloping demand curve and chooses both prices and
quantity to maximize profits. We let the monopoly choose quantity q and the demand
determine the price p(q) because it is more convenient.
The monopoly’s problem is to choose q to maximize profit:
max  (q )  TR (q)  TC (q )
q
The monopoly’s total revenue is:
TR(q)  qp(q)
where p(q) is given by the demand.
Monopoly’s problem
5
max  (q )  TR (q)  TC (q)  p(q)q  TC (q)
q
The optimality condition is
The marginal cost is
MR(q)  MC(q)
MC(q) 
TC
q
The marginal revenue is the rate at which TR changes with q
MR 
TR(q) 
p(q)
 [ p(q)q] 
q  p(q)
q
q
q
Marginal revenue
6
The marginal revenue
TR (q)
p(q)
MR(q) 
 p(q)  q
q
q
p
Key property:
The marginal revenue lays below the
demand curve:
MR(q)  p(q)
Example: demand is p(q) =12-q.
What are TR(q) and MR(q)?
D
q
MR
Example 1
7
Suppose that demand and marginal cost are linear:
p(q)  a  bq
MC(q)  cq
where a,b,c>0 are constants. What is the monopolist’s optimal quantity and price?
TR (q )  qp(q )  aq  bq2
MR(q )  a  2bq
MC(q )  MR(q )
cq  a  2bq
a
q
c  2b
a
p  a  b(
)
c  2b
Monopoly and consumer surplus
8
Relationship between the monopoly's price and the perfectly
competitive price that maximizes consumer surplus, pcs.
p
Consumer surplus is the area
between the demand curve and
the market price.
MC
pm
The monopoly charges a higher
price, and produces less units.
MR
pcs
qm
D
qcs
q
What is the surplus (welfare)
cost of the monopolist to
consumers?
Monopoly and total surplus
9
Consumer surplus is the area between
the demand curve and the market
price.
p
Producer surplus is the area between
the marginal cost curve and the
market price.
MC
pm
pc
The sum of these measures total
(market) surplus.
MR
qm
qc
D
qcs
q
Is total surplus maximized at quantity
qm? At qcs? At qc? How is pc called?
Loss in surplus: dead weight loss
10
Relationship between the monopoly's price and the perfectly competitive price pc
(that maximizes total surplus).
p
Dead weight loss
pm
The monopoly charges a higher
price, and produces less units than
a competitive market.
MC
pc
What is the social welfare cost of
the monopolist?
MR
qm
qc
D
q
Dead weight loss: the area
between the maximum total surplus
possible and the surplus created by
the monopoly.
Dead weight loss
11
Relationship between the monopoly's price and the perfectly competitive price pc
(that maximizes total surplus).
p
Key Property:
Dead weight loss
pm
The “distance” from price pc is negatively
related to how much demand reacts to
price changes (which is shown by how flat
the demand curve is).
MC
pc
MR
qm
qc
D
q
The flatter (more elastic) is the demand
curve, the smaller is the difference between
pc and the monopoly price pm.
The steeper (more inelastic) is the demand
curve, the larger is the difference.
Dead weight loss
12
Relationship between the monopoly's price and the perfectly competitive price pc
(that maximizes total surplus).
p
Key Property:
Dead weight loss
pm
The “distance” from price pc is negatively
related to how much demand reacts to
price changes (which is shown by how flat
the demand curve is).
MC
pc
MR
qm
qc
The flatter (more elastic) is the demand
curve, the smaller is the deadweight loss.
D
q
The steeper (more inelastic) is the demand
curve, the larger is the deadweight loss.
Monopoly
Q: Why do monopolies arise?
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
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, Satellite companies