CHAPTER 14
MONOPOLY
Chapter Overview
1.The Monopolist’s Profit Maximization Problem
• The Profit Maximization Condition
• Equilibrium
• The Inverse Pricing Elasticity Rule
• Effects of Shift in demand and MC.
• Effects of a Tax
2. Multi-plant Monopoly and Cartel Production
3. The Welfare Economics and Monopoly
4. Monopsony
5. Multi – Price Monopoly
A Monopoly
● Monopoly
Market with only one seller.
●
Monopsony
Market with only one buyer.
●
Market power Ability of a seller or buyer to
affect the price of a good.
Average Revenue and Marginal Revenue
Marginal revenue Change in revenue resulting
from a one-unit increase in output.
●
Consider a firm facing the following demand curve:
P=6Q
TABLE 10.1
TOTAL, MARGINAL, AND AVERAGE REVENUE
PRICE (P)
QUANTITY (Q)
TOTAL REVENUE
(R)
MARGINAL REVENUE
(MR)
AVERAGE REVENUE
(AR)
$6
0
$0
—
—
5
1
5
$5
$5
4
2
8
3
4
3
3
9
1
3
2
4
8
1
2
1
5
5
3
1
Marginal Revenue Curve and Demand
Price
The MR curve lies below the demand curve.
P(Q0)
P(Q), the (inverse) demand curve
MR(Q0)
MR(Q), the marginal revenue curve
Q0
Quantity
5
The Monopolist’s Output Decision
PROFIT IS MAXIMIZED WHEN MR = MC
At Q* MR = MC.
At Q1it sacrifices some
profit because the extra
revenue that could be
earned from producing
and selling the units
between Q1 and Q*
exceeds the cost of
producing them.
Similarly, output from Q*
to Q2 would reduce profit
because the additional
cost would exceed the
additional revenue.
Elasticity Region of the Linear Demand Curve
Price
a
Elastic region ( < -1), MR > 0
Unit elastic (=-1), MR=0
Inelastic region (0>>-1), MR<0
a/2b
a/b
Quantity
7
Marginal Cost and Price Elasticity Demand
• Profit maximizing condition is MR = MC with
P* and Q*
MR (Q*)  MC (Q*)


1

MC (Q*)  P * 1 
  
Q,P 

• Rearranging and setting MR(Q*) = MC(Q*)
P * MC *
1

P*
 Q,P
8
Inverse Elasticity Pricing Rule
• Inverse Elasticity Pricing Rule: Monopolist’s
optimal markup of price above marginal cost
expressed as a percentage of price is equal
to minus the inverse of the price elasticity of
demand.
P * MC *
1

P*
 Q,P
9
Market Power
Definition:
An agent has Market Power if s/he can
affect, through his/her own actions, the
price that prevails in the market.
Sometimes this is thought of as the
degree to which a firm can raise price
above marginal cost.
The Lerner Index of Market Power
Definition: the Lerner Index of market power is the
price-cost margin, (P*-MC)/P*.
This index ranges between 0 (for the competitive
firm) and 1, for a monopolist
Restating the monopolist's profit maximization
condition, we have:
P*(1 + 1/) = MC(Q*) …or…
[P* - MC(Q*)]/P* = -1/
In words, the monopolist's ability to price above
marginal cost depends on the elasticity of demand.
Comparative Statics – Shifts in Market Demand
• Rightward shift in the demand curve causes an
increase in profit maximizing quantity.
• (a) MC increases as Q increases, P ↑
Comparative Statics – Shifts in Market Demand
In (a), the demand curve D1
shifts to new demand curve D2.
But the new MR2 curve
intersects MC at the same
point as the old curve MR1.
The profit-maximizing output
therefore remains the same,
although price ↓ from P1 to P2.
In (b), the new MR2 intersects
MC at a higher output level Q2.
But because demand is now
more elastic, price remains the
same.
Comparative Statics – Shifts in Marginal Cost
• When MC shifts up, Q ↓ and P ↑
Comparative Statics – Revenue and MC shifts
• Upward shift of MC
decreases the profit
maximizing
monopolist’s total
revenue.
• Downward shift of
MC increases the
profit maximizing
monopolist’s total
revenue.
Effect of a Tax
Suppose a specific tax of t dollars per unit is levied. The
monopolist must remit t dollars to the government for every
unit it sells. If MC was the firm’s original marginal cost
EFFECT OF EXCISE TAX
ON MONOPOLIST
With a tax t per unit, the
firm’s effective MC is
increased by the amount t
to MC + t.
In this example, the
increase in price ΔP > tax t.
Multi-Plant Monopoly
Suppose a firm has two plants. What should its total
output be, and how much of that output should each
plant produce?
● Step 1. Whatever the total output, it should be
divided between the two plants so that MC is the
same in each plant.
Otherwise, the firm could reduce its costs and
increase its profit by reallocating production.
●
Step 2. We know that total output must be such that
MR = MC.
Otherwise, the firm could increase its profit by
raising or lowering total output.
Multi-Plant Monopoly
The monopolist has two plants: one plant has MC1(Q)
and the other has MC2(Q).
Whenever the marginal costs of the two plants are
not equal, the firm can increase profits by reallocating
production towards the lower marginal cost plant and
away from the higher marginal cost plant.
Example:
Suppose the monopolist wishes to produce 6 units
3 units per plant with
• MC1 = $6 and MC2 = $3
Reducing plant 1's units and increasing plant 2's units
raises profits
Multi-Plant Marginal Costs Curve
The profit maximization condition that
determines optimal total output is now:
• MR = MCT
The marginal cost of a change in output for the
monopolist is the change after all optimal
adjustment has occurred in the distribution of
production across plants.
Multi-Plant Monopolistic Maximization
Price
MC1
MC2
MCT
P*
MR
Quantity
20
Multi-Plant Monopolistic Maximization
Price
MC1
MC2
MCT
P*
Demand
Q*1 Q*2
Q*T
MR
Quantity
21
Cartel
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.
22
Cartel
The problem of optimally allocating output across cartel
members is identical to the monopolist's problem of
allocating output across individual plants.
Therefore, a cartel does not necessarily divide up market
shares equally among members: higher marginal cost firms
produce less.
This gives us a benchmark against which we can compare
actual industry and firm output to see how far the industry
is from the collusive equilibrium
The Welfare Economies of Monopoly
Since the monopoly equilibrium output does not, in
general, correspond to the perfectly competitive
equilibrium it entails a dead-weight loss.
Suppose that we compare a monopolist to a
competitive market, where the supply curve of the
competitors is equal to the marginal cost curve of the
monopolist
The Welfare Economies of Monopoly
Shaded area show
changes in CS and PS
when moving from
competitive price and
quantity, Pc and Qc, to a
monopolist’s price and
quantity, Pm and Qm.
Consumers lose A + B and
Producer gains A − C.
Deadweight loss = B + C.
Price Regulation
Initially a monopolist
produces Qm and charges
Pm.
If a price ceiling of P1 is
imposed the firm’s AR and
MR are constant and equal
to P1 for output levels up to
Q 1.
For larger output levels, the
original AR and MR curves
apply.
The new MR curve is,
therefore, the dark purple
line, which intersects the
marginal cost curve at Q1.
(1 of 2)
Natural Monopolies
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.
Benchmark: Produce where P = AC
Natural Monopolies
Price
Natural Monopoly falling
average costs
AC
Demand
Quantity
28
THE PRICE OF A NATURAL MONOPOLY
A firm is a natural monopoly
because it has economies of
scale (declining average and
marginal costs) over its entire
output range.
Produce at Qr and charge
price at Pr.
If price were regulated to be Pc
the firm would lose money and
go out of business. Setting the
price at Pr yields the largest
possible output consistent with
the firm’s remaining in
business; excess profit is zero.
A Monopsony
● Monopsony
power
price of a good.
Buyer’s ability to affect the
● Marginal
value Additional benefit derived from
purchasing one more unit of a good.
● Marginal
expenditure Additional cost of buying
one more unit of a good.
● Average
good.
expenditure
Price paid per unit of a
COMPETITIVE BUYER VERSUS COMPETITIVE SELLER
In (a), the competitive buyer takes market price P* as given.
Therefore, ME and AE are constant and equal;
quantity purchased is found by equating price to MV (demand).
In (b), the competitive seller also takes price as given. MR and AR
are constant and equal;
quantity sold is found by equating price to marginal cost.
MONOPSONIST BUYER
The market supply curve is
monopsonist’s AE. Because
AE is rising, ME lies above it.
The monopsonist purchases
quantity Q*m, where ME and
MV (demand) intersect.
The price paid per unit P*m is
then found from the AE
(supply) curve.
In a competitive market, price
and quantity, Pc and Qc, are
both higher.
They are found at the point
where AE (supply) and MV
(demand) intersect.
Monopsony and Monopoly Compared
(a) The monopolist produces where MR = MC.
AR exceeds MR, so that P exceeds MC.
(b) The monopsonist purchases up to the point
where ME = MV.
ME exceeds AE, so that MV exceeds P
MONOPSONY POWER: ELASTIC VERSUS INELASTIC SUPPLY
•Monopsony power depends on the elasticity of supply.
•When supply is elastic, as in (a), ME and AE do not
differ by much, so price is close to what it would
be in a competitive market.
•The opposite is true when supply is inelastic, as in (b).
The Welfare Economies of Monopsony
Shaded area show
changes in buyer and
seller surplus when
moving from competitive
price and quantity, Pc and
Qc, to the monopsonist’s
price and quantity, Pm
and Qm.
Both price and quantity
are lower, .
CS = A − B.
PS = - A – C
DWL = B and C.
1. Price Discrimination
• First Degree
• Second Degree
• Third Degree
2. Tie-in Sales
• Requirements Tie-ins
• Package Tie-ins (Bundling)
Uniform Price Vs. Price Discrimination
•Definition: A monopolist charges a uniform price if
it sets the same price for every unit of output sold.
•While the monopolist captures profits due to an
optimal uniform pricing policy, it does not receive
the consumer surplus or dead-weight loss
associated with this policy.
•The monopolist can overcome this by charging
more than one price for its product.
•Definition: A monopolist price discriminates if it
charges more than one price for the same good or
service.
Forms of Price Discrimination
Definition: A policy of first degree (or perfect) price
discrimination for prices of each unit sold at the
consumer's maximum willingness to pay.
This willingness to pay is directly observable by the
monopolist.
Definition: A policy of second degree price discrimination
allows the monopolist to offer consumers a quantity
discount.
Definition: A policy of third degree price discrimination
offers a different price for each segment of the market (or
each consumer group) when membership in a segment
can be observed.
Price Discrimination
First-Degree Price Discrimination
Reservation priceMaximum price that a
customer is willing to pay for a good.
● First degree price discrimination Practice
of charging each customer her reservation
price.
●
Variable profit Sum of profits on each
incremental unit produced by a firm; i.e., profit
ignoring fixed costs.
●
Uniform Price Vs. Price Discrimination
Price
PU E F
H
G
P1
K
MC
J
N
L
MR
D
Quantity
40
First Degree Price Discrimination
When the monopolist sells an
additional unit, it does not have to
reduce the price on the other units
it is selling.
Therefore, MR = P. or demand curve.
Price
20
11
MC
2
9
18
D
20
MR (uniform pricing)
Quantity
41
Second-Degree Price Discrimination
● Practice
of charging different prices per unit for different
quantities of the same good or service.
● Block
pricing: Practice of charging different prices for
different quantities or “blocks” of a good.
Here, there are 3 blocks, with
prices P1, P2, and P3.
There are also economies of
scale, and average and
marginal costs are declining.
Second-degree price
discrimination can then make
consumers better off by
expanding output and
lowering cost.
Block Pricing
If the monopolist could set a
different block price for each
customer, it would capture the
same amount of surplus as a
perfectly price
discriminating
monopolist.
Third-Degree Price Discrimination
● Practice of dividing consumers into two or more
groups with separate demand curves and charging
different prices to each group.
If third-degree price discrimination is feasible, how
should the firm decide what price to charge each
group of consumers?
1. We know that however much is produced, total
output should be divided between the groups of
customers so that MR for each group are equal.
2. We know that total output must be such that the
MR for each group of consumers is equal to the MC
of production.
Let P1 be the price charged to the first group of consumers, P2 the
price charged to the second group, and C(QT) the total cost of
producing output QT = Q1 + Q2. Total profit is then
𝜋 = 𝑃1 𝑄1 + 𝑃2 𝑄2 − 𝐶 𝑄𝑇
∆𝜋
∆ 𝑃1 𝑄1
∆𝐶
=
−
=0
∆𝑄1
∆𝑄1
∆𝑄1
MR1 = MC
MRMR
= MC
1 =2MR
2 = MC
DETERMINING RELATIVE PRICES
𝑀𝑅 = 𝑃 1 + 1 𝐸𝑑
𝑃1
1 + 1 𝐸2
=
𝑃2
1 + 1 𝐸1
THIRD-DEGREE PRICE DISCRIMINATION
There are 2 groups of
consumers.
The optimal prices and
quantities are such that the
MR1 = MR2 = MC
Here group 1, with demand
curve D1, is charged P1, and
group 2, with the more elastic
demand curve D2, is charged
the lower price P2.
Marginal cost depends on the
total quantity produced QT.
Note that Q1 and Q2 are chosen
so that MR1 = MR2 = MC.
Third Degree Price Discrimination
P
Market 1
P
100
Demand 1
80
60
Market 2
Demand 2
50
20
0
MR1
100
Q
0
20
40
MR2
Q
47
NO SALES TO SMALLER MARKETS
Even if third-degree price
discrimination is feasible, it
may not pay to sell to both
groups of consumers if
marginal cost is rising.
Here the first group of
consumers, with demand D1,
are not willing to pay much for
the product.
It is unprofitable to sell to them
because the price would have
to be too low to compensate
for the resulting increase in
marginal cost.
Intertemporal Price Discrimination and PeakLoad Pricing
Consumers are divided
into groups by changing
the price over time.
Initially, the price is high.
The firm captures
surplus from consumers
who have a high demand
for the good and who are
unwilling to wait to buy it.
Later the price is
reduced to appeal to the
mass market.
Intertemporal Price Discrimination and Peak-Load
Pricing
Demands for some goods
and services increase
sharply during particular
times of the day or year.
Charging a higher price P1
during the peak periods is
more profitable for the firm
than charging a single price
at all times.
It is also more efficient
because marginal cost is
higher during peak periods.
Tie-in Sales – Bundling
• Package
tie-in sales (or bundling) occur when
goods are combined so that customers cannot buy
either good separately.
Bundling may be used in place of price
discrimination to increase producer surplus when
consumers have different willingness to pay for
the goods sold in the bundle.
But bundling does not always pay…
Tie-in Sales – Bundling
Reservation Price
Computer
Monitor
Customer 1
$1,200
$600
Customer 2
$1,500
$400
Marginal Cost $1,000
$300
Tie-in Sales – Bundling
Optimal Pricing Policy
Without bundling: pc = $1500 pm = $600
• Profit cm = $800
With bundling: pb = $1800
• Profit b = $1000
Tie-in Sales – Bundling
Reservation Price
Computer
Monitor
Customer 1
$1,200
$400
Customer 2
$1,500
$600
Marginal Cost $1,000
$300
Tie-in Sales – Bundling
Optimal Pricing Policy
Without bundling: pc = $1500 pm = $600
• Profit cm = $800
With bundling: pb = $2100
• Profit b = $800
In general, bundling a pair of goods only pays if their
demands are negatively correlated (customers who are
willing to pay relatively more for good A are not willing to
pay as much for good B).