Monopoly: Applications

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Lecture 17 Monopoly Applications Lecturer
Martin Paredes
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Outline

1. Natural Monopoly
2. Multi-plant Monopoly
3. Cartels
4. Price Discrimination

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Natural Monopoly

• Definition A market is a natural monopoly if,
  over the relevant range of production, the total
  cost of production incurred by a single firm is
  lower than the combined total cost of two or more
  firms, producing the same output level.
• In other words, it is a market in which
  production is cheaper when there is only one firm.

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Natural Monopoly

• Suppose an industry with a decreasing average
  cost at all points.
• If AC is always decreasing, then AC gt MC.
• Therefore, setting P MC will not be profitable.

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Example Natural Monopoly

Demand
Quantity
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Example Natural Monopoly

AC
Demand
Quantity
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Example Natural Monopoly

2.50
AC
Demand
8000
Quantity
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Example Natural Monopoly

4.80
2.50
AC
Demand
4000
8000
Quantity
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Natural Monopoly

• In a natural monopoly, the appropriate benchmark
  to calculate deadweight loss cannot be PMC,
  because the firm will incur losses.
• For a natural monopoly, the appropriate benchmark
  is PAC.

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Natural Monopoly

• Note
• The definition of whether an industry is a
  natural monopoly depends on the size of the
  market.
• See the following example where AC first falls
  and then raises.

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Example Natural Monopoly with Rising Average
Cost
Price
AC
Quantity
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Example Natural Monopoly with Rising Average
Cost
Price
If demand is given by D1, then the industry is a
natural monopoly.
AC
D1
Quantity
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Example Natural Monopoly with Rising Average
Cost
Price
If demand is given by D2, the industry is no
longer a natural monopoly.
AC
D2
D1
Quantity
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Multiplant Monopoly

• Suppose a monopolist has two plants, but each
  plant has different marginal costs
• Plant 1 MC1(Q)
• Plant 2 MC2(Q)
• How should the monopolist allocate production
  across the two plants?

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Multiplant Monopoly

• When the marginal costs of the two plants are not
  equal, the firm can increase profits by
  reallocating production
• Away from the plant with higher marginal cost.
• Towards the plant with lower marginal cost.

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• Example
• Suppose MC1 4Q MC2 2Q
• Suppose the monopolist produces 100 units.
• Will it choose to split the production equally
  between both plants?
• MC1 450 200
• MC2 250 100
• Reducing production in plant 1 units and
  increasing it in plant 2 raises profits
• Produce more than 50 units in plant 2.

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Example Multi-Plant Monopolist

MC1
MC2

200

100
Quantity
50
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Multiplant Monopoly

• Definition The Multi-Plant Marginal Cost Curve
  traces out the set of points generated when the
  marginal cost curves of the individual plants are
  horizontally summed.
• In other words, it shows the total output that
  can be produced at every level of marginal cost.
• The monopolists production decision will be
  based on its multi-plant Marginal Cost

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• Back to example
• Given MC1 4Q MC2 2Q
• For a marginal cost of 200
• Plant 1 can produce 50 units
• Plant 2 can produce 100 units.
• So the total production for a cost of 200 is 150
  units
• In fact MCT 4 Q 3

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Example Multi-Plant Monopolist

MC1
MC2

200
Quantity
50
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Example Multi-Plant Monopolist

MC1
MC2


200
Quantity
50 100
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Example Multi-Plant Monopolist

MC1
MC2



200
Quantity
50 100 150
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Example Multi-Plant Monopolist

MC1
MC2
MCT



200
Quantity
50 100 150
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Multiplant Monopoly

• 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.

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Example Multi-Plant Monopolist Maximization
Price
MC1
MC2
MCT
Quantity
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Example Multi-Plant Monopolist Maximization
Price
MC1
MC2
MCT
Demand
Quantity
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Example Multi-Plant Monopolist Maximization
Price
MC1
MC2
MCT
Demand
Quantity
MR
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Example Multi-Plant Monopolist Maximization
Price
MC1
MC2
MCT
P

Demand
Quantity
QT
MR
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Example Multi-Plant Monopolist Maximization
Price
MC1
MC2
MCT
P



Demand
Quantity
Q1 Q2 QT
MR
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Cartels
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.
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Cartels

• The problem of the optimal allocation of output
  across cartel members is identical to the
  monopolist's problem of allocating output across
  individual plants.
• If all firms have the same marginal cost curve,
  production will be equally divided.
• If not, firms will higher marginal cost will
  produce less.

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Price Discrimination

• Definitions
• A monopolist charges a uniform price if it sets
  the same price for every unit of output sold.
• A monopolist price discriminates if it charges
  more than one price for its output

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Price Discrimination

• Motivation
• When the monopolist charges a uniform price, it
  maximises profits, but 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.

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Price Discrimination

• Requirements
• Ability to sort/identify consumers
• No possibility of resale or arbitrage.
• Need market power.

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Example Prices for UA Flight 815
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Forms of Price Discrimination

• Based on the classification by A.C. Pigou
• First degree price discrimination
• Also called personalized pricing.
• Second degree price discrimination
• Also called menu pricing.
• Third degree price discrimination
• Also call group pricing.

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First Degree Price Discrimination

• Definition A policy of first degree (or perfect)
  price discrimination attempts to price each unit
  sold at the consumer's maximum willingness to
  pay.
• The consumer's maximum willingness to pay is also
  called the consumer's reservation price.

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First Degree Price Discrimination

• Recall that the demand curve can be interpreted
  as the consumers willingness to pay for one unit
  of the good.
• In other words, the demand curve represents the
  reservation prices of every consumer in the
  market.

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First Degree Price Discrimination

• If the monopolist can observe the reservation
  price of every consumer, then the monopolist can
  observe demand perfectly and can "perfectly"
  price discriminate.
• The monopolist will continue selling units until
  the reservation price exactly equals marginal
  cost.

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Price
Example Monopoly
MC
D
Quantity
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Price
Example Uniform Pricing
MC
Pm
Consumer Surplus
Producer Surplus
Deadweight Loss
D
Qm
Quantity
MR
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Price
Example First Degree Price Discrimination
MC
D
Quantity
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Price
Example First Degree Price Discrimination
MC
D
Quantity
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Price
Example First Degree Price Discrimination
MC
D
Quantity
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Price
Example First Degree Price Discrimination
MC
Producer Surplus
D
Q
Quantity
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First Degree Price Discrimination

• Notes
• A perfectly price discriminating monopolist will
  produce and sell the efficient quantity of
  output.
• 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. (i.e., the marginal revenue
  curve equals the demand curve.)

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Second Degree Price Discrimination

• Definition A policy of second degree price
  discrimination allows the monopolist to charge a
  different price to different consumers, even
  though the reservation price of any one consumer
  cannot be directly observed.
• The monopolist usually design a menu of options
  and let the consumer select its preferred package
• It involves quantity discounting.

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Second Degree Price Discrimination

• Examples of second degree price discrimination
  include
• Two-part tariff
• Block pricing

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Two Part Tariffs

• Definition A monopolist charges a two part
  tariff if it charges
• A per unit fee, r, plus
• A lump sum fee F.
• The lump-sum fee is paid whether or not a
  positive number of units is consumed.

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Two Part Tariffs

• With two-part tariffs, consumers that demand a
  high quantity are charge a smaller price per unit
  than consumers that demand a low quantity.
• Examples include
• Telephone landlines
• Club membership

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Block Pricing
Definition A monopolist charges a block tariff
if the consumer pays one price for one block of
output and another price for second block of
output
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Third Degree Price Discrimination

• Definition A policy of third degree price
  discrimination offers a different price to each
  consumer group (or segment of the market) when
  membership to a group can be observed.
• Examples include movie ticket sales to older
  people or students at a discount.

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Third Degree Price Discrimination

• Suppose
• A monopolist faces two markets, each with a
  different demand curve
• Marginal cost for the two markets is the same.
• How does a monopolist maximize profit with this
  type of price discrimination?

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Third Degree Price Discrimination

• The monopolist will set the marginal revenue in
  each market equal to marginal cost.
• In other words, the monopolist maximizes total
  profits by maximizing profits from each group
  individually.
• At the optimum MR1 MC MR2
• If not, the monopolist could raise revenues by
  switching sales from the low MR group to the high
  MR group.

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Example Third Degree Price Discrimination
P
P
Market 1
Market 2
D2
D1
Q
Q
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Example Third Degree Price Discrimination
P
P
Market 1
Market 2
D2
D1
Q
Q
MR1
MR2
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Example Third Degree Price Discrimination
P
P
Market 1
Market 2
MC
MC
D2
D1
Q
Q
MR1
MR2
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Example Third Degree Price Discrimination
P
P
Market 1
Market 2
P1
P2
D2
D1
Q1
Q2
Q
Q
MR1
MR2
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Summary

• Price discrimination generally allows a
  monopolist (or any firm with market power) to
  capture more surplus than a uniform pricing
  policy.
• First degree (or perfect) price discrimination
  allows the monopoly to produce efficiently and
  capture all the resulting surplus.

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Summary

1. Second degree price discrimination may or may not
   allow as much surplus to be created and captured
   as perfect price discrimination, depending on the
   precise form of the discrimination.
2. Third degree price discrimination generally does
   not create or allow as much capture of surplus.

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Summary

1. In order to capture surplus from any form of
   price discrimination, a firm must have some
   market power, have some information on the
   differential willingness to pay of customers and
   must be able to prevent resale (arbitrage) among
   customers.