Download (or perfect) price discrimination

Review
Imperfect Competition: Monopoly
• Reasons for monopolies
• Monopolies problem:
Choses quantity such that marginal costs equal to marginal revenue
•
The social deadweight loss of a monopoly
Price discrimination by a monopolist
New topic: Capturing surplus by price discrimination
Definition: A monopolist charges a uniform price if it sets the same price for every unit of
output sold.
Definition: A monopolist price discriminates if it charges more than one price for the same
good or service.
What are examples of price discrimination?
1. Student version of software, various other student/senior citizen discounts.
What is the advantage of this?
Example
Airlines commonly price discriminate, using “Saturday night stay-overs” and other devices.
Suppose you live in Dallas and want to spend two weeks in LA, returning only for the weekend.
-First week: First Monday- Dallas to Los Angeles, then First Friday- Los Angeles to Dallas
-Second week: Second Monday- Dallas to Los Angeles; and Second Friday- Los Angeles to Dallas
The approximate combined cost of these two flights was US$2,000. In contrast, another way of
arranging exactly the same travel is to have two round-trips, one of which originates in Dallas, while the
other originates in Los Angeles:
- Trip One: First Monday- Dallas to Los Angeles; then second Friday- Los Angeles to Dallas
- Trip Two: First Friday- Los Angeles to Dallas; then second Monday:- Dallas to Los Angeles
This pair of round trips involves exactly the same travel as the first pair, but costs less than $500 for both
(at the time of this writing).
Why?
Price discrimination
Two important distinctions:
Discounts to students depend on the identity of the buyers, discounts to overnight
passengers depend on the choices of the buyers.
The first is called “direct price discrimination”, and the second is called “indirect price
discrimination”.
In order for a seller to price-discriminate, the seller must be able to
• Identify (approximately) the demand of groups of customers
• Prevent arbitrage
Types of discrimination
Definition:
A policy of first degree (or perfect) price discrimination prices each unit sold at the
consumer's maximum willingness to pay.
A policy of second degree price discrimination allows the monopolist to offer consumers
a quantity discount.
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.
Uniform pricing
In the previous chapter, the monopolist charges a uniform price:
p
The monopoly produces a quantity
such that marginal costs equals
marginal revenue.
MC
MR(q)  mc(q)
pm
But the price Pmis given by the
demand curve. It is much higher than
the competitive price.
D
qm
q
qc
MR
Question: What happens when the monopolist
can perfectly price discriminate?
First degree price discrimination
What is the marginal revenue curve for perfectly price discriminating monopolist?
When the monopolist sells an additional unit, it does not have to reduce the
price on the other units it is selling.
The consumer’s demand curve is the maximal price that the marginal consumer
is willing to pay.
Key Rule:
When there is first degree price discrimination: The marginal revenue for each additional unit
is the price of the unit .
The monopolist's marginal revenue is given by the demand
MR(Q)=p(q)
The monopolist will produce an additional unit as long as marginal cost is below the
Price. The monopolist produces a quantity such that: p(q)=mc(q)
Example
Suppose a monopolist produces at a constant marginal cost: MC = 2, and faces a
demand curve given by: P = 20 - Q
1. Under uniform pricing: What is the price and quantity charged? What is the
monopoly's profit? What is the consumer surplus?
2. Under perfect price discrimination: What is the quantity produced? What is
the monopoly’s profit?
Uniform pricing:
MR = 20 - 2Q
MR = MC => Q* = 9 and P* = 11
Monopoly's profit: 99-18=81 ; Consumer surplus: 9*9/2=40.5
Perfect price discrimination:
The firm produces q=18 units (or mc(q)=p(q)). As long as q<18, the firm can sell an
additional unit for a price p>2.
Monopoly's profit: 18*18/2=162; Consumer surplus is 0
First degree price discrimination
Key point:
The monopolist will continue selling units until the reservation price exactly equals marginal
cost.
Therefore, under perfect price discrimination, a monopolist will produce and sell the
efficient quantity of output.
The same quantity arises in a perfectly competitive market equilibrium. However, under
perfect price discrimination, the consumer surplus is 0. The monopolist extracts the entire
social surplus.
Indirect price discrimination
Definition: A monopolist charges a two part tariff if it charges a per unit price p, and
a lump sum fee, F.
Examples:
-Electricity often comes with a fixed price per month and then a price per kilowatthour, which is two-part pricing.
- Long distance and cellular telephone companies charge a fixed fee per month, with
a fixed number of “included” minutes, and a price per minute for additional minutes.
Two Part Tariff
Example:
Suppose a monopolist with costs MC = AC = 10 faces 100 identical consumers. Each
has an individual demand of: P = 100 – Q. What is the optimal two part tariff?
11
Two Part Tariff
Example:
Suppose a monopolist with costs MC = AC = 10 faces 100 identical consumers. Each
has an individual demand of: P = 100 – Q. What is the optimal two part tariff?
100
Solution two steps:
P
(1) maximize the benefits to the consumers by
charging p = MC = 10.
(2) capture this benefit by setting F = consumer
benefits = 4050.
4050
10
12
90 100
Q
Two Part Tariff
Main take-away: When facing identical consumers the monopolist can
capture the entire surplus using a two part tariff
The monopolist maximizes the size of the "pie", then sets the lump sum fee so as to
capture the entire "pie" for itself.
The total surplus captured is the same as in the case of perfect price discrimination.
13
Third degree price discrimination
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.
Example: Movie ticket sales to older people or students at discount
The monopolist sets a uniform price for each segment of the market.
14
Third degree price discrimination
Example: Suppose a monopolist with costs MC = AC = 20 faces two types of consumers: P1
= 100 - Q1 and P2 = 80 - 2Q2 . The monopolist can charge different prices to each group.
What are the optimal prices?
MR1 = 100 - 2Q1
MR2 = 80 - 4Q2
Set each equal to marginal cost.
Q1* = 40 and P1* = 60, and Q2* = 15 and
P2* = 50
15
Third degree price discrimination
MR1 = 100 - 2Q1 and MR2 = 80 - 4Q2 Set each equal to marginal cost. Q1* = 40 and
P1* = 60, and Q2* = 15 and P2* = 50
P
100
P
Market 1
Demand 1
80
60
Market 2
Demand 2
50
20
0
16
MR1
100
Q
0
20
40
MR2
Q