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 ofoutput sold.

Definition: A monopolist price discriminates if it charges more than one price for the samegood 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.

Option 1:-Outbound (Dallas-LA) on first Monday; inbound (LA-Dallas) on first Friday-Outbound (Dallas-LA) on second Monday; inbound (LA-Dalls) on second Friday.

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 whichoriginates in Dallas, while the other originates in Los Angeles

Option 2:- Outbound (Dallas-LA) first Monday; inbound (LA-Dallas) on second Friday- Outbound (LA-Dallas) first Friday; inbound (Dallas-LA) on second Monday

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 overnightpassengers depend on the choices of the buyers.

The first is called “direct price discrimination”, and the second is called “indirect pricediscrimination”.

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 theconsumer's maximum willingness to pay.

A policy of second degree price discrimination allows the monopolist to offer consumersa quantity discount.

A policy of third degree price discrimination offers a different price for each segment ofthe 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:

qm

p

q

D

MC

qc

MR

pm

The monopoly produces a quantity

such that marginal costs equals

marginal revenue.

But the price is given by the

demand curve. It is much higher than

the competitive price.

)()( qmcqMR

Pm

Question: What happens when the monopolistcan perfectly price discriminate?

First degree price discrimination

What is the marginal revenue curve for perfectly price discriminating monopolist?

Key Rule: Under first degree price discrimination the monopolist's marginal revenue equals the demand curve. (Because the marginal revenue for each additional unit is the price of the unit) .

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)

The monopolist will charge the maximal price that the marginal consumer is willing to pay.

When the monopolist sells an additional unit, it does not have to reducethe price on the other units it is selling.

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 - 2QMR = MC => Q* = 9 and P* = 11Monopoly'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 marginalcost.

Therefore, under perfect price discrimination, a monopolist will produce and sell theefficient quantity of output.

The same quantity arises in a perfectly competitive market equilibrium. However, underperfect price discrimination, the consumer surplus is 0. The monopolist extracts the entiresocial surplus.

Indirect price discrimination

Definition: A monopolist charges a two part tariff if it charges a per unit price p, anda lump sum fee, F.

Examples:-Electricity often comes with a fixed price per month and then a price per kilowatt-hour, which is two-part pricing.

- Long distance and cellular telephone companies charge a fixed fee per month, witha 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?

12

10090

100

Q

P

10

4050

Solution two steps:

(1) maximize the benefits to the consumers by charging p = MC = 10.

(2) capture this benefit by setting F = consumer benefits = 4050.

Two Part Tariff

Main take-away: When facing identical consumers the monopolist can capture the entire surplus using a two part tariff

13

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.

Third degree price discrimination

14

Definition: A policy of third degree price discrimination offers a different price foreach segment of the market (or each consumer group) when membership in asegment 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.

Third degree price discrimination

15

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

Third degree price discrimination

16

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

0

80

50

20 40Q

Demand 2

MR2

0 100

20

60

P

Demand 1

MR1 Q

Market 1 Market 2