Chapter 11
Monopoly
Objective
 How does a monopolist set its price and output?
 What is wrong with monopoly?
 What are some other pricing strategies a monopolist can
use?
Causes of a Monopoly
 Barriers to entry –
 Technical barriers to entry




Diminishing average cost over a broad range of output like a natural monopoly.
Special knowledge of a low-cost method of production.
Ownership of a key resource
Possession of unique managerial talent.
 Legal barriers to entry.
 Patents and copyrights.
 Exclusive franchise or license.
Definitions
 Revenue = price * quantity
 TR=pq
 Profit = Revenue – Costs
 π = TR – C
 Marginal revenue= ΔTR/Δq
 Change in total revenue from selling an extra unit of output
Revenue Analysis for a Monopoly
A Monopoly’s Revenue
 Marginal Revenue
 ∆TR/∆Q = MR
 How does MR compare to P in a monopoly market?
 To sell an extra unit the monopolist has to lower
price.
 He sells the extra unit at the new price (thus total
revenue rises), but lowers price on all previous
units sold (which reduces total revenue)
 MR<P
A Monopoly’s Revenue
An increase in sales has two effects on total
revenue
 The output effect—revenue earned on the extra unit
 The price effect—revenue lost on previous units.
MR=P + (Δp/Δq)(q)
$5
$4
$5
$4
$5
$4
$4
P
Q
TR
$5
3
15
$4
4
16
MR
$1
Note that MR<P
Total Revenue
Price
$11
10
9
8
7
6
5
4
3
2
1
0
–1
–2
–3
–4
Total Revenue increases and
then decreases.
Total
Revenue
1
2
3
4
5
6
7
8
9
Quantity
• Marginal Revenue is
the slope of the total
revenue curve
Total
Revenue
Q
Marginal
Revenue
Q
• Marginal revenue is
positive (negative)
when total revenue is
increasing
(decreasing)
• Marginal revenue is
zero when total
revenue reaches a
maximum
10
Marginal Revenue
 Marginal revenue curve




Below demand curve
Slope = 2* Slope of demand curve
MR=P + (Δp/Δq) (q)
MR=p-|Δp/Δq|(q)=p(1-1/|ξ|)
 ξ = elasticity of demand
Marginal revenue and demand
11
Price
• Inverse demand function p= f(q)=A-bq
Price – from any given quantity
• Demand function: q = f(p)= (A-p)/b
quantity demanded at each price
a
p = A - bq
MR =
A - 2bq
D
0
Quantity
The marginal revenue curve is steeper than the demand curve. With a
straight-line demand curve, the slope of the marginal revenue curve is twice
the slope of the demand curve
12
Demand and Elasticity
Price
pMAX
|ξ|>1
p1
|ξ|=1
μ
|ξ|<1
Quantity demanded: q = A - bp
0
A
Quantity
13
Pricing and Quantity Decisions
 The Elasticity Rule
 The firm will never choose a point on inelastic portion of demand
curve
 When |ξ|<1, then marginal revenue is negative
 Selling an extra unit of output will reduce profit
 It increases costs and
 decreases revenue
14
Optimal Price and Quantity Results
 Profit-maximizing quantity, q*
 Increase production if MR>MC
 Until MR=MC
 Profit-maximizing price, p*
 On demand curve, at q*
Optimal price and quantity
15
Price
MC
p*
The profit-maximizing
price and quantity equate
marginal cost with
marginal revenue
ρ
MR
α
D
0
q*
Quantity
16
Optimal Price and Quantity Results
 # 2: Profit-maximizing price
 On the demand curve
 At optimal quantity
 MR=p(1-1/|ξ|)
 p=MR(1-1/|ξ|);
 MR=MC
 p=MC(1-1/|ξ|)
17
Optimal Price and Quantity Results
 Deadweight loss
 Dollar measure - Loss to society
 Profit maximization results in units not produced where marginal
social benefit > marginal social cost
 Some of the consumer surplus under perfect competition is
transferred to the monopolist.
The socially optimal price
18
Price
d
MC
Compared to perfect
competition, a monopoly
produces less output and
charges a higher price
b
p
f
D
MR
0
q
Quantity
Two-Part Tariffs
 Monopolist charges
 A lump sum fee
 A unit price
 The two part tariff allows the monopoly to
 Capture consumer surplus
 Earn extra-normal profit
 Sell the optimal output level
19
Two-Part Tariffs
 Assume there are identical consumers in the market
 Consumers buy more of the good as its price declines
 Each gets the same consumer surplus
21
Two-Part Tariffs
Price
The producer charges each
consumer, in addition to the
per-unit price, a fixed fee equal
to her share of the consumer
surplus:
Fee=CS/N
c
Fee
d
Unit Price
e
MR
b
0
a
MC
Quantity
22
Two-Part Tariffs and Profit
Price
The producer earns a higher
profit
c
d
Unit Price
e
Profit
MR
b
0
a
MC
Quantity
23
Two-Part Tariffs and A Higher Profit
Price
The producer earns a higher
profit if he lowers the price to
MC and charges a higher fee
e
Profit
MR
Unit Price
MC
0
Quantity
24
Two-Part Tariffs and Efficiency
Price
The producer is efficient:
• He sells the socially optimal
amount
• Sets a price equals MC
e
Profit
MR
Unit Price
MC
0
Quantity
Two-Part Tariffs when the
monopoly realizes a loss
Price
MC
AC
A two-part tariff
enables the
monopolist to earn
positive profits
E
p
c
0
q
Quantity
Problems with uniform Pricing
 When consumers are not identical
 Some buyers with a willingness to pay above marginal cost do
not buy because the price is high
 Lowering price to capture this market segment may reduce
monopoly profit.
When the monopoly charges a
single price……
27
Price
d
Transactions
represented by the blue
line are not undertaken
MC
p
b
f
0
MR
q
D
Quantity
Two part Tariff may not be optimal
when consumers are not identical
Price
• Half the consumers
are type A and half
are B
• The monopoly sets a
fee=A+B/2
B
p*
A
DElizabeths
DGeoffreys
0
q1
q2
• The Elizabeths are
willing to pay the fixed
fee, but the Geoffreys
are not
Quantity
Non uniform pricing / Price
Discrimination
 Separate consumers
 Groups/ markets
 Slightly different products
 Tastes
 No reselling
 Different prices
30
Price Discrimination
 Price discrimination
 Charge different prices to different consumers
 Segmented markets
 Physical separation/other characteristics
 Arbitrage - impossible
Price Discrimination: the Market for
Movie Tickets
(b) Demand by people below age 60
(b) Senior citizen demand
P
P1
The relative prices
charged will depend on the
price elasticity of demand
in each market:
1
1
2
P1

P2 1  1
1
P2
Marginal cost
Demand
Demand
MR
MR
Q1
Q2
Price Discrimination
 Price Discrimination in Segmented Markets
 Produce q* (profit maximizing quantity)
 Marginal revenue (any market) = marginal cost
 Marginal revenue (one market) = Marginal revenue (other) market
 MRg=MRe=MCt
Practice Questions: #1
 Given:
 Inverse demand: P=100 - Q
 MC constant at $50 and no fixed costs
 Find
 Socially optimal output level
 Monopoly output and price
 If the monopoly can charge a fee in addition to the above price,
what is the fee? The profit?
 What is the optimal price and fee? The profit?
Practice Questions: #2
 Given:
 Two groups of buyers: P1=130-2Q1 and P2=60-Q2
 MC constant at $50 and no fixed costs
 Find
 Price and quantity to each group
 Is the monopoly output socially efficient?