Lecture 1: Review of Monopoly
Pricing by a Firm with Market Power
Total Revenue (TR) = PQ
Average Revenue (AR) = TR/Q=P
Marginal Revenue = Revenue from an
additional unit = DTR/DQ = d(TR)/dQ
Marginal Revenue is lower than Average Revenue (price). Why?
MR = d(TR)/dQ = P + Q dP/dQ < P
1
Increase Q if MR > MC
Decrease Q if MR < MC
Optimum: MR = MC
$
$
MR=MC
p*
D
P*
MR
MC
Q
Q*
2
Q
Q*
Example: Automobile Industry Pricing
Toyotas.
Suppose that the demand for Toyotas is given
by P =12000-Q, and MC =$3000.
Assume than unit costs are $3000 per vehicle
and fixed costs=$7,500,000
TR=PQ= (12000-Q)Q = 12000Q-Q2
MR=12000-2Q
TC= 7,500,000 + 3000Q
MC=3000
3
MR=MC implies that Q*=4500
Price (from demand curve) = 12000-4500=7500
Profits = PQ
- VC
-
FC
Profits = 7500*4500-3000*4500-$7,500,000
Profits = 20,250,000 –7,500,000=$12,750,000
Another way to solve problem
p= TR - TC = 12000Q- Q2 - (3000Q + 7,500,000)
p = 9000Q - Q2 -7,500,000.
d p/dQ = 9000 – 2Q=0 which implies Q*=4500
as before.
F Note that the fixed costs only affect the decision
4
whether to produce or not and not how much to produce.
Optimal Pricing, margins and the elasticity of demand
It can be shown that MR = p + Q dp/dQ = p (1-1/e)
From the above equation MR=MC can be rewritten
in two ways:
margin  (p-MC)/p = 1 / e
p = MC / (1-1/e)
P
P
D
D
MR
MR
MC
5
MC
Q
+ low e, high m
Q
+ high e, low m
Example: Automobile Industry Pricing
Toyotas in Two Different Markets
Market 1 (US) P1 =12000-Q1, MC1 =3000
Market 2 (Japan) P2=14000-2Q2, MC2=2000
Optimal Prices: P(US)=$7500, P(JAPAN)= $8000
Is this dumping? How can the price in the U.S.
exceed the price in Japan?
e1 = 1.66, -(dQ1 /dP1) P1/Q1
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e2 = 1.33, -(dQ2 /dP2) P2/Q2
Monopolist with multiple plants
Example
Demand: P=100-Q
Plant 1: TC1=2Q12
Plant 2: TC2=Q22.
Optimal MR=MC1=MC2
MC1= 4Q1, MC2=2Q2. MC1=MC2 implies that Q2=2Q1.
Q= Q1+Q2 = 3Q1.
TR=100Q-Q2. Thus, MR=100-2Q=100-6Q1.
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MR=MC implies that 100-6Q1=4Q1or Q1=10.
Since Q2=2Q1, Q2=20 and Q=30.
Check: When Q=30,
MR=40,
MC1= 4Q1=40 ,
MC2= 2Q2=40.
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Bundling
Suppose there are two goods (A,B):
There are three possible pricing strategies (options:)
separate pricing – pA and pB only
Pure bundling –pAB only
Mixed bundling – pA , pB , and pAB
Examples: ‘Hot Triple’ and restaurant pricing
Individual Pricing
Value of
A
Buys A
only
Buys both
Buys
nothing
Buys B only
pA
pB
Value of B
Pure Bundling
pAB = x
Buys bundle
Value of
A
Buys
nothing
pAB = x
Value of B
Mixed Bundling
I,II,III, IV – buys both; V,VI buys B; VII,VIII buys A
VIII
pAB=12
pA=8
IV
I
VII
II
III
4
VI
V
4
pB=8
pAB=12
Profitability of Mixed Bundling
• For a monopoly, mixed bundling always
(weakly) better than pure bundling
• Trade off between mixed bundling and
separate pricing
• In mixed bundling, price of bundle less than
the price of individual goods
• Optimal strategy depends on distribution of
consumers and costs
Example
• Cost of entrée (A) = $6, cost of desert (B) =$2
• Three types of consumers with following reservation
values: (10,1) (8,4) (5,4)
• Individual pricing: pA=8, pB=4, π=2(8-6)+2(4-2)=8
(could also charge pA=10, pB=4, π=(10-6)+2(4-2)=8)
• Pure bundling pricing: pAB=11, π=2(11-8)=6
• Mixed bundling pricing: pA=10, pB=4, pAB=11.99,
π=(10-6)+(4-2)+(11.99-8)=9.99
• What about pricing bundle at 10.99?
π=2(10.99-8)+(4-2) =7.98