MicroEconomics 5e by besanko braeutigam chapter 11

Copyright (c)2014 John Wiley & Sons, Inc.

Chapter 11

Monopoly and Monopsony

1


Chapter Eleven Overview

1.

The Monopolist’s Profit Maximization Problem

•
•
•

The Profit Maximization Condition
Equilibrium
The Inverse Pricing Elasticity Rule

2. Multi-plant Monopoly and Cartel Production

The Welfare Economics and Monopoly

Chapter Eleven

Copyright (c)2014 John Wiley & Sons, Inc.

3.

2


A Monopoly
Definition:
Definition:AAMonopoly
MonopolyMarket
Marketconsists
consistsofofaasingle
singleseller
sellerfacing
facingmany
manybuyers.
buyers.
The
Themonopolist's
monopolist'sprofit
profitmaximization
maximizationproblem:
problem:
Max
Maxπ(Q)
π(Q)==TR(Q)
TR(Q)- -TC(Q)
TC(Q)QQ
where:
where:TR(Q)
TR(Q)==QP(Q)

QP(Q)and
andP(Q)
P(Q)isisthe
the(inverse)
(inverse)market
marketdemand
demandcurve.
curve.

Copyright (c)2014 John Wiley & Sons, Inc.

The
Themonopolist's
monopolist'sprofit
profitmaximization
maximizationcondition:
condition:
∆TR(Q)/∆Q
∆TR(Q)/∆Q==∆TC(Q)/∆Q
∆TC(Q)/∆Q
MR(Q)
MR(Q)==MC(Q)
MC(Q)

Chapter Eleven

3


A Monopoly – Profit Maximizing

Monopolist’s demand Curve is downward-sloping

•

Along the demand curve, different
revenues for different quantities

•

Profit maximization problem is the
optimal trade-off between volume
(number of units sold) and margin

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(the differential between price).

Chapter Eleven

4


A Monopoly – Profit Maximizing

P (Q) = 12 − Q

Demand Curve:
Total Revenue:

TR (Q) = Q × P (Q) = 12Q − Q

•

Total Cost (Given):

•

Profit-Maximization: MR = MC

2

1 2
TC (Q ) = Q
2
Copyright (c)2014 John Wiley & Sons, Inc.

•
•

Chapter Eleven

5


A Monopoly – Profit Maximizing

•

As Q increases TC increases, TR
increases first and then

decreases.

•

Profit Maximization is at MR =

Copyright (c)2014 John Wiley & Sons, Inc.

MC

Chapter Eleven

6


A Monopoly – Profit Maximizing

•

MR>MC, firm can increase Q and increase profit
MRMR=MC , firm cannot increase profit.

Profit Maximizing Q:

MR (Q*) = MC (Q*)

Chapter Eleven

7

Copyright (c)2014 John Wiley & Sons, Inc.

•
•
•


Marginal Revenue
Price

Price

Competitive Firm

Monopolist

Demand facing firm

Demand facing firm
P0

C

P1

A

B

q q+1

A

Firm output

B

Q0
Chapter Eleven

Q0+1

Firm output
8

Copyright (c)2014 John Wiley & Sons, Inc.

P0


Marginal Revenue Curve and Demand
Price

The MR curve lies below the demand curve.

P(Q0)

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P(Q), the (inverse) demand curve

MR(Q0)

MR(Q), the marginal revenue curve

Quantity

Q0
Chapter Eleven

9


Marginal Revenue Curve and Demand

•

To sell more units, a monopolist has
to lower the price.

•

Increase in profit is Area III while
revenue sacrificed at a higher price is
Area I
Change in TR equals area III – area I
Copyright (c)2014 John Wiley & Sons, Inc.

•

Chapter Eleven

10


Marginal Revenue Curve and Demand

Area III = price x change in quantity = P(ΔQ)
Area I = - quantity x change in price = -Q (ΔP)
Change in monopolist profit: P(ΔQ) + Q (ΔP)

∆TR P∆Q + Q∆P
∆P
MR =
=
= P+Q
∆Q
∆Q
∆Q

Chapter Eleven

11

Copyright (c)2014 John Wiley & Sons, Inc.

•
•
•

Marginal Revenue

Marginal revenue has two parts:
P: increase in revenue due to higher volume-the marginal units
Q(ΔP/ΔQ): decrease in revenue due to reduced price of the inframarginal units.
The marginal revenue is less than the price the monopolist can charge to sell
that quantity for any Q>0
Copyright (c)2014 John Wiley & Sons, Inc.

•
•
•

Chapter Eleven

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Average Revenue

Since

TR PxQ
AR =
=
=P
Q
Q

The price a monopolist can charge to sell quantity Q is determined by the market
demand curve the monopolists’ average revenue curve is the market demand

Copyright (c)2014 John Wiley & Sons, Inc.

curve.

AR(Q ) = P (Q )
Chapter Eleven

13


Marginal Revenue and Average Revenue

•

The demand curve D and average
revenue curve AR coincide

•

The marginal revenue curve MR lies

Copyright (c)2014 John Wiley & Sons, Inc.

below the demand curve

Chapter Eleven

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Marginal Revenue and Average Revenue

∆P
= −1
∆Q

When P decreases by $3 per ounce,

TR = P × Q = 7 × 5 = $35 million per year
TR 35
AR =
=
= $7 per ounce
Q
5

(from $10 to $7), quantity increases
by 3 million ounces (from 2 million
to 5 million per year)

Chapter Eleven

Copyright (c)2014 John Wiley & Sons, Inc.

∆P
MR = P + Q

= 7 + 5(−1) = $2 per ounce
∆Q

15


Marginal Revenue and Average Revenue

Conclusions if Q > 0:
MR < P
MR < AR
MR lies below the demand curve.

Copyright (c)2014 John Wiley & Sons, Inc.

•
•
•
•

Chapter Eleven

16


Marginal Revenue and Average Revenue

•

Given the demand curve, what are the average and marginal revenue curves?

P = a − bQ

AR = a − bQ
∆P
= −b
∆Q

∆P
MR (Q ) = P +
Q
∆Q

Copyright (c)2014 John Wiley & Sons, Inc.

MR = a − bQ + Q(−b)
= a − 2bQ
Vertical intercept is

Horizontal intercept is

a
Q=

a
2b
Chapter Eleven

17

Profit Maximization
Given the inverse demand and MC, what is the profit maximizing Q and P for the monopolist?

P = 12 − Q

MC = Q

Here a = 12, b = 1

MR = 12 − 2Q

MR = MC = 12 − 2Q = Q

Q=4

P = 12 − 4 = 8

Chapter Eleven

Copyright (c)2014 John Wiley & Sons, Inc.

•

18


Profit Maximization

•

•

Profit Maximizing output is at MR=MC
Monopolist will make 4 million ounces and
sells at $8 per ounce

Chapter Eleven

TR = Areas B + E + F
Profit (TR-TC) is B + E
Consumer surplus is area A

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Copyright (c)2014 John Wiley & Sons, Inc.

•
•
•


Shutdown Condition

In the short run, the monopolist shuts down if the most profitable
price does not cover AVC. In the long run, the monopolist shuts
down if the most profitable price does not cover AC. Here, P*

Copyright (c)2014 John Wiley & Sons, Inc.

exceeds both AVC and AC.

Chapter Eleven

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Positive Profits for Monopolist

This
Thisprofit
profitisispositive.
positive. Why?
Why? Because
Becausethe
themonopolist
monopolisttakes
takesinto
intoaccount
accountthe
the
price-reducing
price-reducing effect
effect ofof increased
increased output
output soso that
that the
the monopolist
monopolist has
has less
less

incentive
incentivetotoincrease
increaseoutput
outputthan
thanthe
theperfect
perfectcompetitor.
competitor.

Profit
Profitcan
canremain
remainpositive
positiveininthe
thelong
longrun.
run. Why?
Why? Because
Becausewe
weare
areassuming
assuming
that
thatthere
thereisisno
nopossible
possibleentry
entryininthis
thisindustry,
industry,sosoprofits

profitsare
arenot
notcompeted
competed
Copyright (c)2014 John Wiley & Sons, Inc.

away.
away.

Chapter Eleven

21


Equilibrium

AAmonopolist
monopolistdoes
doesnot
nothave
haveaasupply
supplycurve
curve(i.e.,
(i.e.,an
anoptimal
optimaloutput
outputfor
forany
any
exogenously-given

exogenously-given price)
price) because
because price
price isis endogenously-determined
endogenously-determined by
by
demand:
demand:the
themonopolist
monopolistpicks
picksaapreferred
preferredpoint
pointon
onthe
thedemand
demandcurve.
curve.

One
Onecould
couldalso
alsothink
thinkofofthe
themonopolist
monopolistchoosing
choosingoutput
outputtotomaximize
maximizeprofits
profits

Copyright (c)2014 John Wiley & Sons, Inc.

subject
subjecttotothe
theconstraint
constraintthat
thatprice
pricebe
bedetermined
determinedby
bythe
thedemand
demandcurve.
curve.

Chapter Eleven

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Price Elasticity of Demand
Market A profit maximizing price is PA.

•

Market B profit maximizing price is PB. Demand is less elastic in Market B

Copyright (c)2014 John Wiley & Sons, Inc.

•

Chapter Eleven

23


Inverse Elasticity Pricing Rule

We
Wecan
canrewrite
rewritethe
theMR
MRcurve
curveasasfollows:
follows:

MR = P + Q(∆P/∆Q)
MR = P + Q(∆P/∆Q)
= P(1 + (Q/P)(∆P/∆Q))
= P(1 + (Q/P)(∆P/∆Q))

Copyright (c)2014 John Wiley & Sons, Inc.

= P(1 + 1/ε)
= P(1 + 1/ε)
where: ε is the price elasticity of demand, (P/Q)(∆Q/∆P)
where: ε is the price elasticity of demand, (P/Q)(∆Q/∆P)

Chapter Eleven

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Inverse Elasticity Pricing Rule

Using
Usingthis
thisformula:
formula:

•• When
Whendemand
demandisiselastic
elastic(ε(ε<<-1),
-1),MR
MR>>00
•• When
Whendemand
demandisisinelastic
inelastic(ε(ε>>-1),
-1),MR
MR<<00

Chapter Eleven

Copyright (c)2014 John Wiley & Sons, Inc.

•• When
Whendemand

demandisisunit
unitelastic
elastic(ε(ε==-1),
-1),MR=
MR=00

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