Download Document

Monopoly
Maximize Profit Condition
A Monopolistic maximizes profit by producing
quantity Q* where marginal revenue equals
marginal cost
MR ( Q* ) = MC ( Q* )
d
dTR(q) dTC (q)
0

dq
dq
dq
dTR(q)
MR 
dq
dTC (q)
MC 
dq
MR  MC
Slope(TR)  Slope(TC )
Marginal Revenue
P
P
D
P1
2
1
D
Q1 Q1+1
Q
Q1 Q1+1
Q
Marginal Revenue
ΔTR=Area1-Area2
ΔTR=PQ-QP
ΔTR
ΔP
MR=
=P+Q
ΔQ
ΔQ
Average Revenue
TR
AR=
Q
P×Q
AR=
=P
Q
AR(Q)=P(Q)
ΔTR
ΔP
MR=
=P+Q
ΔQ
ΔQ
AR(Q)=P(Q)
MR < P , when output is positive
AR, P
MR
D = AR = P
Q
Exercise
Suppose that the equation of the market demand
curve is P = a – bP
What are the expressions for the average and
marginal revenues
Profit Maximization
 (q)  TR(q)  TC (q)
Max (q)  Max{TR(q)  TC (q)}
Profit Maximization Condition
d (q)
0
dq
TR,TC
TR
Competitive Market
TC
Profit
0
Q
MC
MR = P
0
Q
MC > MR
MC < MR
MC = MR
MC > MR
TR,TC
TC
Monopoly
TR
0
Q
Profit
MC
0
MR
MC < MR
MC = MR
MC > MR
D
Q
AR, AC, P
MC
AC
P1
C1
M
F
D = AR
MR
Q*
Q
AR, AC, P
Cost Changes
MC
AC
P1
M
D = AR
MR
Q*
Q
AR, AC, P
MC
AC
P1
M
D = AR
MR
Q*
Q
Equilibrium in Long Run
Less than optimal Scale of Plant
Optimal Scale of Plant
Greater than optimal Scale of Plant
Exercise
The equation of monopolist’s demand curve is
P = 12 – Q
While the equation of marginal cost is
MC = Q
Where Q is expressed in millions of ounces
What is the profit maximizing quantity and price
for the monopolist ?
Exercise
The equation of monopolist’s short run cost
curve is
C(Q) = 12 + Q2
While the equation of marginal revenue is
MR = 24 - 2Q
Where Q is expressed in millions of ounces
What is the profit maximizing quantity and price
for the monopolist ?
AR, AC, P
Firm Produce at MC < MR
MC
P1
M
AC
P*
F
D = AR
MR
Q*
Q
AR, AC, P
Firm Produce at MC > MR
MC
M
AC
P*
P1
F
D = AR
MR
Q*
Q
Monopolist & Supply Curve
AR, P
MC
D1
MR1
Q1
MR2
D2
Q
Elasticity and Profit Maximized
AR, P
AR, P
P2
P1
MR1
Q1
MC
MC
D1
D1
Q
Q2 Q1
Q
Marginal Revenue and Elasticity
P
MR=P+Q
Q
Q ΔP
MR=P(1+
)
P ΔQ
P ΔQ
=ε Q,P
Q ΔP
MR=P(1+
1
 Q,P
)
AR, AC, P
MR=P(1+
Unitary elastic
Elastic
1
 Q,P
MR = 0
MR > 0
Inelastic
MR < 0
D
Q
MR
)
Rule of thumb for Pricing
MR=P(1+
MR=P(1+
MR=MC
P+
MC
P=
1
1
 Q,P
1
 Q,P
1
 Q,P
P
 Q,P
)
)=MC
=MC
P-MC
1
=P
ε Q,P
Exercise
Market demand curve given by
Q = 100P-2
While the equation of marginal cost is
MC = 50
A ) What is the Monopolist’s optimal price?
B ) Suppose that the market demand curve is
given by the equation
Q = 100P- 5
What is the monopolist’s optimal price?
Exercise
Market demand curve given by
Q = 200 - P
While the equation of marginal cost is
Mc = 50
A ) Find the profit maximizing price and quantity
for the monopolist using the Inverse Elasticity
Price Rule ( IEPR )
B ) Find the profit maximizing price and quantity
for the monopolist by equating MC = MR
AR, AC, P
Produce on Elastic Region
B
1
A
2
D
Q
MR
AR, AC, P
Shift in Market Demand
MC
P2
P1
MR1
Q1 Q2
D1
MR2
D2
Q
AR, AC, P
Shift in Market Demand
P1
P2
MC
MR1
Q1
Q2
D1
MR2
D2
Q
Shift in MC
AR, AC, P
MC2
MC1
P2
P1
Increase in MC must decrease TR
D
Q
Q2 Q1
MR
Regulated Monopoly
Price Regulation
Average Cost Pricing
Marginal Cost Pricing
Tax Regulation
Specific Tax
Lump Sum Tax
AR, AC, P
Average Cost Pricing
MC
P1
AR = AC
AC
M
F
PF
MR
D = AR
Q
QM
QF
AR, AC, P
Marginal Cost Pricing
MC
P1
AR = MC
AC
M
I
PI
MR
D = AR
Q
QM QI
AR, AC, P
Specific Tax
MCt
MR = MC + t
MC
AC + t
Pt
P1
AC
I
MR
D = AR
Q
Qt Q 1
AR, AC, P
Lump Sum Tax
MR = MC
MC
AC + t
P1
AC
I
Ct
C1
MR
D = AR
Q
Q1
AR, AC, P
Multiplant Monopoly
MC1
MC2
MCT
M
PT
D = AR
MR
Q
1
Q2
QT
π=PQT -C1 (Q1 )-C2 (Q2 )
dπ dPQT dC1 (Q1 )
=
0
dQ1
dQ1
dQ1
MR=MC1
dPQ T dC 2 (Q 2 )
dπ
=
0
dQ 2
dQ 2
dQ 2
MR=MC2
MR=MC1 =MC2
Exercise
Market demand curve for monopolist given by
P = 120 – 3Q
The monopolist has 2 plants, the first plant has a
marginal cost function given by
MC1 = 10 + 20Q1
The second plant’s marginal cost curve is given by
MC2 = 60 + 5Q2
Find the monopolist’s optimal total quantity and price.
Also find the optimal division of the monopolist’s
quantity between its two plants
Monopoly Power
AR, P
AR, P
Market Demand
MC
P
D1
Q
Q1
Qf
Q
Measuring Monopoly Power
(P-MC)
1
L=
=P
ε Q,P
MC
P=
1
1+
ε Q,P
AR, P
AR, P
MC
P
P-MC
P-MC
AR
MR
D1
Q
Q1
Q1
Q
Source of Monopoly Power
The Elasticity of Market Demand
The Number of Firm
The Interaction among the Firm
The Welfare Economics of Monopoly
AR, AC, P
MC1
PM
M
C
D = AR
MR
O
QM
AR, AC, P
Monopoly Deadweight Loss
MC1
A
M
PM
B
D
C
E
C
D = AR
MR
O
QM
Natural Monopoly
P, AC, MC
PM
PR
AC
PC
MC
AR
MR
0
Q
QM
QR
QC
Monopsony
Monopsony is a market consisting of single
buyer that can purchase from many sellers.
Some buyers may have monopsony power :
a buyer’s ability to affect the price of a good.
Monopsony power enables the buyer to
purchase the good for less than the price
that would prevail in the competitive market
Competitive Buyer & Competitive Seller
AR, P
AR, P
MC
AR = MR
ME = AE
P*
D = MV
Q
Q*
Q
Q*
AR, AC, P
Monopsonist Buyer
ME
S = AE
P
C
PM
MV
QM
QC
Monopoly and Monopsony
AR, AC, P
AR, AC, P
ME
MC
S = AE
PM
PC
PC
PM
MR
QM
QC
AR
MV
QM
QC
AR, AC, P
AR, AC, P
ME
ME
S = AE
S = AE
MV – P*
P*
MV – P*
P*
MV
Q*
MV
Q*
Source of Monopsony Power
The Elasticity of Market Supply
The Number of Buyer
The Interaction among Buyers
AR, AC, P
Deadweight Loss
ME
S = AE
B
P
C
C
A
PM
MV
QM
QC