Download - 08.IMG7 Monopoly
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Monopoly Market
Dr. Subhasis Bera
Business EconomicsIMG 7
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Monopoly Market
This an extreme market situation where there is only one seller and many buyers.In a monopoly market, as a sole producer of the product, firm can control the price and quantity suppliedbut up to a certain extent.This indicates that firm can not charge any price it wants at least with an objective to maximize profit.
A monopolists individual demand curve possesses the same general properties as the industry demand curvefor perfectly competitive market. Clearly, this indicates that firms Individual demand curve is the industrydemand curve.
The quantity of its sales is a single-valued function of the price which it charges: q = f(p), where
Therefore the inverse demand curve will be a single valued function of quantity p= F(q) , where
This indicates that firm can not set both p and q independently.
0dq
dp
0dp
dq
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Occurs of Monopoly
A monopoly occurs when barrier to entry prevents a second firm from entering a profitable market.
Among the possible barriers to entry are patents, network externalities, government licensing, theownership or control of a key resources, large economies of scale in production.
Another way to get monopoly power is to hire lobbyists and other policy makers to grant monopolypower.
Rent seeking is a process of using public policies to gain economic profit. Rent seeking is inefficientbecause it uses resources that could be used in other ways. (e.g., Coca cola in campus, Casino inKolkata)
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AR and MR of Monopoly
Total revenue = TR = p.q
Since
[ in case of perfect competition market buttherefore an increase in the volume of sales increases the TR]
Here, monopolist must decrease his price if it wants to sale extra unit of its output. This indicates that MRwill be downward from left to right.Since MR is downward sloping, AR will also be downward sloping.
( ). .
d TR dp dpMR p q AR q
dq dq dq
0 dq
MR pdp
( ).
d TR dpMR p q
dq dq 0
dp
dq
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AR and MR of Monopoly
Demand is monotonically decreasing.
MR < price for every output greater than zero., because
in case of monopoly
Therefore
And
Since
The distance between the two curves
is a linear function of output.
output
Price per unit
AR (Demand)
MR
( ).
d TR dpMR p q
dq dq
0butdp
dq
p a bq
2TR aq bq
2dR
MR a bqdq
Constantdp
bdq
dp
q bqdq
and TR
AR a bqq
Therefore from the slope of MR and AR we can say slope MR is twice steeper than the slope of AR. Thus MR passes through the half of the distance from intersection point between AR and horizontal axes.
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Output Decision of a Monopoly
Market equilibrium condition is MR=MC.
Here equilibrium output is Q*.
Is this profit maximizing output?
If monopoly produces an amount Q1 > Q* he will be able to sellthat at the price P1.
In this case MR>MC and firm will produce more to increase itstotal profit.
Similarly if firm produces Q2 > Q* then MC> MR and in thiscase firm can increase its profit by reducing the level ofproduction from Q2.
Therefore output will be maximum at MR=MC
output
Price per unit
AR (Demand)
MR
AC
MC
Q*
P*
Q1
P1
Lost profit from producing too little (Q1) and selling at too high
price( p1)
Lost profit from producing too much (Q2) and selling at too
low price( p2)
Q2
P2
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Output Decision of a Monopoly
The monopolists total revenue and total cost can be expressed as a function of output.
From F.O.C. of profit maximization we get
Monopolist can increase profit by expanding or contracting its output, as long as the addition to its revenue (i.e.,MR) exceeds the addition to its cost (i.e., MC).
to get the condition from the S.O.C. of profit maximization we get
( )TR f q ( )TC h q
therefore, = ( ) ( )f q h q
' '( ) ( ) ( ) ( ) 0d d TR d TC
f q h qdq dq dq
. , 0. MRi e MC
2' ' ' '
2( ) ( ) 0
df q h q
dq
' ' ' 'or, ( ) ( ) i.e., slope of MR < slope of MCf q h q
MR ARqq0
MC
p0
p
MR ARq
MC
p
MR ARq
MCp
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Equilibrium output of a Monopoly
If demand faced by a monopolist is p= 100-4q
And cost function is C= 50+20q
Then profit will be
Where
From profit max condition we get
Here in this problem
Therefore
Now substituting the value of q in the demand function we get
And from profit function we get
from the SOC we get
TR TC 2. 100 4TR p q q q
( ) ( )0
d d TR d TCMR MC
dq dq dq
100 8MR q 20MC
100 8 20q
or, 10q
60p
350 2
28 0
d
dq
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Effects on price and quantity: PC market vs Monopoly market
Equilibrium in Monopoly attains at A where MR=MC and price is P1 and output is Q0Equilibrium at PC market attains at C where equilibrium output and price are Q1 and P0 respectively.
This indicates that monopoly produces less than what it could produce in the perfectly competitive market and charges higherprice than the perfect competition market.
Clearly monopoly will produce less efficiently than what it could produce in the PC market.
Q(drugs/hour)
AR
P0MR
LAC=LMC
Price
P1
Q0 Q(drugs/hour)
AR
P0 LAC=LMC
Price
Q1
Market Demand Market
Demand
A
B
C
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Monopoly and Elasticity of Demand
In case of monopoly MR will be positive.again from the relation between MR and Elasticity we know that
This indicates that monopoly will produce at a point where its demand curve is elastic.
11 1
q dpMR p p
p dq e
1Therefore 1 0p
e
1or, 1 0, since > 0p
e
1or, 1>
e
or, 1e
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A Rule of Thumb for Pricing
How a manager of a firm find the correct price and output.most managers have limited information about AR and MR that their firms face.
Similarly, they might know the firms marginal cost only over a limited output range.We therefore want to translate the condition that MR = MC into a rule of thumb that can be more easilyapplied in practice.We know
Note that extra revenue from an incremental unit of quantity, has two components:
1. Producing one extra unit and selling it at price p brings in revenue (1)(P)=P.2. Because of the downward-sloping demand curve one extra unit of sell results a small drop
in price , which reduces the revenue from all units sold ( i.e., changes in revenue
Therefore
( . )dTR d PQMR
dQ dQ
( . )d PQ
dQ
dP
dQ.dP
QdQ
.dp q dp
MR p q p pdq p dq
1
D
MR p pe
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From profit max condition MR=MC we get
LHS shows the mark up over marginal cost as a percentage of price. Rearranging the term we get
1
D
MC p pe
1,
D
p MCor
p e
11
D
MCp
e
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Monopoly Power
In a perfectly competitive market price equals to MC whereas in Monopoly price exceeds MC.
Therefore we can measure monopoly power by examining the extent to which the profit-maximising price exceeds MC.This measure was introduced by Learner.
Learners Index of Monopoly
Sources of Monopoly Power
From the Learners equation we observed that lesser the elasticity of demand higher will be the monopoly power.
This elasticity depends on-
1. Nature of the demand of the product
2. Numbers of firms producing close substitute (greater number of firms reduces the monopoly power)
3. Interaction among the firms ( less aggressive attitude can help the firms to earn more profit).
( )P MCL
P
1,
D
or Le
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Price Discrimination
The monopolist need not always sell her entire output in a single market for a uniform price. We candiscuss two different cases here.Market discriminationThere are two markets. Revenue earned from each markets are R1(q1) and R2(q2).Total cost of producing q1 and q2 units in two different markets is C(q1 +q2 )Therefore
Now from the F.O.C. we get
Equating these two get
This implies that MR in each market must be equal to the MC of total output as a whole
1 1 2 2 1 2( ) ( ) ( )R q R q C q q
' '
1 1 1 2
1
( ) ( ) 0d
R q C q qdq
' '
2 2 1 2
2
( ) ( ) 0d
R q C q qdq
' ' ' '
1 1 1 2 2 2 1 2( ) ( ) ( ) ( )R q C q q R q C q q
' ' '
1 1 2 2 1 2, ( ) ( ) ( )or R q R q C q q
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Price Discrimination
Sometimes monopoly firm charge different price for different consumer.
Basic idea of price discrimination is to increase total revenue. Depending on the pattern of the pricecharged price discrimination can be classified as
1st order price discrimination- Every consumer pays a different price which is equal to his or herwillingness to pay.
2nd order price discrimination- in this case consumer pays the minimum amount that he/she is willingto pay for a particular product.
3rd order price discrimination- in this case monopoly charge different price for different groups ofcustomer.
A monopolist may charge different price in the different price in the different market depending on thenature of the market.
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Price Discrimination: Math Problem
Suppose market demand in market 1 and market 2 are andAnd Cost function is where,
Therefore andOr,
And MC of total output as a whole
Therefore from equilibrium condition we get
Solving equation (i) and (ii) we get
What are the conditions of price discrimination?
1 180 5p q 2 2180 20p q
1 250 20( )C q q
2
1 1 180 5R q q 2
2 2 2180 20R q q
1 180 10MR q 2 2180 40MR q
20dC
MCdq
1 2q q q
1 180 10 20.........( )MR q i
2 2180 40 20.......( )MR q ii
1 1
2 2
6 50
4 100
450
q p
q p
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Price Discrimination: Math Problem
Problem: A monopoly sells in two markets:
p1(x1)=100-x1 and p2(x2)=80-x2.
a) Calculate the profit-maximizing quantities and the profit at these quantities, if the cost function isgiven by C(X)=X2.
b) Calculate the profit-maximizing quantities and the profit at these quantities, if the cost function isgiven by C(X)=10X.
c) What happens if price discrimination between the two markets is not possible anymore? ConsiderC(X)=10X.
Hints: Differentiate between quantities below and above 20.
Solution :a) 1400,
b) 3250,
c) 3200
M
M
M
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Multi-plant Monopolist
A monopolist selling in a single market but producing at different location
In this case his profit function will be
From F.O.C. we get
From the above two equation we get
This indicates that MC in each plant must be equal the MR of the output as whole.
1 2 1 1 2 2( ) ( ) ( )R q q C q C q
' '
1 2 1 1
1
( ) ( ) 0d
R q q C qdq
' '
1 2 2 2
2
( ) ( ) 0d
R q q C qdq
' ' '
1 2 1 1 2 2( ) ( ) ( )R q q C q C q
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Taxation and Monopoly Output
Types of tax can be
1. Lump-sum tax
2. Profit tax
3. Sales tax based upon the quantity sold or value of sales
Lump-sum tax
Monopolist cannot avoid lump-sum tax regardless the physical quantity or value of its sales.
In this case
From FOC we get
Therefore
Or, MR=MC
( ) ( )R q C q T ' '( ) ( ) 0
dR q C q
dq
' '( ) ( ) 0R q C q
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Taxation and Monopoly Output
Profit tax
A profit tax requires that the monopolist pay the government a specified proportion of the differencebetween its TR and TC. If the tax is a flat rate t of profit then
From the FOC we get
Therefore MR= MC
( ) ( ) ( ) ( )R q C q t R q C q
, (1 ) ( ) ( )or t R q C q where, 0< 1t
' '(1 ) ( ) ( ) 0d
t R q C qdq
' ', ( ) ( ) 0or R q C q since (1 ) 0t
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Taxation and Monopoly Output
Specific tax
If a specific sales tax of t Rs. Per unit of output is imposed then
From FOC we get
therefore monopolist maximizes profit after tax payment by equating MR with MC plus the unit tax
( ) ( ) .R q C q t q
' '( ) ( ) 0d
R q C q tdq
' ', ( ) ( )or R q C q t
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Thank You!