monopoly market
DESCRIPTION
Monopoly MarketTRANSCRIPT
FMG 24: 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 supplied but 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 monopolist’s individual demand curve possesses the same
general properties as the industry demand curve for perfectly
competitive market. Clearly, this indicates that firm’s Individual
demand curve is the industry demand curve.
Monopoly Market
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
0dq
dp
0dp
dq
Monopoly Market
This indicates that firm can not set both p and q independently.
A monopoly occurs when barrier to entry prevents asecond 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 economiesof scale in production.
Another way to get monopoly power is to hire lobbyistsand other policy makers to grant monopoly power.
Rent seeking is a process of using public policies to gaineconomic profit. Rent seeking is inefficient because ituses resources that could be used in other ways. (e.g.,Coca cola in campus, Casino in Kolkata)
Reasons for Monopoly
Total revenue = TR = p.q
Since
[ in case of perfect competition market but
therefore 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 MR will 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
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 linearfunction of output.
output
Price per unit
AR (Demand)MR
( ).
d TR dpMR p q
dq dq 0but
dp
dq
p a bq
2TR aq bq
2dR
MR a bqdq
Constantdp
bdq
dpq bq
dq
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.
AR and MR of 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 sell that at the price P1.
In this case MR>MC and firm will produce more to
increase its total profit.
Similarly if firm produces Q2 > Q* then MC> MR and in
this case firm can increase its profit by reducing the
level of production from Q2.
Therefore output will be maximum at MR=MC
output
Price per unit
AR (Demand)
MR
ACMC
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
Output Decision of Monopoly
The monopolist’s 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
' '( ) ( )( ) ( ) 0
d d TR d TCf q h q
dq 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 AR
qq0
MC
p0
p
MR AR
q
MC
p
MR AR
q
MC
p
Output Decision of 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
Equilibrium Output of a Monopoly
Equilibrium in Monopoly attains at A where MR=MC and price is P1 and output is Q0
Equilibrium 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 higher price than the perfect competition market.
Clearly monopoly will produce less efficiently than what it could produce in the PC market.
We assume that industry is a constant cost industry.
Q(drugs/hour)
AR
P0
MR
LAC=LMC
Price
P1
Q0Q(drugs/hour)
AR
P0LAC=LMC
Price
Q1
Market Demand Market
Demand
A
B
C
Effects on Price and Quantity: Monopoly Market Vs PC Market
In case of monopoly MR will be positive.
again from the relation between MR and Elasticity we know that
Since a producer will produce the unit for which MR > 0
11 1
q dpMR p p
p dq e
1Therefore 1 0p
e
1or, 1 0, since > 0p
e
1or, 1>
e
or, 1e
Monopoly and Elasticity of Demand
This indicates that monopoly will produce at a point where its demand curve is elastic
Monopoly does not have a supply curve. There is no function of price that
determines what quantity a firm will offer given a price. Instead, the quantity a firm
offers is determined by the entire demand curve it faces.
In a competitive market supply decisions are made based on just price (the
demand curve faced by a single firm is horizontal at some price). In a monopoly,
supply decisions need more than just the knowledge of one price.
Supply Curve of Monopoly
Since there is no supply curve how a monopolist will set the price?
Most managers have limited information about AR and MR that their firms face.
Similarly, they might know the firm’s 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 moreeasily applied 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 inprice , which reduces the revenue from all units sold ( i.e., changes in revenue
Therefore
( . )dTR d P QMR
dQ dQ
( . )d P Q
dQ
dP
dQ.dP
QdQ
.dp q dp
MR p q p pdq p dq
1,
D
or MR p pe
A Rule of Thumb for Pricing
How a manager of a firm find the correct price and output?
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
1Therefore,
D
MC p pe
1,
D
p MCor
p e
11
D
MCp
e
A Rule of Thumb for Pricing
A Monopolist with the help of its cost structure and elasticity of demand can set the price
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.
Learner’s Index of Monopoly
From the Learner’s 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
Monopoly Power
Sources of Monopoly Power
The monopolist need not always sell her entire output in a single market for a uniform
price.We can discuss two different cases here.
There 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
Or, MR1= MR2=MC
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
Price Discrimination
This implies that MR in each market must be equal to the MC of total output as a whole
Market Discrimination
1st order price
discrimination-
Every consumer pays a
different price which is
equal to his or her
willingness to pay.
2nd order price
discrimination-
in this case consumer
pays the minimum
amount that he/she is
willing to pay for a
particular product.
3rd order price
discrimination- in this
case monopoly charge
different price for
different groups of
customer.
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
price charged price discrimination can be classified as
A monopolist may charge different price in the different price in the
different market depending on the nature of the market.
In Sarojini Nagar Market or at Lajpat
Nagar Market or any other flea market
buyers often need to bargain to show that
his/her willingness to pay is minimum
for a specific good. Seller normally sells
at a max price that a consumer willing to
pay given that the price is above his cost
of production.
This helps to increase sell
Price Discrimination: Example of First Degree Price Discrimination
In the year 2004 one Financial Times reporter pretended to book a car rental
through Avis Website for four days from Los Angeles International Airport. As a
part of the booking process you are asked for your home country. The reporter
examined with different countries and received the following rate quotes.
Price Discrimination: Example of Third Degree Price Discrimination
Country Rate
Australia $198
India $198
UK $162
France $159
Germany $156
South Africa $156
United States $153
Canada $132
Brazil $120
Suppose market demand in market 1 and market 2 are and
And Cost function is where,
Therefore and
Or,
And MC of total output as a whole
Therefore from equilibrium condition we get
Solving equation (i) and (ii) we get
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
Price Discrimination: Math Problem(Demonstration)
What are the conditions of Price Discrimination?
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 is given by C(X)=X2.
b) Calculate the profit-maximizing quantities and the profit at these quantities, if the cost
function is given by C(X)=10X.
c) What happens if price discrimination between the two markets is not possible anymore?
Consider C(X)=10X.
Hints: Differentiate between quantities below and above 20.
Solution :a) 1400,
b) 3250,
c) 3200
M
M
M
Price Discrimination: Math Problem
Very often we find firms distribute coupons (by mail or in newspapers) which give
a rebate for the product.
1
2
3
Coupon users are more price-sensitive
Only a small proportion of coupon receivers actually use them
to claim the rebate
Coupon reminds the customer each time that she gets lower
price
Why is it better to give out coupons as compared to a general price cut??
Price Discrimination: Discount Coupon for Price Discrimination
Price elasticities of rich (R) and poor (P) clients: and
Now let regular price = P
And Price with coupon = P-X
Also assume that MC = 2
When a firm sets price in two different market, equilibrium attains at
Now if elasticity of demand with rich and poor people are eR and eP respectively
then from the equilibrium condition we get
Solving this we get P=4, X=1.5
1 1
or, 1 1R P
P P X MCe e
2Re 5Pe
1 2MR MR MC
How to set an optimal coupon?
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
Or, MR = MC1 = MC2
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
Multi-plant Monopolist
This indicates that MC in each plant must be equal the MR of the output as whole
Problem: Suppose the inverse demand for a monopolist’s product is given by
The monopolist can produce output in two plants. The marginal cost of producing
in plant 1 is MC1 = 3Q1,
and the marginal cost of producing in plant 2 is MC2 = Q2.
How much output should be produced in each plant to maximize profits, and what
price should be charged for the product?
Solution: Do it Yourself
( ) 70 0.5P Q Q
Multi-plant Monopolist: Math Problems
Types of tax can be
1. Lump-sum tax
2. Profit tax
3. Sales tax based upon the quantity sold or value of sales
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
' '( ) ( ) 0d
R q C qdq
' '( ) ( ) 0R q C q
Taxation and Monopoly Output
Lump-sum Tax
A profit tax requires that the monopolist pay the government a specified
proportion of the difference between 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
Taxation and Monopoly Output
Profit Tax
In this case total volume of profit will be less
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
Specific Tax
Taxation and Monopoly Output
Now we can deal with some real world problems
In this case equilibrium price and output will change
Thank You!