Monopoly Market

Dr. Subhasis Bera

Business EconomicsIMG 7

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

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)

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

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.

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

Thank You!