DUOPOLYPresented By:

Usama QadriUmair ShaukatFazeel Ahmad

Usman KhanShahid Tanveer

DUOPOLY INTRODUCTION:

Two Words Duo---Two Polies---Sellers Market with TWO sellers Just below Monopoly Simplest Form of Oligopoly Have Power to control Market Super Normal Profits Two Classifications: One in which there is coordination b/w duopolists. One in which there is no coordination.

COLLUSION OR CARTEL:

Type of Duopoly in which Duopolists coordinate with each other.

Turns out to be a kind of Monopoly i-e single decisions are made by both duopolists which create Monopoly in the market. e.g. Drug Cartels, OPEC etc.

Usually banned by govt. because govt. usually try to avoid this monopoly as it is harmful for market environment and consumers.

NON COOPERATING/NON COLLUSIVE DUOPOLY

Duopolists don’t cooperate with each other. Super Normal Profit. Both have impact on market. Strategic Planning. Example to explain Duopoly:

BOXING SPRINT RACE

REAL WORLD EXAMPLES OF DUOPOLY:

GAME THEORY

A tool to analyze strategic interaction. Determine strategies adopted by players. More Formally “The study of mathematical models of

conflict and cooperation between intelligent rational decision-makers.”

Some of them are Battle of the sexes, Peace war game, Pirate game, Prisoner’s Dilemma, and Trust game etc.

Game theory selected to understand Duopoly is :

PRISONER’S DILEMMA EXPLANATION:

Consider two robbers.

Decided to Rob a bank and went to do it.

The Plan went wrong and get caught.

Both were kept in separate cell to avoid interaction.

Each of them provided with same set of offers, that are:

PRISONER’S DILEMMA (CONT..)THE PREVIOUS PICTURE IN

TABULATION Dominance Strategy: the thing I preferred keeping other person’s views in mind.

Nash Equilibrium: if no player can do better by unilaterally changing his strategy, then such a set of strategies is Nash Equilibrium. (I don’t want to change my strategy given your strategy)

Pareto Efficient: both maximize utility to the most.

Confess

Deny

Confess

5 years5 years

0 years20 years

Deny 20 years0 years

1 year1 year

MARKET MODEL Major

Assumption: MC=0 and

constant

MC=0a/2b COURNOT a/b

PERFECT COMPETITION

P

MONOPOLY

MR(x)=

a-2

bx

DC

P(x)=a-bx

As MR is two times steeper than DemandIn monopoly MC = MRIn PC MC = P

As firms don’t know each others strategy so they can’t create monopoly and produces more than it with the same slope that of monopoly

CALCULATIONS

Incase of Monopoly:As MR(x)= a-2bxand MR=P

Þ P= a-2bx --------(1)But MC(x)= 0Þ P= 0 -------------(2)Þ a-2bx= 0Þ x= a/2b

Incase of Perfect Comp.As P= a-bxP=MC(x)

Þ a-bx= 0 -----------(3)Þ x=a/b

Here x = x1+x2 i.e. quantity produce by both duopolist…

COURNOT OR QUANTITY SETTING GAME

What’s the NASH EQUILIBRIUM?(a/b – a/2b)/2

And, for 2 firmsx1= (a/b – x2)/2------(A)

and x2 = (a/b – x1)/2------

(B)Put value of x1 in x2 we

get,x2=(a/b – (a/b-x2)/2)/2 on solving we get,

x2 = a/2b – a/4b + x2/4x2 = a/4b+x2/4x2 – x2/4 = a/4b

and we get,x2 = a/3b

Similarly we can get,x1 = a/3b

RESPONSE CURVE OF BOTH FIRMS

X

X

1

2

a/3b

a/2b

a/2ba/3b

a/4b

a/4b

N

R1

R2

M

P

Here,P = Competitive EquilibriumN = Nash EquilibriumandM = Collusion Equilibrium

As quantity is divided b/w two firms so Monopolistic output i.e. a/2b becomes a/4b and competitive output i.e. a/b becomes a/2b and so cournot demand which lies b/w M and P is a/3b …….

BERTRAND OR PRICE SETTING GAME The basic assumptions we take in this price setting game are:

>The firms are identical in their technology.>Sell homogeneous goods.>Both firms have constant return to scale, with a constant cost

function. Now suppose a price is set in a duopoly market. Suddenly Firm 1 (F1) decreases the price to P1. In response to this the other firm that is Firm 2 (F2) will also

decrease its price to the same volume to under cut that price. Now the F1 will decrease again its price to P2, then the F2 will

show the same response to undercut price difference. The procedure will continue until it is not profitable to

undercut i.e. MC=P.

MARSHALLIAN DEMAND CURVE:

Marshallian demand curve was presented by The Great Sir Alfred Marshall. It is the simple demand curve we study in our text books of economics showing the effect of price on quantity demanded.This demand curve gives us relation that price and quantity demanded are inversely relational to each other as if we increase price of a good its demand will decrease.Here we have to show how marshallian demand curve will response in Duopoly market keeping in view a duopoly firm let suppose PepsiCo.In duopoly marshallian demand curve gets a shape called KINKED DEMAND CURVE.

INTRODUCTION KINKED DEMAND

The kinked demand curve was first used by Paul.M.Sweezy to explain price rigidity.

The assumption behind this theory of kinked demand is that each duopolist will act and react in a way that keeps condition tolerable by both duopolist.

Such a situation is most likely to occur where products are quite similar and, therefore their prices almost same.

Similar to Price Setting Game. If one firm is selling at a price lower than that of its

competitor, then the other firm will be compelled to reduce its prices to match this firm’s price.

On the other hand if one firm decides to sell at a higher price the other firm does not react by raising its price.

So, in the first situation (i.e. Price reduction) the firm does not gain, while the latter the firm loses its customer to its rival.

The duopoly firm probably realises that it is better to accommodate its rival rather than start a price war.

So in non-collusive duopoly the price is tend to be sticky i.e. there is a price rigidity.

The most significant aspect of the solution of an oligopoly situation is the presence of kink in the demand curve of the firm.

KINKED DEMAND (CONTD..)

KINKED DEMAND CURVE

P

Q

Equilibrium Price

P*

P1

P

Q Q2 Q* 1

2

D

MR

MC

E’

E

MC’

The kink shows that price reduction by a firm is followed by its rival (competitors).

Therefore firm will not move away from the kink.

For finding out the profit maximizing price-output combination, MR curve corresponding to kinked demand has been drawn.

MR curve associated with kinked demand curve is always discontinuous.

The MR curve has two portions the upper portion gives MR in highly elastic demand and lower portion shows the MR in highly inelastic demand keeping in mind that MR is two times steeper than D.

Now drawing the MC curves showing long run and short run MC.

As profit maximizing output is at MC=MR so we can it is at Q*

So Q* is the equilibrium point for Duopolist Firm.

CHANGES IN DEMAND DO NOT AFFECT THE OLIGOPOLY PRICE

p MC

D’D

R R’

H H’

D

D

M M’

MR MR’

OUTPUT

Pri

ce

K K’

Likewise when demand condition changes the price may remain stable.

The demand for duopolist from K to K’ the marginal cost curve MC also cuts the new MR’ curve.

Thus same price P continues to prevail in the duopoly.

Criticism /drawback…kinked demand curve

The kinked demand curve model has been criticized on some counts:-

There are also some other valid explanation for price rigidity, such as nationally advertised prices, catalogued prices, reluctance(unwillingness) to disrupt(upset) customers relations, and fears that recurrent(regular) price cuts may trigger a price war.

The model does not explain how the firm arrive at the kink in the first place.