2. 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.
3. 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.
4. 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
6. 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 :
9. The Plan went wrong and get caught.
Both were kept in separate cell to avoid interaction.
10. Each of them provided with same set of offers, that are:
11. 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 years
5 years
0 years
20 years
Deny 20 years
0 years
1 year
1 year
12. MARKET MODEL
Major Assumption:
MC=0 and
constant
MC=0
a/2b COURNOT a/b
PERFECT COMPETITION
P
MONOPOLY
As MR is two times steeper than
Demand
In monopoly MC = MR
In 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
13. CALCULATIONS
Incase of Monopoly:
As MR(x)= a-2bx
and MR=P
P= a-2bx --------(1)
But MC(x)= 0
P= 0 -------------(2)
a-2bx= 0
x= a/2b
Incase of Perfect Comp.
As P= a-bx
P=MC(x)
a-bx= 0 -----------(3)
x=a/b
Here x = x1+x2 i.e.
quantity produce by
both duopolist…
14. COURNOT OR QUANTITY SETTING GAME
What’s the NASH
EQUILIBRIUM?
(a/b – a/2b)/2
And, for 2 firms
x1= (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 + x2/4
x2 = a/4b+x2/4
x2 – x2/4 = a/4b
and we get,
x2 = a/3b
Similarly we can get,
x1 = a/3b
15. 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 Equilibrium
N = Nash Equilibrium
and
M = 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 …….
16. 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.
17. 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.
18. 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.
19. 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..)
20. 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.
21. CHANGES IN DEMAND DO NOT AFFECT THE
OLIGOPOLY PRICE
p MC
D’
D
R R’
H
H’
D
D
M M’
MR MR’
OUTPUT
Price
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.
22. Criticism/drawback…kinkeddemand 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.
