Download Oligopoly

Oligopoly
Overheads
Market Structure
Market structure refers to all characteristics of a market
that influence the behavior of buyers and sellers,
when they come together to trade
Market structure refers to all features of a market that affect
the behavior and performance of firms in that market
Definition of a competitive agent
A buyer or seller (agent) is said to be competitive if the
agent assumes or believes that the market price is given
and that the agent's actions do not influence the market price
We sometimes say that a competitive agent is a price taker
Common Market Structures
Perfect (pure) competition
Agents take prices as given
Entry and exit barriers are minimal or nonexistent
Common Market Structures
Monopoly (seller) or Monopsony (buyer)
Firm sets price
(faces market demand or supply curve)
Entry and exit barriers result in the existence of
one seller or one buyer
Common Market Structures
Oligopoly
Firm sets prices (faces residual demand)
Entry and exit barriers result in the existence of
few sellers or buyers
Common Market Structures
Monopolistic competition
Firm sets prices (faces residual demand)
Entry and exit barriers are minimal
Strategic interdependence
When individuals make decisions in environments
characterized by strategic interdependence,
the welfare of each decision maker depends not only
on her own actions, but also on the actions of
the other decision makers (firms).
Moreover, the actions that are best for her to take
may depend on what she expects the other firms to do
Formal definition of oligopoly
Noncooperative oligopoly is a market structure
where a small number of firms act independently,
but are aware of each other's actions
A noncooperative oligopoly is a market structure
in which a small number of firms are
strategically interdependent
Cooperative oligopoly is a market structure
in which a small number of firms coordinate
their actions to maximize joint profits
Oligopoly is an intermediate market structure in the
sense that the firms are price makers as compared
to the price takers of perfect competition,
but because there are others firms in the market,
the firm cannot act in the independent fashion
of the monopolist
Duopoly
A duopoly is a market with only two firms,
each selling the same or similar product
A Duopoly Model
Two firms with no additional entry
Each firm produces a homogeneous product such
that q1 + q2 = Q, where Q is industry output
and qi is the output of the ith firm
There is a single period of production & sales (zucchini)
The market demand and inverse demand are linear
Demand
1
Q  q1  q2  14  p
2
p  28 2Q  28 2q1 2q2
Marginal and average cost are constant
and equal to $4.00
Cost ( q1)  4q1
Cost ( q2)  4q2
MC1  AC1  4
MC2  AC2  4
Monopoly solution
Firm 1 is the only firm in the market
Revenue is given by
Revenue (q1)  pq1
 (28 2q1 ) q1

2
28q1 2q1
Using the same intercept, twice the slope rule,
marginal revenue is given by
MR (q1)  28 4q1
If we set marginal revenue equal to marginal cost
we can obtain the optimal level of q1
MR (q1)  28 4q1  4  MC (q1 )
 24  4q1
 6  q1
If we substitute this into the demand equation
we can find the market price
p  28 2 q1
 28 (2)(6)
 16
Profit for Firm 1 is given by revenue minus cost or
Profit  π  R C
 pq1 c (q1 )
 (16)(6) (4)(6)
 96 24
 72
Zucchini Market
Monopoly
30
$ 25
Demand/P
MR
20
15
10
5
0
MC
0
2
4
6
8
10
12
14
16
Quantity
Q
0.00
Price
28.00
TR
0.00
MR
Cost
28.00 0.00
MC
4.00
Profit
0.00
1.00
26.00
26.00 24.00 4.00
4.00
22.00
2.00
2.50
24.00
23.00
48.00
57.50
20.00
18.00
8.00
10.00
4.00
4.00
40.00
47.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
22.00
21.00
20.00
19.00
18.00
17.00
16.00
66.00
73.50
80.00
85.50
90.00
93.50
96.00
16.00
14.00
12.00
10.00
8.00
6.00
4.00
12.00
14.00
16.00
18.00
20.00
22.00
24.00
4.00
4.00
4.00
4.00
4.00
4.00
4.00
54.00
59.50
64.00
67.50
70.00
71.50
72.00
7.00
8.00
9.00
10.00
14.00
12.00
10.00
8.00
98.00
96.00
90.00
80.00
0.00
28.00
32.00
36.00
40.00
4.00
4.00
4.00
4.00
70.00
64.00
54.00
40.00
44.00
4.00
22.00
11.00 6.00
66.00
Competitive Solution
We set price (p) equal to marginal cost (MC)
MC  4  p
Notice that MC doesn’t depend on qi or Q
If we substitute p = 4 in the demand equation we obtain
1
Q  q1  q2  14  p
2
1
 14  (4)
2
 14 2
 12
Profits will be zero
Zucchini Market
Competition
30
$ 25
Demand/P
20
15
10
5
0
MC
0
2
4
6
8
10
12
14
Quantity
16
Cooperative (collusive) oligopoly solution
If the two firms in this market were to coordinate
their actions and maximize joint profit,
they would choose the monopoly output and price
Such cooperative agreements are called cartels
The two firms together would produce 6 units
and charge a price of $16.00
The division of the output between the firms
would have to negotiated between them
Noncooperative Oligopoly
Joint profits maximized with Q = 6 and p = $16
Will this outcome occur?
Individual firm conjectures and market equilibrium
Conjecture
A supposition or guess
Each firm makes a conjecture about the action
of the other firm and then chooses its own action
Story
Firm 1 conjectures that Firm 2 will produce 3 units
Why?
Inverse demand given the conjecture
p  28 2q1 2q2
 28 2q1 (2)(3)
 22 2q1
Revenue for Firm 1 given the conjecture
Revenue ( q1 , q2)  pq1
 (22 2q1 ) q1

2
22q1 2q1
Marginal revenue is given by
MR (q1)  22 4q1
because
p  22 2q1
If we set marginal revenue equal to marginal cost
we can obtain the optimal level of q1
MR (q1)  22 4q1  4  MC (q1 )
 18  4q1
 4.5  q1
If Firm 2 produced 3 units, price would be
p  28 2q1 2q2
 28 (2)(4.5) (2)(3)
 28 9 6
 13
Profit for Firm 1 is given by revenue minus cost or
Profit  π  R C
 pq1 c (q1 )
 (13)(4.5) (4)(4.5)
 58.5 18
 40.5
Profit for Firm 2 is given by
Profit  pq2 c (q2 )
 (13)(3) (4)(3)
 39 12
 27
Total profit for the two firms is $67.50
Monopoly profit was $72
Is Firm 2 happy?
Is Firm 2 content?
Is Firm 2 going to keep producing 3 units?
Let’s See
Suppose Firm 2 conjectures that
Firm 1 will produce 4.5 units
Inverse demand given the conjecture
p  28 2q1 2q2
 28 2(4.5) (2)q2
 19 2q2
Marginal revenue is given by
MR (q2)  19 4q2
because
p  19 2q2
If we set marginal revenue equal to marginal cost
we can obtain the optimal level of q2
MR (q2)  19 4q2  4  MC (q2 )
 15  4q2
 3.75  q2
If Firm 1 produces 4.5 units and Firm 2
produces 3.75 units, price will be
p  28 2q1 2q2
 28 (2)(4.5) (2)(3.75)
 28 9 7.5
 11.5
Profit for Firm 1 is given by
Profit  p q1 c (q1 )
 (11.5)(4.5) (4) (4.5)
 51.75 18
 33.75
Profit for Firm 2 is given by
Profit  pq2 c (q2 )
 (11.5) (3.75) (4) (3.75)
 (7.5) (3.75)
 28.125
Total profit for the two firms is $61.875
Monopoly profit was $72
Because Firm 2 is producing 3.75 and not 3 units
Firm 1 will want to adjust its output level
And then Firm 2 will want to change its output
This silly game could go on forever
We can compute the best response for each firm
given the action of the other firm to see this
Other q
3.00
3.25
3.50
3.75
4.00
4.25
4.50
4.75
5.00
q1*
4.500
4.375
4.250
4.125
4.000
3.875
3.750
3.625
3.500
q2
4.500
4.375
4.250
4.125
4.000
3.875
3.750
3.625
3.500
What if Firm 1 conjectures that
Firm 2 will bring 4 units to market?
Other q
3.75
4.00
4.25
4.50
q1*
4.125
4.000
3.875
3.750
q2
4.125
4.000
3.875
3.750
Firm 1 will bring 4 units to market!
What if Firm 2 conjectures that
Firm 1 will bring 4 units to market?
Other q
3.75
4.00
4.25
4.50
q1*
4.125
4.000
3.875
3.750
q2
4.125
4.000
3.875
3.750
Firm 2 will bring 4 units to market!
Both firms are happy and content
We have an equilibrium!!
Graphically
Zucchini Market
Response Functions
14
q1 12
q 1*
10
8
q 2*
6
4
2
0
0
2
4
6
8
10
12
q2
14
16
A situation in which all economic actors (firms)
interacting with one another choose their
best strategy, given the strategies that all other actors
have chosen, is called a Nash Equilibrium
A market outcome is a Nash Equilibrium if no firm
would find it beneficial to deviate from its output level
provided that all other firms do not deviate from their
output levels at this market outcome
The market outcome of this noncooperative
oligopoly market is an output of 8 units
with a price of $12.00.
The output is lower than the competitive
output but higher than the monopoly output
The price is lower than the monopoly price
but higher than the competitive one
This is a result that holds generally
Results
Total Firm 1 Firm 2
Q
q
q
Monopoly
6
6
-Perfect Competition
12 ?
?
Cooperative Oligopoly
6
?
?
Noncooperative Oligopoly 8
4
4
P
16
4
16
12
Total
B
$72
$0
$72
$64
Firm 1 Firm 2
B
B
$72
-$0
$0
?
?
$32
$32
Oligopoly and the number of firms
Small number of firms  large price impact of individual
Larger number of firms  less price impact
As the number of firms in an oligopoly rises,
the impact of any one firm on price falls
As numbers keep getting larger, firms start to act
more and more like price takers
The End