UNIT 11 COLLUSIVE OLIGOPOLY
Structure
11.0 Objectives
11.1 Introduction
11.2 Collusive Oligopoly
11.2.1 Cartel
11.2.2 Mergers
11.2.3 Price Leadership
11.2.4 Basing-point Price System
11.3 Let Us Sum Up
11.4 Key Words
11.5 Some Useful Books
11.6 Answers or Hints to Check Your Progress
11.7 Exercises
11.0 OBJECTIVES
After going through this unit, you will be able to:
• understand the collusive oligopolistic market structure; and
• evaluate the prices and output determination in such markets.
11.1 INTRODUCTION
In the case of collusive oligopoly the competing firms collude in order to
reduce the uncertainties cropping out of the inherent rivalries among them.
The colluding firms are usually bound by agreements whereby they seek to
maximise the joint profit of the group. OPEC is an example of such type of
collusion. In the following discussion, we would analyse the behaviour of
firm by considering ― Cartels, Mergers, Price Leadership and Basing-point
Price System.
11.2 COLLUSIVE OLIGOPOLY
11.2.1 Cartels
Mainly, cartels are formed among the firms due to the uncertainty arising out
of mutual interdependence. Typically, there can be two types of cartels, viz.,
a) cartels aiming at joint profit maximisation
b) cartels aiming at the sharing of markets
a) Cartels Aiming at Joint Profit Maximisation
Often cartels are formed for maximising the industry profit. The situation is
similar to that of a multi-plant monopolist. Generally, the firms appoint a
central agent to which they delegate the authority to decide the total quantity
to be produced and the price to be charge, to maximise the joint profit. It is the
central agency, which allocates the output to be produced among the firms,
and it distributes the joint profit. To be able to do this, the central agency must
have an access to the cost conditions of the firms. This knowledge is crucial as
allocation and distribution depend crucially on them.
24
,To analyse let us consider two profit maximising firms A and B forming a Collusive Oligopoly
cartel for joint profit maximisation. The cost conditions are represented in
terms of the marginal and average cost curves (MC and AC respectively).
Based on the individual MC curves of the two firms, we derive the aggregate
MC curve (AMC) as the horizontal summation of MC1 and MC2. Given the
market demand curve (DD1), by equating MR with AMC, we can derive the
industry output and the corresponding industry price as shown in Figure 11.1.
Fig. 11.1: Distribution of Output Among Firms
The individual output of each firm is obtained by drawing a line through the
point E (where MR = AMC) and extending it back to the two adjoining
figures whereby we get MC1 = MC2 = AMC = MR. Dropping perpendiculars
from the point of intersection of the line MC1 = MC2 = AMC = MR we get the
output to be produced by each firm.
We find that the firm having the flatter MC, implying lesser per unit cost,
produces the more output. But this by no way means that the firm with the
flatter MC or the least cost gets a bigger share of the profit of the cartel.
Drawbacks in Cartels
There might arise situations when the joint profit maximisation of the firm
may not be achieved. The main reasons could be the following:
1) Mistakes in the estimation of the market demand.
2) Mistakes in the estimation of the MC
3) Slow process of cartel negotiations
4) ‘Stickiness’ of the negotiated price
5) ‘Bluffing’ nature of the members
6) Existence of high-cost firm
7) Government interference
Mathematical Representation of Cartel Equilibrium
Supposing there are two firms in the market, joint profit maximisation implies
that the firms maximise their respective profits i.e., maximise Π = П1 + П2.
Let P = f(X) = f(X1 + X2) be the demand function and
C1 = f1(X1) and C2 = f2 (X2) be the cost functions of the two firms. Then,
П1 = R1 - C1 and П2 = R2 – C2.
Therefore, П = П1 + П2 = R1 - C1 + R2 – C2 = R – C1 – C2
25
, Price and Output The first order condition for profit maximisation requires that we differentiate
Determination-II
П with respect to X1 and X2 separately and set the derivatives equal to zero.
So,
∂П/∂X1 = ∂R/∂X1 – ∂C1/∂X1= 0 and
∂П/∂X2 = ∂R/∂X2 – ∂C2/∂X2= 0
From the above equations, the optimality condition is,
MR = MC1 = MC2
That is, at the optimum, the marginal costs from each plant must be equal and
such equality should again be equal to the marginal revenue. Otherwise, the
firms would still have some incentive to reshuffle the level of output
production from each plant.
The second order condition for joint profit maximisation requires that,
∂2R/∂X2 < ∂2C1/∂X21 and ∂2R/∂X2 < ∂2C2/∂X22
This implies that for each plant, it should be such that once the profit
maximising output level has been reached, any additional unit of output would
have the MR falling at a faster rate than MC.
A Numerical Example
The market demand function P = 100 – 0.5(X) = 100 – 0.5(X1 + X2)
The cost functions of the two firms are C1 = 5X1 and C2 = 0.5X22. Then
the total profit of the colluding firms is given by
П = П1 + П2
= P (X1 + X2) – C1 – C2
= [100 – 0.5(X1 + X2)] (X1 + X2) – 5X1 – 0.5 X22
= 95 X1 – 100X2 – 0.5 X21 – X22 – X1X2
The first order condition for profit maximisation requires that,
∂П/ ∂X1 = 95 – X1 – X2 = 0
∂П/ ∂X2 = 100 – X1 –2X2 = 0
Solving for X1 and X2 we get, X1 = 90 and X2 = 5
From the demand function, we get P = 100 – 0.5(X1 + X2) = 52.5
The maximum joint profit obtained is given by,
П = PX1 - C1 + PX2 – C2 = 52.5(90+5) – 5(90) - 0.5(5)2 = 4525
b) Market Sharing Cartels
This form of collusion is more popular. Here the firms agree to share the
market but at the same time maintain a considerable degree of freedom
regarding product differentiation, selling activities and other business
decisions. There are two basic methods of sharing the market:(1) Non-price
competition and (2) Quota system
1) Non-price competition
In this form of a ‘loose’ cartel, the member firms agree on a common
price, at which each of them can sell any quantity demanded. The price is
set by the process of bargaining, with the low-cost firms pressing for a
lower price and the high-cost ones for a higher price. The agreed price
26 must be such as to allow some profits to all the members. The firms agree
Structure
11.0 Objectives
11.1 Introduction
11.2 Collusive Oligopoly
11.2.1 Cartel
11.2.2 Mergers
11.2.3 Price Leadership
11.2.4 Basing-point Price System
11.3 Let Us Sum Up
11.4 Key Words
11.5 Some Useful Books
11.6 Answers or Hints to Check Your Progress
11.7 Exercises
11.0 OBJECTIVES
After going through this unit, you will be able to:
• understand the collusive oligopolistic market structure; and
• evaluate the prices and output determination in such markets.
11.1 INTRODUCTION
In the case of collusive oligopoly the competing firms collude in order to
reduce the uncertainties cropping out of the inherent rivalries among them.
The colluding firms are usually bound by agreements whereby they seek to
maximise the joint profit of the group. OPEC is an example of such type of
collusion. In the following discussion, we would analyse the behaviour of
firm by considering ― Cartels, Mergers, Price Leadership and Basing-point
Price System.
11.2 COLLUSIVE OLIGOPOLY
11.2.1 Cartels
Mainly, cartels are formed among the firms due to the uncertainty arising out
of mutual interdependence. Typically, there can be two types of cartels, viz.,
a) cartels aiming at joint profit maximisation
b) cartels aiming at the sharing of markets
a) Cartels Aiming at Joint Profit Maximisation
Often cartels are formed for maximising the industry profit. The situation is
similar to that of a multi-plant monopolist. Generally, the firms appoint a
central agent to which they delegate the authority to decide the total quantity
to be produced and the price to be charge, to maximise the joint profit. It is the
central agency, which allocates the output to be produced among the firms,
and it distributes the joint profit. To be able to do this, the central agency must
have an access to the cost conditions of the firms. This knowledge is crucial as
allocation and distribution depend crucially on them.
24
,To analyse let us consider two profit maximising firms A and B forming a Collusive Oligopoly
cartel for joint profit maximisation. The cost conditions are represented in
terms of the marginal and average cost curves (MC and AC respectively).
Based on the individual MC curves of the two firms, we derive the aggregate
MC curve (AMC) as the horizontal summation of MC1 and MC2. Given the
market demand curve (DD1), by equating MR with AMC, we can derive the
industry output and the corresponding industry price as shown in Figure 11.1.
Fig. 11.1: Distribution of Output Among Firms
The individual output of each firm is obtained by drawing a line through the
point E (where MR = AMC) and extending it back to the two adjoining
figures whereby we get MC1 = MC2 = AMC = MR. Dropping perpendiculars
from the point of intersection of the line MC1 = MC2 = AMC = MR we get the
output to be produced by each firm.
We find that the firm having the flatter MC, implying lesser per unit cost,
produces the more output. But this by no way means that the firm with the
flatter MC or the least cost gets a bigger share of the profit of the cartel.
Drawbacks in Cartels
There might arise situations when the joint profit maximisation of the firm
may not be achieved. The main reasons could be the following:
1) Mistakes in the estimation of the market demand.
2) Mistakes in the estimation of the MC
3) Slow process of cartel negotiations
4) ‘Stickiness’ of the negotiated price
5) ‘Bluffing’ nature of the members
6) Existence of high-cost firm
7) Government interference
Mathematical Representation of Cartel Equilibrium
Supposing there are two firms in the market, joint profit maximisation implies
that the firms maximise their respective profits i.e., maximise Π = П1 + П2.
Let P = f(X) = f(X1 + X2) be the demand function and
C1 = f1(X1) and C2 = f2 (X2) be the cost functions of the two firms. Then,
П1 = R1 - C1 and П2 = R2 – C2.
Therefore, П = П1 + П2 = R1 - C1 + R2 – C2 = R – C1 – C2
25
, Price and Output The first order condition for profit maximisation requires that we differentiate
Determination-II
П with respect to X1 and X2 separately and set the derivatives equal to zero.
So,
∂П/∂X1 = ∂R/∂X1 – ∂C1/∂X1= 0 and
∂П/∂X2 = ∂R/∂X2 – ∂C2/∂X2= 0
From the above equations, the optimality condition is,
MR = MC1 = MC2
That is, at the optimum, the marginal costs from each plant must be equal and
such equality should again be equal to the marginal revenue. Otherwise, the
firms would still have some incentive to reshuffle the level of output
production from each plant.
The second order condition for joint profit maximisation requires that,
∂2R/∂X2 < ∂2C1/∂X21 and ∂2R/∂X2 < ∂2C2/∂X22
This implies that for each plant, it should be such that once the profit
maximising output level has been reached, any additional unit of output would
have the MR falling at a faster rate than MC.
A Numerical Example
The market demand function P = 100 – 0.5(X) = 100 – 0.5(X1 + X2)
The cost functions of the two firms are C1 = 5X1 and C2 = 0.5X22. Then
the total profit of the colluding firms is given by
П = П1 + П2
= P (X1 + X2) – C1 – C2
= [100 – 0.5(X1 + X2)] (X1 + X2) – 5X1 – 0.5 X22
= 95 X1 – 100X2 – 0.5 X21 – X22 – X1X2
The first order condition for profit maximisation requires that,
∂П/ ∂X1 = 95 – X1 – X2 = 0
∂П/ ∂X2 = 100 – X1 –2X2 = 0
Solving for X1 and X2 we get, X1 = 90 and X2 = 5
From the demand function, we get P = 100 – 0.5(X1 + X2) = 52.5
The maximum joint profit obtained is given by,
П = PX1 - C1 + PX2 – C2 = 52.5(90+5) – 5(90) - 0.5(5)2 = 4525
b) Market Sharing Cartels
This form of collusion is more popular. Here the firms agree to share the
market but at the same time maintain a considerable degree of freedom
regarding product differentiation, selling activities and other business
decisions. There are two basic methods of sharing the market:(1) Non-price
competition and (2) Quota system
1) Non-price competition
In this form of a ‘loose’ cartel, the member firms agree on a common
price, at which each of them can sell any quantity demanded. The price is
set by the process of bargaining, with the low-cost firms pressing for a
lower price and the high-cost ones for a higher price. The agreed price
26 must be such as to allow some profits to all the members. The firms agree
