Question

Can collusion between duopolists lead to a better outcome than if they were involved in quantity competition between themselves? Discuss, with diagrams and/or equations, the Cournot-Nash equilibrium with quantity competition under a duopoly, and compare with the cooperative solution. In this context, discuss the concepts of duopolists’ reaction functions and of their isoprofit curves.

Answer 1

Duopolists or Cournot equilibrium occurs when two firms compete on quantity. They tend to produce more than the monopoly output.

But once they cooperate , they will create monopoly market and output fall to level of monopoly. Or when they become cooperative, they create monopoly market.

Following is diagram:

In above diagram,

Reaction function of A and B firms have been given.

Counot equilibrium occurs where both reactions functions of both firm intersects each other.

If they cooperate, they tend to create monopoly.

Numerical example:

P = 120 -Q

MC = 0

Competitive output

P = MC

120 - Q = 0

Q = 120

Cournot output or duopolist output:

=(2/3) *Competitive output

= (2/3)*120

= 80 units'

P =120 - 80

=$ 40

Each firm produce 80 units

Cooperation and monopoly:

P = 120-Q

MC= 0

TR = 120Q- Q^2

MR = 120 - 2Q

MR = MC

120 - 2Q = 0

Q = 120 /2

= 60

Each firm will produce 30 units'

P = 120 -60

= 60