Question

If duopoly behaviour is one that is described by Cournot, the market demand curve is given by the equation q = 200 − 4p and both the firms have zero costs, find the quantity supplied by each firm in equilibrium and the equilibrium market price.

Answer 1

Market demand curve

Q = 200 − 4p

When the demand curve is a straight line and total cost is zero, the duopolist finds it most profitable to supply half of the maximum demand of a good.

At P = Rs 0, market demand is

Q = 200 − 4 (0)

= 200 units

If firm B does not produce anything, then the market demand faced by firm A is 200 units.

∴ The supply of firm A = units

In the next round, the portion of market demand faced by firm B is = 100 units

∴ Firm B would supply = 50 units

Thus, firm B has changed its supply from zero to 50 units. To this firm A would react accordingly and the demand faced by firm A will be

= 200 − 50

= 150 units

∴ Firm A would supply =

The quantity supplied by firm A and firm B is represented in the table below.

Round	Firm	Quantity Supplied
1	B	0
2	A
3	B
4	A
5	B

Therefore, the equilibrium output supplied by firm A

Similarly, the equilibrium output supplied by firm B = units.

Market Supply = Supply by firm A + Supply by firm B

Equilibrium output or Market Supply = Q = units — (1)

For equilibrium price

Q = 200 − 4p

4p = 200 − Q

p = Rs

Therefore, the equilibrium output (total) is units and equilibrium price is Rs .