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.
Given – Market demand curve
Q = 200 - 4p
When the demand curve is a straight line and total cost is zero, the duopolistic 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. Therefore, The supply of firm A = 100 units
In the next round, the portion of market demand faced by firm B is =200 - 100 = 100 units. Therefore, 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
Therefore, Firm A would supply = =75 units.
The quantity supplied by firm A and firm B is represented in the table below –
Round | Firm | Quantity Supplied |
1 | B | 0 |
2 | A | 1/2 of 200 = 100 |
3 | B | 1/2 (200 – 100) = 50 |
4 | A | 1/2 (200 – 50 ) = 75 |
5 | B | 1/2 (200 – 75 ) = 62.5 |
Therefore, the equilibrium output supplied by firm A = 200/3 units = the equilibrium output supplied by firm B
Market Supply = 200/3 + 200/3 = 400/3 units
For equilibrium price
q = 200 - 4p
4p = 200 – q
P = 50 – q/4
P = 50 – (400/3) /4
P = 50 – 400/12 = 16.67