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.
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Answer:
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 .