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 = 1/2 x 200 = 100 units
In the next round, the portion of market demand faced by firm B is 200 - 200/2 =200 - 100 = 100units
Therefore, Firm B would supply 1/2 x (200 - 200/2) = 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 - 1/2 x(200 - 200/2)
= 200 – 50 = 150 units
Therefore, Firm A would supply = 150/2 = 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 x 200 = 200/2 = 100 |
| 3 | B | 1/2 x [200 - 1/2 x 200] = 200/2 - 200/4 |
| 4 | A | 1/2 x [200 - 1/2(200 - 1/2 x 200)] = 200/2 - 200/4 + 200/8 |
| 5 | B | 1/2{200 - 1/2[200 - 1/2(200 - 1/2 x 200)]} = 200/2 - 200/4 + 200/8 - 200/16 |
Therefore, the equilibrium output supplied by firm A
= 200/2 - 200/4 + 200/8 - 200/16 + 200/32 + 200/64 + 200/128 + 200/256 + ...... = 200/3 units
Similarly, the equilibrium output supplied by firm B = 200/3 units.
Market Supply = Supply by firm A + Supply by firm B = 200/3 + 200/3
Equilibrium output or Market Supply = Q = 400/3 units ………………. (1)
For equilibrium price
Q = 200 - 4p
4p = 200 – Q
p = 50 - Q/4
p = 50 - 1/4(400/3) [from (1)]
p = 50 - 100/3
p = (150 - 100)/3
p = Rs 50/3
Therefore, the equilibrium output (total) is 400/3 units and equilibrium price is Rs 50/3.
