# If duopoly behavi

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 –

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

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