Question

1. The demand function in a duopoly is: P = 100 – 2(Q₁ + Q₂). If the first firm decides to sell 10 units while the second firm sells 20 units, which of the following will be true?

   		The second firm will earn twice as much revenue as the first firm.
   		The second firm will sell at a lower price than the first firm.
   		An increase in one firm’s output will not affect the other firm’s revenue.
   		The first firm will earn a higher profit than the second firm.
   		The market price will be determined by the second firm’s output which is larger than the first firm’s output.

Answer 1

The correct answer is (a) The second firm will earn twice as much revenue as the first firm.

Given that Firm 1 will produce 10 units => Q₁ = 10

Given that Firm 2 will produce 20 units => Q₂ = 20

Hence Market price = P = 100 – 2(Q₁ + Q₂) = 100 - 2(10 + 20)

= 40

Hence, Firm 1 Total Revenue = PQ₁ = 40*10 = 400

Firm 2 Revenue = PQ₂ = 40*20 = 800

Hence Firm 2 Revenue is twice of Firm 1 revenue and hence option (a) is correct.

Now Let see why others are incorrect.

Market Price will be same for both the firms and as calculated above Price = 40 and hence both firm will charge same price.

Hence option (b) is incorrect.

Increase in one firm output will result in increase in Q₁ + Q₂ and hence P = 100 – 2(Q₁ + Q₂) will decrease and hecne Revenue of other firm will decrease. Hence option (c) is incorrect

In order to calculate each firm's profit we need to know there cost functions and hence we cannot say about the profit . Hence with the given information option (d) is incorrect.

Market Price (P) = 100 – 2(Q₁ + Q₂), Hence market price is determined by total market output which includes Q₁ as well and hence Market price will be decided by both firms output. Hence Option (e) is incorrect.

Hence, the correct answer is (a) The second firm will earn twice as much revenue as the first firm.