the inverse demand in a Cournot dupoly is P=a-b(Q1+Q2) and costs are c1(Q1)=c1Q1

Question

the inverse demand in a Cournot dupoly is P=a-b(Q1+Q2) and costs are c1(Q1)=c1Q1,and C2(Q2)=c2Q2. The government has imposed a per unit tax of $t on each unit sold by each firm. The tax revue is ?

a. t times the total output of the 2 firms should ther be no sale tax

b. less than t times the total output of the 2 firms should there be no sale tax

c. greater than t times the total output of the 2 firms should there be no sale tax

d. none of the above.

I initially answered (d). The problem does not tell how many unit sold.

Explanation / Answer

The concept of Cournot dupoly is that the total market demand is equal to the quantity supplied by all firms. The market price is set to satisfy such equality.

Here $t has to be multiplied with the aggregate of supplied units to get the amount of tax revenue. Therefore, the tax revenue is t times the total output.

Answer: The right answer is ‘a’.

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