Suppose the market demand curve is given by $P = 100 - 2 Q$. If one Cournot duopolist produces $Q _ { 1 } = 10$, the residual demand curve faced by the other Cournot duopolist is:
A) $P = 90 - 2 Q _ { 2 }$.
B) $P = 80 - 2 Q _ { 2 }$.
C) $Q _ { 2 } = 80 - P$.
D) $Q _ { 2 } = 80 - 2 P$.

Question

Quizplus · Accepted Answer

When the first firm produces 10 units, the total industry quantity is 10+Q2. Plugging this quantity into the demand function, we get P = 100 - 2(10+Q2) = 80 - 2Q2. Hence, the residual demand curve faced by the second duopolist is P=80-2Q2. When one Cournot firm produces $Q _ { 1 } = 10$, the market demand curve for the remaining firm becomes:

$Q _ { 2 } = \frac { 1 } { 2 } ( 100 - P ) - 10$

Solving for $P$ yields:

$P = 80 - 2 Q _ { 2 }$

Therefore, the correct answer is (B).

Suppose the Market Demand Curve Is Given By P=100−2QP = 100 - 2 QP=100−2Q

Suppose the Market Demand Curve Is Given By $P = 100 - 2 Q$