Suppose P = 20 − 2Q is the market demand function for a local monopoly.The marginal cost is 2Q.The local monopoly tries to maximize its profits by equating MC = MR and charging a uniform price.What will be the equilibrium price and output?
A) $6.33, 3.33 units
B) $6.33, 5 units
C) $13.33, 3.33 units
D) $10, 5 units

Question

Quizplus · Accepted Answer

To find the equilibrium price and output, we need to equate MC = MR:
MC = 2Q
MR = P + dP/dQ * Q
dP/dQ = -2 (since P = 20 - 2Q, the derivative of P with respect to Q is -2)
MR = 20 - 4Q
Equating MC and MR, we get:
2Q = 20 - 4Q
6Q = 20
Q = 3.33
Substituting Q back into the demand equation, we get:
P = 20 - 2(3.33)
P = $13.33
Therefore, the equilibrium price and output are $13.33 and 3.33 units respectively. Therefore, the correct choice is C.

Suppose P = 20 − 2Q Is the Market Demand