The demand for health club services is Q = 100

Question

The demand for health club services is Q = 100 - 2P,and the marginal cost of providing these services is MC = -110 + 2Q.If a two-part tariff pricing system is used,what is the optimal price and quantity combination?
A) P = 18 and Q = 64.
B) P = 199 and Q = 52.
C) P = 26 and Q = 162.
D) P = 162 and Q = 26.
E) None of the above.

Quizplus · Accepted Answer

The optimal quantity is where MC = 0, so 0 = -110 + 2Q, giving Q = 55. Substituting Q = 55 into the demand equation gives P = 100 - 2(55) = 100 - 110 = -10, which is not feasible. Therefore, the closest feasible option is A, where P = 18 and Q = 64.