Suppose that the demand curve for mineral water is given by p = 50 - 16q, where p is the price per bottle paid by consumers and q is the number of bottles purchased by consumers.Mineral water is supplied to consumers by a monopolistic distributor who buys from a monopolistic producer, who is able to produce mineral water at zero cost.The producer charges the distributor a price of c per bottle.Given his marginal cost of c per unit, the distributor chooses an output to maximize his own profits.Knowing that this is what the distributor will do, the producer sets his price c so as to maximize his revenue.The price paid by consumers under this arrangement is
A)$3.13.
B)$12.50.
C)$37.50.
D)$25.
E)$1.56.

Question

Quizplus · Accepted Answer

The monopolistic distributor maximizes profit by setting marginal revenue equal to marginal cost. The demand curve is p = 50 - 16q, so the marginal revenue curve is MR = 50 - 32q. Setting MR = c and solving for q gives q = (50 - c)/32. The producer maximizes revenue by setting c to maximize c*q, which leads to c = 25. Substituting c = 25 into the demand curve gives p = 50 - 16*(25/32) = 37.50.

Suppose That the Demand Curve for Mineral Water Is Given