You are the manager of a monopoly that faces a demand curve described by P = 63 − 5Q.Your costs are C = 10 + 3Q.The profit-maximizing price is:
A) 20.
B) 27.
C) 33.
D) 55.

Question

Quizplus · Accepted Answer

To find the profit-maximizing price for a monopoly, we first need to determine the marginal revenue (MR) and marginal cost (MC) and then set MR = MC. The demand curve is given by P = 63 - 5Q, and the cost function is C = 10 + 3Q.1. To find the MR, we need to find the derivative of the total revenue (TR), which is P*Q. Since P = 63 - 5Q, TR = (63 - 5Q)Q = 63Q - 5Q^2. The derivative of TR with respect to Q (which gives us MR) is d(TR)/dQ = 63 - 10Q.2. The MC is the derivative of the total cost (TC) with respect to Q, which is simply the coefficient of Q in the cost function, C = 10 + 3Q. So, MC = 3.Setting MR = MC to find the profit-maximizing quantity:63 - 10Q = 360 = 10QQ = 6Substitute Q = 6 back into the demand equation to find the price:P = 63 - 5*6 = 63 - 30 = 33Therefore, the profit-maximizing price is $33.

You Are the Manager of a Monopoly That Faces a Demand