If the demand facing a monopolist is P = 100 ? 10Q and marginal cost is constant at 20, then the profit maximizing price and quantity for this monopolist are:
A)P = 60 and Q = 4
B)P = 20 and Q = 8
C)P = 90 and Q = 10
D)P = 4 and Q = 60

Question

Quizplus · Accepted Answer

To find the profit-maximizing price and quantity for a monopolist, we first need to determine the marginal revenue (MR) and set it equal to the marginal cost (MC). The demand function is P = 100 - 10Q. To find MR, we differentiate the total revenue (TR = P*Q) with respect to Q. Since P = 100 - 10Q, TR = (100 - 10Q)Q = 100Q - 10Q^2. Differentiating TR with respect to Q gives MR = 100 - 20Q. Setting MR equal to MC (which is constant at 20) and solving for Q gives: 100 - 20Q = 20, which simplifies to 80 = 20Q, so Q = 4. Substituting Q = 4 into the demand equation to find P gives P = 100 - 10(4) = 60. Therefore, the profit-maximizing price and quantity are P = 60 and Q = 4.

If the Demand Facing a Monopolist Is P = 100