6. You are the manager of a monopoly, and your demand and cost functions are
given by P = 480 - 8Q and C(Q) = 500 + 4Q2, respectively.
- What price-quantity combination maximizes your firm's profits
- Calculate the maximum profits.
- Is demand elastic, inelastic, or unit elastic at the profit-maximizing price
- What price-quantity combination maximizes revenue?
- Calculate the maximum revenues.
(a) R(Q) = PQ = (480 - 8Q)Q = 480Q - 8Q^2
Profit = R(Q) - C(Q) = 480Q - 8Q^2 - 500 - 4Q^2 = -12Q^2 + 480Q - 500
For maximum profit, the derivative of the profit function = 0
-24Q + 480 = 0
Therefore Q = 20
P = 480 - 8(20) ...
This solution shows all the steps for calculating a series of problems based on a companies demand and cost functions.