You are the manager of a monopoly, and your demand and cost functions are given

Question

You are the manager of a monopoly, and your demand and cost functions are given by P = 300 - 3Q and C(Q) = 1,500 + 2Q^2, 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-quantity combination? What price-quantity combination maximizes revenue? Calculate the maximum revenues. Is demand elastic, inelastic, or unit elastic at the revenue-maximizing price-quantity combination?

Explanation / Answer

a. Equating MR with MC of the monopolist -

MR = 300 - 6Q

MC = 4 Q

So, Q = 30 units , P = 300 - 3 * 30 = $210

b. Total revenue at Q = 30 = 300 * 30 - 3 * 30 * 30 = 6300

Total Cost = $3300

Profits = Total Revenue - Total Cost = $3000

c. Monopolist lies on the elastic portion of the demand curve when he maximizes profit.

d. Total revenue = Price * Quantity = 300 Q - 3 Q2

Differentiating it with respect to Q and eqauting to zero, we get, 300 - 6 Q = 0 . Q = 50 units, Price = 300 - 3 * 50 = $150

e.Maximum revenue = 300 * 50 - 3 * 50 *50 = 15000 - 7500 = $7500

f. Demand is elastic.

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