Question

As before, a drug company has a monopoly on a new class of corticosteroid. The market demand is given by P = 210 - 0.003×Q. The monopolist's costs are described by TC = 3,000,000 + 3Q. The profit-maximizing price is? ___________

Answer 1

A profit maximizing monoply produces at the point where MR = MC and sets it's profit maximizing price at the point where the profit maximizing quantity lies on the demand curve.

The demand curve is given as, P = 210 - 0.003Q

Or, Multiplying both sides by Q we get,

PQ = TR = 210Q - 0.003Q²

Or, MR = d(TR)/dQ = 210 - 0.006Q

The TC equation is given as, TC = 3,000,000 + 3Q

Or, MC = d(TC)/dQ = 0+3 = 3

Now, setting MR = MC we get,

210 - 0.006Q = 3

Or, 0.006Q = 207

Or, Q = 34,500

Now from the demand equation we get, when Q = 34,500

P = 210 - (0.003 * 34,500) = 210 - 103.5 = 106.5

Therefore, the profit maximizing price is $106.5