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Pharmaceutical Companies: Monopoly Over Production

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Suppose that a pharmaceutical company has a monopoly over the production of master cream, a drug used on skin rashes. Further suppose that the demand for master cream is given by the expression QD = 1,500 - P, where QD is the quantity demanded (in bottles) and P is the price. Assume that the company's costs are given by the expression
TC = 100 - Q^2 + 5Q^3.

a) What is the profit-maximizing level of output of master cream (in bottles)?
b) What is the profit-maximizing price?
c) What is the maximum level of profit?

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Solution Summary

This solution shows how to calculate the profit-maximizing quantity and price for a pharmaceutical company that has a monopoly over the production of a master cream. All the calculations are shown in detail.

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a) The profit-maximizing level of output is where Marginal Revenue (MR) = Marginal Cost (MC)

To find MR, first find Total Revenue (TR)
TR = PQ

Because the company is a monopoly, its ...

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