Question

Consider a single firm producing an allergy medication under patent. (You can think of the quantity of allergy medication in terms of bottles of medication). The demand for allergy medication is given by ?? = 100 ? 0.1????. The marginal cost of producing allergy medication is given by ???? = 5 + 0.3???? .

a. Graphically illustrate the profit maximizing quantity of allergy medication and the price the firm charges. Though you do not have an equation, draw in an average cost curve for the monopolist in your graph.

b. Label profit in your graph. In the graph you’ve drawn, is the monopolist earning positive economic profit? Does this tell you whether the monopoly is operating in the long run or the short run?

c. Calculate and label the allocative efficient quantity of allergy medication in your graph.

d. Does the monopolist charge a markup above marginal cost? If so, calculate the size of the markup.

Answer 1

We need to find Marginal revenue. From demand function, TR = PQ

= (100 - 0.1Q)Q

= 100 - 0.1Q^2

Now marginal revenue = dTR/dQ = 100 - 0.2Q

For a monopoly that has patent, MR = MC

100 - 0.2Q = 5 + 0.3Q

95 = 0.5Q

Qm = 190

Pm = $81 per unit

We are not given any average total cost but from the theory of a monopoly that has patent we assume that this monopoly has a lower average total cost than the price and so it earns a profit. These are short run economic profits and short run is the period vaild before the expiry of the patent

c. The allocative efficient quantity of allergy medication is the one where P = MC. This occurs when

100 - 0.1Q = 5 + 0.3Q

95 = 0.4Q

Q = 237.5. Here efficient price = MC = 5 + 0.3*237.5 = 76.25

d. Does the monopolist charge a markup above marginal cost? If so, calculate the size of the markup.

Mark up = P - MC/P = (81 - 62)/62 = 30.64%. (MC can be found by placing Q = 190 in MC function, MC = 5 + 190*0.3 = $62).