## 8.6Solved Problem

### SOLVED PROBLEMPainkiller Pricing

When suffering from sore muscles, a headache, or a fever, many of us turn to the painkiller ibuprofen for relief. Until 1986, a British pharmaceutical company, Boots Laboratories, held the patent for ibuprofen, which it sold under the brand name Advil. Boots, then, had a monopoly on producing and selling the drug. At the time, a 100-tablet bottle of ibuprofen cost about \$5, which is equivalent to \$10 in today’s dollars. But, when the patent expired in 1986, generic drug manufacturers entered the market and the price of that 100-tablet bottle dropped below \$2.

The table below shows a hypothetical demand schedule for ibuprofen.

 Price Quantity of 100-tablet bottle (millions) \$20 0 18 1 16 2 14 3 12 4 10 5 8 6 6 7 4 8 2 9

Assuming that the marginal cost of producing a 100-tablet bottle of ibuprofen is \$2, calculate total revenue, marginal revenue, and the profit-maximizing price and quantity for a bottle of Advil before generic drug producers enter the market. Then, assuming a perfectly competitive industry, explain what happens to equilibrium price and quantity when generic drug producers enter the market.

STEP | 1 Construct a marginal revenue schedule to find Advil’s optimal price and quantity for producing bottles of ibuprofen.Review pages 239–242.

Total revenue is found by multiplying price and quantity (TR = P × Q). The marginal revenue is the change in total revenue divided by the change in quantity (MR = ΔTR/ΔQ). In the upcoming table, the total revenue for producing 1 million 100-tablet bottles is \$18 million or simply 1 million times \$18. The total revenue for 2 million bottles is \$32 million or 2 million times \$16. The marginal revenue from producing an extra million bottles, 2 million bottles, is (32 − 18)/(2 − 1) or \$14, the change in total revenue from producing an extra 1 million bottles, \$14 million, divided by the change in quantity or 1 million bottles.

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 Price Quantity of 100-tablet bottle (millions) Total Revenue (millions of dollars) TR = P × Q Marginal Revenue per 100- tablet bottles (dollars) MR = ΔTR/ΔQ \$20 0 \$0 \$18 18 1 18 14 16 2 32 10 14 3 42 6 12 4 48 2 10 5 50 −2 8 6 48 −6 6 7 42 −10 4 8 32 −14 2 9 18

STEP | 2 Determine the optimal price and quantity of bottles of ibuprofen to produce.Review pages 242–244.

A monopolist maximizes profit by producing the quantity where marginal revenue equals marginal cost. In this case, Advil has a marginal cost of \$2 per bottle. The purple shading in the table shows that marginal revenue is \$2 at a quantity of 5 million bottles. You can also verify that profit is highest, \$40 million, when price is set at \$10 per bottle and Advil manufactures 5 million bottles.

STEP | 3 Determine what happens to equilibrium price and quantity when generic drug manufacturers are allowed to enter the industry and produce ibuprofen.Review pages 246–247.

When the patent for ibuprofen expired, many firms began producing the drug, making the industry almost perfectly competitive—causing price to equal marginal cost. Looking at the area shaded green in the table, you can see that marginal cost, \$2, is equal to price at a quantity of 9 million bottles.