Suppose that drugs can be assigned a value W from 0 to 100 that indicates their quality.
Question:
Suppose that drugs can be assigned a value W from 0 to 100 that indicates their quality. Perhaps a drug with W = 1 is a hangnail medication that barely works, while a drug with W = 99 is a life-saving cancer treatment. In general, suppose the annual demand for drug i in the nation of Pcoria is
where Wi is the quality of drug i and Pi is its price.
a. Assume that a company has a one-year patent on drug j with quality Wj. What is the profit-maximizing price Pj that the company will charge if it is free to choose its own price, as a function of quality? Assume that the drug costs nothing to manufacture.
b. How much profit does the company make on the drug in its one-year patent period as a function of Wj?
c. Suppose the drug discovery process at Drugs-R-Us Inc. works as follows: Drugs-RUs decides to invest a certain amount of money Ik in creating a new drug k, and the new drug is likely to have higher quality Wk if the company invests more money.
Assume for all new drugs that
where Ik is the amount of money invested in drug k. Assume the firm can only make profits during its one-year patent period. Find the profit-maximizing investment I*
that Drugs-R-Us will make on each drug.
d. Now suppose that Pcoria implements a price control because the impoverished citizens of Pcoria do not have access to the best medicines. The Supreme Pcoria Drug Council rules that any drug with Wi > 50 must be made available for only $25 per unit.What is the optimal investment for Drugs-R-Us under these rules? What happens to average drug quality as a result?
e. Suppose that there was a blockbuster drug with W = 100 already in existence before the price controls. How much extra consumer surplus do Pcorians enjoy on this drug due to the price controls compared with the unrestrained monopoly pricing regime? Answer this question graphically.
f. What are the costs and benefits of any price control initiative like this? Why might it matter if other nations have citizens with the same ailments that the Pcorians have?
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