Price controls and induced innovation. Suppose that drugs can be assigned a value W from 0 to 100 that indicating the quality of the drug. For example, a drug with W = 1 is basically useless, while a drug with W: 99 is a life-changing cancer treatment. In general, suppose the annual demand for drugi in the country is as follows: Qt : Wt _ Pi where WI. is the quality of drug 1' and PI. is its price. (a) Assume that a company has a one-year patent on drug j with quality W}. What is the profitmaximizing price PJ that the company will charge if it is free to choose its own price, as a function of quality? Assume that the marginal cost of producing the drug is zero. (b) How much profit does the company make on the drug in its one-year patent period as a function of \"G? (c) Suppose the drug discovery process at Consolidated Drug Co. works as follows: ConDrugCo 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 1 Wk: 1-\": where Ik is the amount of money invested in drug it. Assume the firm can only make profits during its oneyear patent period. Find the profit maximizing investment 1" that ConDrugCo will make on each drug. Also compute the associated profit maximizing quality level. (d) Now suppose that the government implements a price control because the impoverished citizens 0 not have access to the best medicines. The National Drug Council rules that any drug with W. > 50 must be made available for only $25 per unit. What IS the optimal investment for ConDrugCo 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 the citizens enjoy on this drug due to the price controls compared to the unrestrained monopoly pricing regime? Feel free to draw a graph to answer the question. (f) Briey discuss the costs and benefits of any price control initiative like this