New pharmaceuticals developed in the U.S. get patent protection from competition (a monopoly) that lasts 17 years. After the patent expires, other firms can enter the market and produce generic versions of the drug. However, the original firm still maintains exclusive rights to the brand name version of the drug. (For example, Tylenol is the brand name and acetaminophen is the name of the chemical compound that makes-up the well-known pain relief drug.) Although generic versions of drugs are required by the FDA to have the same efficacy of the branded versions, many consumers prefer to buy the original brand name drug because they perceive it to be of higher quality than generic substitutes. Often, the manufacturer of a brand name version will begin selling a generic version shortly before a patent expires in order to serve customers in both generic and brand name markets. The generic version of the drug is typically produced in the same plant and on the same production line as the brand name drug, but is sold with a different label. (Store brands such as CVS or Love=s are examples of generic labeling.)
You are the brand manager for Cigarex, a drug that controls the addiction to cigars, which is nearing the end of its patent protection. The brand name drug has the following demand curve: PB = 10,000 - 1.5 QB . The demand for the generic version is described as: PG = 6,000 - 4.5 QG . For the purposes of this problem, you can assume that the Abrand@ market and the Ageneric@ market consist of different groups of consumers. Both the generic and brand name versions of Cigarex are produced in the same factory with marginal cost equal to .25Q, where Q is the total quantity of Cigarex produced for both markets. That is, marginal cost = 0.25(QB + QG).
1. As brand manager, you have to decide the total production of Cigarex, the allocation of that quantity across the brand name and generic markets, and the sale price in each market. Compute the profit maximizing values of all these variables.