Suppose that the pharmaceutical rm Merck is deciding whether todevelop a new diagnostic procedure that can detect early-stageAlzheimer's disease more accurately than existing tests. Developingthis technology would require an up-front fixed cost FC > 0. IfMerck develops the technology, it can screen Q patients forAlzheimer's at the variable cost VC(Q) = 20Q. Merck estimates thatmarket demand for the procedure would be p(Q) = 80 - (1/10)Q
a. Suppose that other companies can quickly copy Merck'sprocedure as soon as it is developed so that the market for medicaltests will become perfectly competitive. If Merck develops theprocedure, what are the equilibrium price pc and quantity Qc? If FC= 5000, will Merck develop the procedure? What about if FC =10,000?
b. Now suppose that, if Merck develops the procedure, it willreceive a patent that allows it to operate as a uniform-pricingmonopolist. In this case, if Merck develops the procedure, how manypatients will it screen (Qm), and what will it charge (pm)? If FC =5000, will Merck develop the procedure? What about if FC =10,000?
c. Now suppose that, if Merck develops the procedure, it islegally permitted (and able) to engage in perfect pricediscrimination. If Merck develops the procedure, what are itsoptimal quantity Qppd , revenue R(Qppd ), and variable costsVC(Qppd )? If FC = 5000, will Merck develop the procedure? Whatabout if FC = 10,000?
d. Suppose that FC = 5000. Using your answers above, computeconsumer surplus, producer surplus, and total surplus under each ofthe following policies:
i. No patent protecting Merck's innovation (as in part a).
ii. A patent letting Merck operate as a uniform-pricingmonopolist (as in b).
iii. Legal permission for Merck to engage in perfect pricediscrimination (as in c).
(If Merck develops the procedure, make sure to subtract FC fromthe producer surplus.)
If we are trying to maximize total surplus, which of thesepolicies is best? If we are instead trying to maximize consumersurplus, which policy is best?
