Consider a government that wants to promote research on the cure for cancer. The government estimates the
Question:
Consider a government that wants to promote research on the cure for cancer. The government estimates the gains of curing cancer to be 100. The government also realizes that the probability of achieving the cure is directly related to the number of firms n doing research on this topic such that Prob(cure) = [(n)1/2]/25. At the same time, the cost of running a research lab is equal to 1 and therefore the total cost of investment will be proportional to the number of firms doing research and equal to n.
a) Find the number of firms n that maximize expected society welfare.
b) Now find the number of firms that will enter the industry (up to the point where expected profit equals zero) if, once the cure is obtained, the successful firm keeps all the 100 units of benefit through exploitation of a patent. Is the number of firms higher or lower than the optimal number you found in part a).
c) Assume now that the government wants to set a contest with prize Z for the firm achieving the cure for cancer. What Z will induce the optimal number of firms to do research?
Fundamentals of Thermal-Fluid Sciences
ISBN: 978-0078027680
5th edition
Authors: Yunus A. Cengel, Robert H. Turner, John M. Cimbala