Generica Corporation is deciding how many resources to devote to a research and development project. The units of input are "laboratories" consisting of smart people in white coats and a proportional amount of lab apparatus. The probability of a successful invention depends on the number of laboratories (L) Generica sponsors to perform research. This is according to a Poisson (see your statistics textbook for details) process in which: Pr(successful invention) = 1-e^-L

a. What is the probability of being unsuccessful for a given L?

b. Write an expression for the expected sum of future profit for Generica if it successfully innovates this period (monopoly begins at t = 0).

c. What is the finite value to which this series converges?

d. Write the expected ex ante profit, i. e., prior to knowing whether a new invention occurs.

e. Write an expression for the marginal benefit of an extra laboratory. If f(x) = e^bx then delta f(x)/delta x = be^bx

f. Each laboratory has a (marginal) cost of 1. Write the condition that will hold when Generica is choosing the optimal number of laboratories.

g. Speculate about the effect that weaker patent enforcement would have on research and development in this model. Consider the likelihood that this affects the size of the innovators profit as well as the number of future competing R&D laboratories.