A profit-maximizing company has the chance to research the cure for the common cold (CCC). If it spends Z>1 on R&D, then it has probability p(Z) = 1-1/Z of discovering the CCC (and zero probability otherwise). Assume that the company has no other costs besides research costs, no other revenues other than those from selling the CCC if it discovers it. The present value (PV) of revenue from the CCC once discovered is > 5. Units for research costs, and CCC profits are millions of dollars.

(a) How much will the company spend on research as a function of ?

(b) What are the expected profits in terms of ? What happens if < 4?