Smith & Co., a well-known producer of hand tools, wishes to hire a researcher to speed the development of the next generation of left-handed screwdrivers. If the researcher works hard, there is an 80% chance that she will make the crucial breakthrough and allow her firm to earn $50,000 in revenues and only a 20% chance that she'll make no breakthrough and earn the firm no additional revenue. If the researcher shirks her duties, there is only a 30% chance that she'll be able to make the breakthrough.

a) If researchers can earn $20,000 in other jobs, what contract should Smith & Co. offer to a researcher? Assume that the hard effort by a researcher is equivalent to a cost of $10,000 and shirking is equivalent to a cost of $0. Also assume that Smith & Co. cannot observe the effort level of the researcher and that there is no cost of effort in the other jobs.

b) If researchers can earn $45,000 in other jobs, what is the optimal contract that Smith & Co. should offer?

c) What is the maximum amount that researchers can earn in outside jobs such that Smith & Co. would still find it profitable to hire a researcher?