Exercise 1 - Moral Hazard Problem with Uncertainty A rm is trying to incentivize a worker to put in effort. It is risk-neutral. A worker can put in low effort at zero cost and high effort with a cost of 10,000 (opportunity cost). Her outside option is 4,000 and she is risk-neutral too. The rm's sales depend both on the effort the worker exerts and random luck (for example, demand shocks). Sales are as follows where bad and good luck each occur 50% of the time. Bad Luck Good Luck Low effort $10,000 $20,000 High effort $20,000 $40,000 Consider rst what happens if the rm simply offers a at wage of 12,000. That is, the wage does not depend on the rm's sales. a) In equilibrium, find if the worker will accept the contract and if she will put in high effort. b) Calculate the expected prot of the rm Suppose the rm can now observe effort. It can then induce high effort by paying a higher wage if the worker exerts effort. Suppose the rm offers a wage of 0 for low effort and 14,000 for high effort. c) In equilibrium, nd if the worker will accept the new contract and if she will put in high effort. d) Calculate the expected prot of the rm Finally, suppose the rm can only condition on sales. Note rst that sales don't directly reveal effort because if sales are 20,000, it could be due to low effort/ good luck or high effort/bad luck. Suppose the rm offers no wage, but a bonus of 0 if sales are 0 or 20,000, but 28,000 if sales are 40,000 e) Find if the worker will accept this contract and if she will put in high effort f) Calculate the expected prot of the rm