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Moral Hazard. Jerry has some non-wage income $20,000 and a job that pays $50,000 if he can manage to keep the job. If Jerry chooses a high level of effort, he will lose his job with probability p = 0.1. If Jerry chooses a low level of effort, he will lose his job with probability p = 0.5. Low effort is costless, but high effort costs Jerry $10,000. Jerry's expected utility follows EU = (1 - p) square root Cg + p square root Cb where Cg represents Jerry's consumption if he keeps his job and Cb represents Jerry's consumption if he loses his job.
a) Suppose there is no insurance. What is Jerry's expected utility from choosing low effort? What about from choosing high effort? Will Jerry choose low or high effort?
b) Suppose that the government provides free unemployment insurance, so that Jerry gets $30,000 if he loses his job. Will Jerry choose high or low effort now?
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