Each worker produces either a high output 1.2 or low output 0.8 after his employer takes the fair share. When a worker put effort in the production, the chance of high output is 0.6; when a worker shirks, the chance of high output is 0.4. The utility cost of effort is 1. Workers value their income according to the utility function u(c) = 100 ln (c). Workers are obviously risk averse. There is a value for an employer with a large number of workers to provide insurance against each worker's idiosyncratic productivity risks. The employer can do so by offering its workers a wage that only partially depends on their performance. If an employer decides to do so, he must consider the moral hazard problem such insurance may incur.
1) without insurance from his employer, would a worker work or shirk?
(I think a worker will shirk because he does not have an incentive to work hard if insurance, which partially reflects his productivity, is not provided by employer.)
2) suppose the employer can observe workers' effort without any cost. Competition amount employers will drive the wage to its actuarially fair level. What is the actuarially fair wage for a hardworking worker? What is the actuarially fair wage for a shirker?
(don't have a clue..)