Question

7.5. Worker Effort (easy A worker can be Careful or Careless, efforts which generate mistakes with probabilities 0.25 and 0.75. His utility function is U = 100 10/w -x, where w is his wage and x takes the value 2 if he is careful, and 0 otherwise. Whether a mistake is made is contractible, but effort is not. Risk-neutral employers compete for the worker, and his output is worth 0 if a mistake is made and 20 otherwise. No computation is needed for any part of this problem 7 (a) Will the worker be paid anything if he makes a mistake? (b) Will the worker be paid more if he does not make a mistake? (c) How would the contract be affected if employers were also risk averse? (d) What would the contract look like if a third category, "slight mistake," with an output of 19, occurs with probability 0.1 after Careless effort and with probability zero after Careful effort?

Answer 1

a) The worker is risk averse, his wage should be even across states. Hence, the answer is 'yes'.

b) Careful effort is efficient and lack of mistakes is a good statistic for careful effort. Hence, the worker be paid more if he does not make a mistake.

c) If the employers were also risk averse,the workers should be less insured and perhaps should even be insuring the employer, hence the wage may vary more across states.

d) The contract would pay equal amounts whether or not a mistake was made.