Question

Problem 3: 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) VC, + PVC where C, represents Jerry's consumption if he keeps his job and C, represents Jerry's con- sumption 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?

Answer 1

a)

In case of low effort

Probability of loosing a job=p=0.50

Consumption if there is a loss of job=Cb=$20000

Probability of not loosing a job=1-p=1-0.50=0.50

Consumption if there is no loss of job=Cg=20000+50000=$70000

E(U)= (1-P) Cg+PVC

E(U)= (1 – 0.50) 70000+ 0.50V20000 = 202.9982 utils

In case of high effort

Probability of loosing a job=p=0.10

Consumption if there is a loss of job=Cb=20000-10000=$10000

Probability of not loosing a job=1-p=1-0.10

Consumption if there is no loss of job=Cg=20000-10000+50000=$60000

E(U)= (1-P) Cg+PVC

E(U)= (1 – 0.10) V60000+ 0.10V10000 = 230.4541 utils

Expected Utility is higher in case of high effort. So, Jerry would choose high effort.

b)

In case of low effort

Probability of loosing a job=p=0.50

Consumption if there is a loss of job=Cb=20000+30000=$50000

Probability of not loosing a job=1-p=1-0.50

Consumption if there is no loss of job=Cg=20000+50000=$70000

E(U)= (1-P) Cg+PVC

E(U)= (1 – 0.50) 70000+ 0.50V50000 = 244.0910 utils

In case of high effort

Probability of loosing a job=p=0.10

Consumption if there is a loss of job=Cb=20000-10000+30000=$40000

Probability of not loosing a job=1-p=1-0.10

Consumption if there is no loss of job=Cg=20000-10000+50000=$60000

E(U)= (1-P) Cg+PVC

E(U)= (1 – 0.10) V60000+ 0.10V 40000 = 240.4541 utils

Expected Utility is higher in case of low effort. So, Jerry would choose low effort now.