Question

Assume a worker is likely to work 30 years. He is likely to find a job with constant wage level, alternatively, he can apply in a job where he works for one year at a lower, zero, or negative wage, but gets a higher wage if he is accepted to the long-term positions after that. (working a negative wage means, that actually the worker is paying in order to work in first year) Assume for first four section interest rate of the worker is 0.

1. What should be the probation wage if the long-term employment wage is 100000$ per year, the wage of the alternative job is 10000$, and the likelihood of being fired is 10%?
2. What should be the probation wage if the long-term employment wage is 20000$ per year, the wage of the alternative job is 10000$, and the likelihood of being fired is 10%?
3. What should be the probation wage if the long-term employment wage is 100000$ per year, the wage of the alternative job is 95000$, and the likelihood of being fired is 90%?
4. What should be the probation wage if the long-term employment wage is 100000$ per year, the wage of the alternative job is 10000$, and the likelihood of being fired is 99.9%?

Answer 1

a. Wage of the long term employment = $100000/ year and wage of the alternative job is = $10000/ year

Here long term employment term = Total years of work- probation period = 30-1=29

Total wage of the long term employment = 100000*29= $2900000

Total wage of alternative job = 10000*30= $300000

Therefore wage differential between two jobs = 2900000-300000= $2600000

Also probability rate of being fired = 10% i.e., probability rate of being not fired =90%

Therefore, probation wage = wage differential * probability rate of being not fired = 2600000*.90= $2340000

b. Wage differential between two jobs = 20000*29-10000*30= $280000

Therefore, probation wage = 280000*.90= $252000

c. Wage differential between two jobs = 100000*29-95000*30= $50000

Therefore, probation wage = $50000*.10= $5000

d. Wage differential between two jobs = 100000*29-10000*30= $2600000

Therefore, probation wage = $2600000*0.001 = $2600