Question

Susan, currently at the age of 20, has a constant value of marginal product at $10 that does not change for the rest of her life. She has 2 job offers. Firm A offers her a competitive wage of $10 as long as she works, and firm B offers her a wage that begins at $6 and increases by 20 cents for each additional year of work, yielding the following age-earnings profile

w = 6 + 0.2x

where w and x stand for wage and years on the job, respectively. For simplicity, we assume that the discount rate is zero, that is, there is no discounting of all future earnings of Susan.

(a) How many years does it take for firm B to pay Susan the market wage of $10?

(b) Suppose Susan is a conscientious worker who never shirks, so she will be employed by either firm until her retirement. Which job will she prefer if she retires at the age of 55? How about if she retires at 65? Show your calculations and graph your results.

(c) What are the possible reasons that firm B offers a delayed compensation contract?

Answer 1

a) For firm B to pay a wage of $10,

w=$10

10 = 6 + 0.2 * x

x= 4/0.2

x=20

So It will Take Susan 21 years till she gets $10 from firm B.

b) If Susan retires at 55, then she would have worked for (55-20) or 35 years.

At firm A, she would have got, 35 * $10= $350

At Firm B, she would have got $6 in first year, $6.2 in second year and so on. So it is an increasing AP with difference of 0.2 ad number of terms 35 and first term $6.

SoTotal Earning from B = 35/2 * (2*6+ (35-1) * 0.2)

= 35/2 * (12+34*0.2)

=35/2* (12+6.8)

= 35/2 * 18.8

=329.

So if she retired at age of 55, she would have preferred to work with firm A.

If she retired at age 65 then she would have worked for (65-20) or 45 years.

At firm A, she would have got, 45 * $10= $450

At Firm B, she would have got $6 in first year, $6.2 in second year and so on. So it is an increasing AP with difference of 0.2 ad number of terms 45 and first term $6.

SoTotal Earning from B = 45/2 * (2*6+ (45-1) * 0.2)

= 45/2 * (12+44*0.2)

=45/2* (12+8.8)

= 45/2 * 20.8

=468

So if she retired at age of 65, she would have preferred to work with firm B.

c) Firm B offers a delayed compensation contract for the following reasons

1) It can check how good or bad the candicate is performing by paying a lower wage

2) If the candicate is good, it can keep on increasing the wage which would also keep the candidate motivated

3) A regularly increasing salary is also attractive once it crosses the flat market rate and candidate will not want to leave the company. Thus firm B can retain employees.

4) The time value of money is used by B wherein it pays low initially and high later to reduce effective outflow.