Question

1. Suppose that a worker currently earns $40,000 per year. He is 60 years old and has ben with the firm for 20 years. You believe that he is so skilled that in order to replace him, you will have to hire two individuals, each of whom earns $30,000 per year. His pension plan offers him the following benefits upon retirement: the worker receives an annual pension of $1.25% of final salary times years of service at retirement. (Assume the relevant interest rate is zero.) Fifteen years of payment are given, irrespective of date of retirement.

a. If you keep his wages constant, what is the maximum salary offer that he will refuse from another firm that gives no pension benefits?

b.    If his next year's salary will rise to $44,000, what is the maximum alternative salary offer he will refuse?

c.      If the worker's salary will rise by $2,000 per year to $50,000 at age 65, how much does the worker lose in benefits if he is fired at age 60 for poor performance?

d.       At this firm, workers are permitted to choose the number of hours they work. In the absence of a pension plan, each worker supplies hours of work according to the following equation:

Annual Hours = 300*(Hourly Wage) – 10*(Hourly Wage)^2.

                                                              i.      If wages are $5/hour how many hours does each worker work?

                                                            ii.      If the previously stated pension formula is in effect, how many hours would the 64-year-old with 14 years of experience work during his final year if he plans to live to 70?

                                                          iii.      If the worker produces $30 of revenue net of expenditures on other factors for the firm per hour worked, does giving the worker the pension in (2) produce more profits for that year than defining his pension to be at the lower level independent of earnings during his final year? Is the worker better off?

Answer 1

Solution

a. Given that the worker is now 60 years old and earns $40,000 per year.His service is 20 years.Assuming he retires at this salary.He would earn a pension of :

    = (1.25/100) * 40,000 * 20

    = $10,000 / year

He will receive this amount for 15 years irrespective for number of years he served.

Total pension amount he would be receiving is $1,50,000 (i.e.,$10,000 * 15)

Total amount he would take up the offer from other firm(which does not offer any pension on retirement) only if they pay an amount /annual salary equal to (or) more than $1,90,000 (i.e.,$40,000 + $1,50,000).

So maximum alternate salary he would refuse is $1,89,999.

At $1,90,000 he would be indifferent to both the options

b.His next year salary is $44,000.His service would become 21 years.So if he retires at the end of next year,his pension would be:

= (1.25/100) * 44,000 * 21

= $11,550 /year

Total pension amount he would be receiving is $1,73,250 (i.e.,$11,550 * 15)

otal amount he would take up the offer from other firm(which does not offer any pension on retirement) only if they pay an amount /annual salary equal to (or) more than $2,17,250 (i.e.,$44,000 + $1,73,250).

So maximum alternate salary he would refuse is $2,17,249

At $2,17,250 he would be indifferent to both the options.

(c) Comparing both the scenarios :

   Retiring at 65 years at a salary of $50,000 he would get a pension of

    = (1.25/100) * 50,000 * 25

    = $15,625 /year

Total pension amount he would receive is $2,34,375 (i.e.,$15,625 * 15)

Amount earned as salary during 5 years (from 60 -65 years) is i.e.,$2,30,000 ($42,000 + $44,000 + $46,000 + $48,000 + $50,000)

If he is fired at 60 years,as calculated above he would earn a total pension of $150,000

So the worker would loose in retirement benefit an amount of $84,375 (i.e.,$2,34375 - $150,000)

Total opportunity cost is $3,14,375(i.e.,$84,375 + $2,30,000)

(d)

(i) Annual hours = (300 * (5)) - (10 * (5) ^ 2)

                        = 1500 - 250

     => Annual hours = 1250 hours

(ii) This part of the question is not clear.Please elaborate more on things like can we assume the 64 year to be earning $48,000 per year (or) $40,000 /year ,if pension plan is not in affect then only the concept of number of hours will come into effect ? , can the hourly wage be assumed as $5 / hour etc.,

(iii)This solution is dependent on part (ii)

Note: Please give some clarity on part d (ii) so that I can work on providing you with the solution to d(ii) and d(iii)

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