Question

Citizens of a given country belong to two categories which are indistinguishable for the employer: the more- and less-talented. All of them finish university studies, however not all of them with distinction. Acquiring a diploma with distinction costs $100,000 for the less-talented persons and $50,000 fr the more-talented ones (involving e.g. effort, private lessons, bribes, etc.) (value calculated for the moment of obtaining the first salary). University alumni sign a contract for an indefinite period envisaging a costant annual salary and discount it based on the 10% annual discount rate. There are no possibilities of promotion. Independently of the obtained diploma and talents, each alumni may take up a job for a market salary of $40,000 per year. A certain company would like to employ only more-talented employees. What could its recruitment and wage policy look like? Problem #8 Seemingly indistinguishable types of persons apply for a job to the mafia tough guys and wimps. In order to select the tough guys the mafia makes each candidate undergo a painful trial. The trial lasting for m minutes decreases the tough guy's utility by m2, while the effect on the wimp's utility is a decrease by 4m2. Being hired by the mafia increases utility by 101, independently of the type. Assuming that the capo di tutti capi accepts only full minutes of the trial (integers), how many different separating equilibria (i.e. such that one type will apply for the job and the other will not) are there? Which of these equilibria will be chosen by the capo-sadist and which by the emphatic capo?

Answer 1

Cost of obtaining diploma:

1) For more-talented guys: Cost, C(M)= $50,000

2) For less-talented guys: Cost, C(L)= $100,000
The wages offered by the company (W₀^C ), should be such that discounted value of wages, follow the below inequality$\$50,000\leq W_0^{C}\leq \$100,000$

Hiring process by Company:

Since the wages are constant for the entire life-time and are equal for more as well as less talented employees, let us calculate the present value (t=0) of the constant salary

$W_0=\sum_{t=0}^{T}m/(1+d)^{t};$

Since employee is assumed to work for all his lifetime, we can safely assume T to be infinite

If m=$40,000, d=0.10, and T is the total time for which employee earns, we have,

$W_0=\$40000\sum_{t=0}^{\inf}/(1+0.1)^{t}; \implies W_0= \$40000*1/(1-1/1.1)\\$\hfill(using formula for sum of infinite G.P.)$\\ \implies W_0=\$40000*11=\$440,000$

Now the benefit of obtaining diploma for more and less talented employees is given by discounted salary at time 0 minus the cost of getting education. Let us denote the benefits as B_M and B_L for more and less talented employees respectively.

Then B_M=$440,000-$50,000=$390,000

and B_L= $440,000-$100,000=$340,000

If a company wants to hire only more-talented employees, it needs to offer a wage, such that benefits for more talented guys are more than or equal to the current benefit of more-talented employees but less than the benefit obtained by less talented employees.