Question

Assume there are two types of workers, A(ble) versus C(hallenged) (the type of a specific applicant is unknown to potential employer): the A type is better, meaning they have a lower cost of taking an additional class ($6k per class vs $9k for C). The potential employer is considering this hiring policy: if an applicant takes more than n classes, they will be hired as A type and get A money ($150K), otherwise they will be hired as C type and make C money ($100k). With what number n would this work?

Answers 0 6 10

Answer 1

Solution:

We have to find a separating equilibrium for such case described. Firstly, as not getting any additional class and getting less than n additional classes will create no difference on income earned, rather earn less profit when taking the class, so 0 additional classes is preferred to less than n classes.

The only optimal way of choosing that n is where the following conditions are satisfied:

Net benefit to C from not taking any additional class > net benefit to C from taking n additional classes (such that amount received is same as type A)

Similarly, for type A, net benefit from taking n additional classes > net benefit of taking 0 additional class

So, 100k - 9k*0 > 150k -9k*n

Or 9kn > 50k ; n > 50/9 or 5.55

And, 150 - 6k*n > 100 - 6k*0

50k > 6kn

n < 50k/6k = 8.33

Thus, optimal value of n that will incentivize each type to indicate the true type is somewhere between 5.55 and 8.33, like 6.

Thus, the correct option is (b) 6.