Question

a) A probationary contract specifies that a worker is paid $2,110 per month for the first m months. After m months the worker is either fired or gets a raise to $2,500 per month for (10-m) months. A low-productivity worker has a 90% chance of being fired at the end of his probationary period. If low-productivity workers can earn $2,200 per month somewhere else, how many months must the probationary period last to keep them from applying?

b) If the chance of being fired at the end of the probationary period falls to 80%, how does your answer to part a) change, if at all? Explain.

Answer 1

(a)

Expected earning for a low productivity worker per month after the end of his probationary period = 0.9*$2,200 + 0.1*$2,500 = $2,230

We should equate the total earning of 10 months when the worker earn $2,200 per month with the expected earnings if he does the other job

-> $2,200 * 10 = $2,110 * m + $2,230 * (10 - m)

-> m = 2.5

Thus, the probationary period must last a miximum of 2.5 months to keep them from applying

(b)

In this case, Expected earning per month after the end of his probationary period = 0.8*$2,200 + 0.2*$2,500 = $2,260

Thus, the required equation is

$2,200 * 10 = $2,110 * m + $2,260 * (10 - m)

-> m = 4

Thus, the answer changes to 4 months