For the High-Productivity Group K the cost of attaining an educational level y i
ID: 1186880 • Letter: F
Question
For the High-Productivity Group K the cost of attaining an educational level y is CH(y)=$5000y
And for the Low-Productivity Group M the cost of attaining that level is CL(y)=$10,000y
Employees will be offered $30,000 if they have y<y?where y? is an education threshold determined by the employer. They will be offered $90,000 if they have y?y?.
A) What is the highest level of y* that can be set and still have the high-productivity people choose to meet it?
B) What is the lowest level of y* that can be set and still have only the high-productivity people meet it?
C) Which of the two groups will choose to attain it is the threshold educational level y* is set at 15? At 8? And at 5?
D) Suppose an employer only wants to hire high productivity workers. What is the range of between which it shoul set y* to ensure such?
Explanation / Answer
For argument's sake, imagine that y=3. Then the cost to Group K is 5000*3 = $15,000. The cost to Group M is 10000*3 = $30,000. So the cost is much higher for Group M than Group K. Specifically, it's twice as high.
If somebody is going to choose to do something, the benefits must be greater than (or equal to) the costs. So imagine a job is offered that requires three years of education (i.e. y=3) and the wage is $25,000. Only Group K will obtain the education necessary for the job because the costs to them of $15,000 are less than the benefits of $25,000. (Group M's will be "losing" $5,000 because the costs to them of $30,000 are less than the benefits of $25,000.)
(when e* = 30)
30*5,000 = 150,000
90,000-60,000 = 30,000 (30,000 = 30,000, so Group K is indifferent and so attain education at e* = 30)
8. Answer: D (when e* = 22.5)
22.5*2,000 = 45,000
90,000-45,000 = 45,000 (45,000 > 30,000, so Group K attain education at e* = 22.5)
22.5*4,000 = 90,000
90,000-90,000 = 0 (0 < 30,000, so Group M don't attain education at e* = 22.5)
At e* = 15, Group M would have been indifferent, and thus attained education.
9. Answer D (when e* = 45, neither group will attain education)
45*2,000 = 90,000
90,000-90,000 = 0 (0 < 30,000, so Group K will not attain education at e* = 45)
45*4,000 = 180,000
90,000 - 180,000 = -90,000 (-90,000 < 30,000, so Group M will not attain education at e* = 45)
10. Answer: C (when e* = 13 1/3, both groups will attain education)
13 1/3*2,000 = 26,660
90,000-26,660 = 63,340 (63,340 > 30,000, so Group K will attain education at e* = 13 1/3)
13 1/3*4,000 = 53,320
90,000-53,320 = 36,680 (36,680 > 30,000, so Group M will attain education at e* = 13 1/3)
11. Answer: A (when e* = 20, only Group K will attain education)
20*2,000 = 40,000
90,000-40,000 = 50,000 (50,000 > 30,000, so Group K will attain education at e* = 20)
20*4,000 = 80,000
80,000-90,000 = 10,000 (10,000 < 30,000, so Group M will not attain education at e* = 20)
For Group M the cost of attaining that level is C(M) =10000y