Problem
Raising Cane is hiring for workers. It knows there are high- and low-skill workers in the labor pool, and it knows that 40% of applicants will be high skill. It cannot distinguish a worker as high- or low-skill when it decides to hire her and make her a wage offer. The value of the marginal product of labor (VMPL) of high-skill workers is 20, while the value of the marginal product of labor (VMPL) of low-skill workers is 10.
1) Suppose that Raising Cane cannot discern worker ability. What wage will it offer high skill workers? What wage will it offer low skill workers?
Now suppose that workers can obtain a high school degree. The cost of staying in school until high school graduation is ch" = 5 for high skill workers and c"7 = 9 for low skill workers. If some workers have the high school diploma and others don't, Raising Cane believes that those with the diploma are high skill and those without are low skill. If all workers have the diploma or no workers have the diploma, Raising Cane will not be able to distinguish worker skill.
2) Suppose that low skill workers do not get the diploma.
a) What is the high skill worker's payoff from getting the diploma
b) What is the high skill worker's payoff from not getting the diploma?
c) What do high skill workers choose to do?
3) Suppose that low skill workers get the diploma.
a) What is the high skill worker's payoff from getting the diploma?
b) What is the high skill worker's payoff from not getting the diploma?
c) What do high skill workers choose to do?
4) Suppose that high skill workers do not get the diploma.
a) What is the low skill worker's payoff from getting the diploma?
b) What is the low skill worker's payoff from not getting the diploma?