In This Problem, a Labor Market Exists Where Employers Hire

In this problem, a labor market exists where employers hire and pay workers according to how much formal education workers possess. Education is a proxy for the level of productivity that employers can expect from workers. Therefore, employers follow a strategy in which they hire workers and pay salaries according to the following conditions:
Degrees Above the Values of Post High School
High School Level Education During Working Life, B(y)
None 0
(y = 0 years)
Associate's Degree $30,000
(y = 2 years)
Bachelor's Degree $51,000
(y = 4 years)
Master's Degree $58,000
(y = 6 years)
Assume that there are only two types of worker abilities, those who are less productive (type L) and those who are highly productive (type H). The less productive workers have to study harder than highly productive workers in order to earn any degree. Consequently, the costs (including the psychic costs of study effort) of attaining various levels of education for these two types of employees are different.
For less productive workers: C_L(y) = $13,000y
For highly productive workers: C_H(y) = $10,000y
a. Draw a diagram with years of education on the horizontal axis. Graph the benefits to education B(y) and the costs of education for each of the two types of workers. Discuss what level of education each type of worker should obtain.
b. Now use the equations above to verify your answer from part (a) mathematically.
c. Explain the value of formal education above the high school level in the market place to employers.