Question

David is a high school senior. He must decide whether to work or go to college. If he has a high school degree, he will make $20,000 per year. If he has a college degree, he will make $35,000 per year. To get a college degree, he must go to school for one period at a tuition cost of $10,000. Assume David lives for 3 periods and his discount is 0.1.

(a) What is David’s direct cost of attending college? What is his opportunity cost? What will he decide to do?

(b) Now, assume David can get a full-ride scholarship (thus H = 0). Now what will he do?

(C) Since David is receiving a scholarship for his undergrad degree, he is now debating about going to grad school. If he decides to get his PhD, he must go to school in the first period (undergrad) at a cost of $0, and he must go to school in the second period (grad school) at a cost of $0. With a PhD, David can make $77,000 per year. Will David go to grad school? You only need to compare undergrad and grad school.

Answer 1

a) direct cost of attending the college is equal to the tuition fee = $10,000

Opportunity cost is the potential income of David if he had decided to work instead = $20,000

His decision depends upon the total cost and total benefit he will incur after going to the college.

Total cost = direct cost + opportunity cost = 10,000+20,000 =30,000

Total benefit = present value of difference in income earned by David after getting the degree and income before getting the degree.

By assuming davDa will live 3 years and discount rate (d) is 0.1

He will start earning in 2nd period

Total benefit = (35000-20000)/(1+0.1) + (35000-20000)/(1+0.1)^2

Total benefit = 15000/1.1 + 15000/1.21 = 13636.36 + 12396.69

Total benefit = 26033.05

He will decide to study if if total benefit - total cost is positive.

Total benefit - total cost = 26033.05 - 30000 = -3966.945

Hence, he will work.

B) assuming that he gets full scholarship, his turion fee is 0.

So total cost = opportunity cost = 20000

Total benefit - total cost = 26033.05 - 20000 = 6033.05 > 0

The difference is positive, so David will study given the scholarship.

C) David will go to the grad school if present value of benefits after going to the grad school is higher than the cost incurred, given that he has already done with under grad college. Now he is already done with undergrad college, which means only 2 time pwriope are left.

Present value of benefits (increase in income) after going to grad. David will have only one year with him after going to grad school.

Total benefits = (77000-35000)/(1+0.1)= 42000/1.1= 38181.18

Total cost = opportunity cost while studying for grad = 35000 (income that he could have earned )

He will go for grad collage if total benefit-total cost is positive.

Total benefit - total cost = 38181.18 - 35000 .= 3181.18 > 0

Hence he will go to grad school.