Question

1 Optimal Education Choice 1. [You can use excel if you want. Show your work| Assume a person's labor market active life has three periods after high school graduation (the day the person turns 18 years old) College age (4 years, until their 22nd birthday) Young professional age (until their 30th birthday) Old professional age (from their 30th birthday until retirement) People that choose not to go to college work. People that choose to go to college make no money during the four years they are in school. After the three periods, the person retires on her 40th birthday. Furthermore, assume that the out-of-pocket expenditures of each year of college are $90,000, and that the yearly earnings schedule is the following: Professional Age Young Old Education Level HS Graduate $30,000 $45,000 College Graduate $50,000 $95,000 Finally, assume a discount rate of 2% (a) [15 points] Graph the age-earning profiles. (b) [10 points] Will the person choose to go to college? 2. Would your result to Q1 change if the discount rate is 3%? (a) 8 points] Show your work. (b) 9 points] If you find you answer for Q1 changes, explain the economic reasons for its change.

Answer 1

1. For, HS graduate, the NPV(net present value) of earnings is as follows:

age 18-30 = 30,000[ 1/(1.02) + 1/(1.02)² + 1/(1.02)³ + 1/(1.02)⁴ + 1/(1.02)⁵ + 1/(1.02)⁶+ 1/(1.02)⁷ + 1/(1.02)⁸ + 1/(1.02)⁹ + 1/(1.02)¹⁰+ 1/(1.02)¹¹ + 1/(1.02)¹²]

age 30-40 = 45,000 [ 1/(1.02)¹³ + 1/(1.02)¹⁴ + 1/(1.02)¹⁵ + 1/(1.02)¹⁶ + 1/(1.02)¹⁷ + 1/(1.02)¹⁸ + 1/(1.02)¹⁹ + 1/(1.02)²⁰ + 1/(1.02)²¹ + 1/(1.02)²² ]

NPV of total yearly earnings of HS graduate = 6,35,982

For college graduate, the NPV of yearly earnings is as follows:

age 18-22 = -90,000 [ 1/(1.02) + 1/(1.02)² + 1/(1.02)³ +1/(1.02)⁴ ]

age 23-30 = 50,000 [ 1/(1.02)⁵ + 1/(1.02)⁶ +1/(1.02)⁷ + 1/(1.02)⁸ + 1/(1.02)⁹ + 1/(1.02)¹⁰ + 1/(1.02)¹¹ + 1/(1.02)¹² ]

age 31-40 = 95,000 [ 1/(1.02)¹³ + 1/(1.02)¹⁴ + 1/(1.02)¹⁵ + 1/(1.02)¹⁶ + 1/(1.02)¹⁷ + 1/(1.02)¹⁸ + 1/(1.02)¹⁹ + 1/(1.02)²⁰ + 1/(1.02)²¹ + 1/(1.02)²² ]

NPV of total yearly earnings of College graduate = 6,68,542

7,00,000 6,00,000 5,00,000 yearly earnings 4,00,000 3,00,000 2,00,000 1,00,000 23-30 31-40 0 18-22 -1,00,000 -2,00,000 -3,00,000 -4,00,000 -5,00,000 age groups

Above is the age -earning profiles graph.

(b). The person will choose to go to college as his higher educational qualification leads to higher earnings.

2. If the discount rate changes to 3%, then,

For, HS graduate, the NPV(net present value) of earnings is as follows:

age 18-30 = 30,000[ 1/(1.03) + 1/(1.03)² + 1/(1.03)³ + 1/(1.03)⁴ + 1/(1.03)⁵ + 1/(1.03)⁶+ 1/(1.03)⁷ + 1/(1.03)⁸ + 1/(1.03)⁹ + 1/(1.03)¹⁰+ 1/(1.03)¹¹ + 1/(1.03)¹²]

age 30-40 = 45,000 [ 1/(1.03)¹³ + 1/(1.03)¹⁴ + 1/(1.03)¹⁵ + 1/(1.03)¹⁶ + 1/(1.03)¹⁷ + 1/(1.03)¹⁸ + 1/(1.03)¹⁹ + 1/(1.03)²⁰ + 1/(1.03)²¹ + 1/(1.03)²² ]

NPV of total yearly earnings of HS graduate = 5,67,851

For college graduate, the NPV of yearly earnings is as follows:

age 18-22 = -90,000 [ 1/(1.03) + 1/(1.03)² + 1/(1.03)³ +1/(1.03)⁴ ]

age 23-30 = 50,000 [ 1/(1.03)⁵ + 1/(1.03)⁶ +1/(1.03)⁷ + 1/(1.03)⁸ + 1/(1.03)⁹ + 1/(1.03)¹⁰ + 1/(1.03)¹¹ + 1/(1.03)¹² ]

age 31-40 = 95,000 [ 1/(1.03)¹³ + 1/(1.03)¹⁴ + 1/(1.03)¹⁵ + 1/(1.03)¹⁶ + 1/(1.03)¹⁷ + 1/(1.03)¹⁸ + 1/(1.03)¹⁹ + 1/(1.03)²⁰ + 1/(1.03)²¹ + 1/(1.03)²² ]

NPV of total yearly earnings of College graduate = 5,45,683

(b) the person here will choose not to go to college as his NPV of toatal earnings declines with higher eduv=cation because here inflation rate has risen from 2% to 3%.