Modeling the Finance of a College Education

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Introductory Video

The Topic

I am interested in how so many university educated people in the United States end up in poverty or even homelessness. I hypothesize that the answer may lie in limelight issues such as student loans and wealth disparity, so I want to analyze how someone could approach the challenge of gaining financial security starting at the university application phase of life. Are there strategies that could minimize the financial burden of ever increasing tuition while still receiving valuable education? Many of my friends are going through the university entrance process and the financial obstacles that I see in many of their futures are astounding. I will use game theory to see if there are any lessons or guiding principles hidden in the financial payoffs of students and universities.

The Problem

We live in an age where going to college no longer guarantees you financial stability. With tuition costs rising and job opportunities becoming ever-more competitive, going to college can leave many students with the feeling that they can never crawl out of debt. Is it really the best choice to go to an IVY league college and take out a loan to pay for a degree or is it better to go for a less prestigious university and save on the cost? I hope to answer this and similar questions by modeling a sequential game between universities and students and solve it using backwards regression.

Definitions and Information

College

College and university are used interchangeably in this project.

Affordable University

For the purposes of this game, an affordable university is one that the student’s family can afford without going into debt or taking out a loan. If the student receives a grant, the university would still qualify as affordable because the student’s family would not need to go into debt.

Unaffordable University

An unaffordable university will be defined as one in which the student’s family needs to go into debt in order for the student to attend the school.

 

The Game

Key

AA Apply to Affordable University
AU Apply to an Unaffordable University
a Accept Student
r Reject Student
f Give Student Financial Aid
GO Go to the School
DG Don’t Go to College
OO Go with Other Options such as community college or reapplying for the next year
TL Take Out a Loan to Pay for the University

 

Payoffs and Justifications

Disclaimer: There were several assumptions made about what an Affordable University really looked like and in order to have concrete data, it was assumed that for the average student, a public university could be considered affordable while a private university could be considered unaffordable.

 

Outcome

Payoff

(Student, University)

Justification

A

(55, 2)

Student

The payoff for a student going to a university they can afford can be calculated by subtracting the average annual cost for in-state tuition and fees at a public college in the United States ($10,000)6 from the average salary of somebody graduating with a bachelor’s degree ($65,000)2 and dividing by 1000 to get a payoff of 55.


University

The payoff of outcome A for the university can be calculated by subtracting the average annual cost educating a student at a public college($14,000)3 from the tuition paid by students ($10,000)6 and the subsidies given by the government ($6,000)3 and dividing that by 1000.

B

(39, 0)

Student

The average salary of someone whose highest educational attainment is a high school diploma in the United States is $39,0002, so the utility becomes 39.


University

As the university can simply fill that place with another student, their payoff for this specific student is 0.

C

(48, 0)

Student

The payoff of the student pursuing other options will be calculated as the average of the payoffs from attending university in outcome A and the playoffs from attaining an associates degree in a community college.


The average salary of someone whose highest educational attainment is an associate’s degree in the United States is $46,0002, and the cost of obtaining the degree is $5,0005 on average. So the payoff is 41. Averaged with the payoff of 55 from outcome A, the payoff for C becomes 48.


University

The payoff of rejecting a specific student is 0 because the potential upside of a different student is not considered in this model and the university needs to do little work to reject the student.

D

(39, 0)

Student

The average salary of someone whose highest educational attainment is a high school diploma in the United States is $39,0002, so the utility becomes 39.


University

The payoff of rejecting a specific student is 0 because the potential upside of a different student is not considered in this model and the university needs to do little work to reject the student.

E

(40, 7)

Student

The salary of those graduating from more ‘prestigious’ universities has been shown by the Washington Post to be essentially the same as that of someone graduating from a less prestigious university if high school performance is taken into account.


Therefore, the payoff for a student going to an unaffordable university with a grant will be the average salary of someone graduating with a bachelor’s degree ($65,000)2 plus the average amount given for grants annually ($9,000)7 minus the average annual cost of tuition for a private college ($35,000)6 divided by 1000. One extra utility point will be added because of the excitement and fulfillment that comes with going to college.


University

The payoff of outcome E for the university can be calculated by subtracting the average annual cost educating a student at a private college ($19,000)8 and the cost of giving the grant ($9,000)7 from the tuition paid by students ($35,000)6 and dividing that by 1000.

F

(39, -5)

Student

The average salary of someone whose highest educational attainment is a high school diploma in the United States is $39,0002, so the utility becomes 39.


University

In this scenario, the university has accepted the student and taken the time to provide them with financial aid. If the student proceeds not to go, the effort would cost them some amount in labor so the payoff is lower than outcome B.

G

(25, 16)

Student

The salary of those graduating from more ‘prestigious’ universities has been shown by the Washington Post to be essentially the same as that of someone graduating from a less prestigious university if high school performance is taken into account.


Therefore, the payoff for a student going to an unaffordable university with a grant will be the average salary of someone graduating with a bachelor’s degree ($65,000)2 minus the average annual cost of a student loan ($5,000)4 and the average annual cost of tuition for a private college ($35,000)6 divided by 1000.


University

The cost of operations per student for the average university is $19,0008 and the average cost of tuition for a university student is $35,0006 so the payoff for a university in outcome G becomes 16.

H

(48, 0)

Student

The payoff of the student pursuing other options will be calculated as the average of the payoffs from attending university in outcome A and the playoffs from attaining an associates degree in a community college.


The average salary of someone whose highest educational attainment is an associate’s degree in the United States is $46,0002, and the cost of obtaining the degree is $5,0005 on average. So the payoff is 41. Averaged with the payoff of 55 from outcome A, the payoff for C becomes 48.


University

As the university can simply fill that place with another student, their payoff for this specific student is 0.

I

(39, 0)

Student

The average salary of someone whose highest educational attainment is a high school diploma in the United States is $39,0002, so the utility becomes 39.


University

As the university can simply fill that place with another student, their payoff for this specific student is 0.

K

(48, 0)

Student

The payoff of the student pursuing other options will be calculated as the average of the payoffs from attending university in outcome A and the playoffs from attaining an associates degree in a community college.


The average salary of someone whose highest educational attainment is an associate’s degree in the United States is $46,0002, and the cost of obtaining the degree is $5,0005 on average. So the payoff is 41. Averaged with the payoff of 55 from outcome A, the payoff for C becomes 48.


University

The payoff of rejecting a specific student is 0 because the potential upside of a different student is not considered in this model and the university needs to do little work to reject the student.

L

(39, 0)

Student

The average salary of someone whose highest educational attainment is a high school diploma in the United States is $39,0002, so the utility becomes 39.


University

The payoff of rejecting a specific student is 0 because the potential upside of a different student is not considered in this model and the university needs to do little work to reject the student.

Solution

 

Game Tree with Payoffs Shown

Using backwards induction, the optimal decisions for each player can be determined as shown below:

 

The solution and outcome can be determined by following the optimal decisions for each player from top to bottom. So in this case, the student decides to apply to an affordable university and the university decides to accept them. Then the student decides to go for a payoff of 55 for the student and 2 for the university.

Result Interpretation

While the depth and complexity of this model is too shallow to grasp the intricate system of socio-economic variables that determine financial success based on college choice, it is still able to capture some key ideas based on actual financial data.

First

The lowest payoff for the student was the one in which they took out a loan to pay for an education that is out of their budget. 

Second

The highest payoff for the university was paired with the lowest payoff for the student. This may be evidence that universities are creating systems in which they profit at the financial detriment of students, a possible factor in the student debt crisis.

Finally

The second best payoff for the student is surprisingly to search for other options if they are either rejected or do not receive financial aid. This is because it provides the opportunity for the student to apply and go to an affordable university or get an associate degree which will, on average, pay better than not going to college.

Sources Cited

Information gathered from sources will be denoted with a superscript showing which source was used.

Source 1

Webber, Doug. “Perspective | The Advantages of Getting into a Name-Brand College Are Wildly Overblown.” The Washington Post, WP Company, 15 Mar. 2019, www.washingtonpost.com/outlook/2019/03/15/advantages-getting-into-name-brand-college-are-wildly-overblown/.

source 2

Stobierski, Tim. “Average Salary by Education Level: Value of a College Degree.” Bachelor’s Degree Completion, 14 Dec. 2020, www.northeastern.edu/bachelors-completion/news/average-salary-by-education-level/.

source 3

Johnson, Nate. “COLLEGE COSTS AND PRICES: SOME KEY FACTS FOR POLICYMAKERS.” Lumina Foundation, Postsecondary Analytics, 2013, www.luminafoundation.org/files/publications/issue_papers/College_Costs_and_Prices.pdf.

source 4

Carter, Matt. “Average Student Loan Payment: Estimate How Much You’ll Pay.” Credible, Credible, 6 Feb. 2021, www.credible.com/blog/refinance-student-loans/how-much-will-you-actually-pay-for-a-30k-student-loan/.

source 5

“Home.” (2021), www.communitycollegereview.com/avg-tuition-stats/national-data.

source 6

Powell, Farran, and Emma Kerr. “See the Average College Tuition in 2020-2021.” U.S. News & World Report, U.S. News & World Report, 14 Sept. 2020, 9:00 am, www.usnews.com/education/best-colleges/paying-for-college/articles/paying-for-college-infographic.

source 7

“Digest of Education Statistics, 2020.” National Center for Education Statistics (NCES) Home Page, a Part of the U.S. Department of Education, 2019, nces.ed.gov/programs/digest/d20/tables/dt20_331.30.asp.

source 8

“The NCES Fast Facts Tool Provides Quick Answers to Many Education Questions (National Center for Education Statistics).” National Center for Education Statistics (NCES) Home Page, a Part of the U.S. Department of Education, 2020, nces.ed.gov/fastfacts/display.asp?id=75.

2 Comments

2 comments

  1. Hey Lucas, I really like how you did such a prevalent problem, especially what many high school students are about to experience. I enjoy the humor you added to your project. I have been thinking about your question of is it worth it a lot. I think you connected this to game-theory so well!

  2. Hi Lucas! This is a super interesting and deep analysis of the student debt crisis. Your solution model exemplifies the effort put into the project and allowed me to consider how it could be implemented in the future. Your clear recognition of so many angles of the issue projects a statement of understanding that helped me learn a lot as well. Amazing work!

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