Jai Ranchod

A recent article in the *Voice* noted that the 3.9 percent increase in comprehensive fee is the lowest in recent years and is significantly lower than the 4.5 percent and 4.6 percent it has been over the previous two years specifically. That the rate of increase is down is undoubtedly good, but it is still not exactly cause for celebration. The fact that there is an annual increase letter that we all get every year without fail is a problem that one slightly lower tuition increase can’t solve. That is, it is the chronic increases that should be the point of focus, not the rate of the increase. To understand this better, it helps to turn to a mathematical model of the situation.

Let’s call the total cost of tuition and fees “*c(t)*”, indicating that total cost is a function of time, and let’s abbreviate time to “*t*.” Finally, let’s call the percentage increase in cost “*k*.” Now we can say that *dc(t)/dt=k*c(t)* where *dc(t)/dt* is the rate of tuition increase with respect to time. This is the rate of increase in general using each year as a data point.

This differential equation is actually well known and easy to solve. The solution for differential equations is not a number, however, it is a function. In this case, we want to solve for a function *c(t)* that will tell us the cost of attending the College of Wooster t years from 2013 and is consistent with the first equation.

It turns out the solution is *c(t)=51,600*e^(kt)* where 51,600 is the total cost of attending Wooster for the 2013 school year. Therefore, our model will describe the total cost from 2013 onward only. We use this because to completely solve equation one for the future, we need to already know the answer for at least one point in time. We know the total cost for all past years, but we are interested in the future cost, so we start with the most recent year.

Now the final part of our model is a value for “k.” For the simplicity of the model, we want to use just a single number for “k,” even though it varies from year to year. 3.9 percent is the lowest percentage in recent years, but let’s be generous to the administration and round that down to 3.5 percent which is the lowest increase in President Cornwell’s tenure according to findthebest.com and collegecalc.com. Now we have our final solution *c(t)=51,600*e(0.035t)* which again describes total cost with respect to the number of years from 2013.

This solution reflects the fact that the larger the tuition is, the larger the cost increase is. This problem wouldn’t be a problem if financial aid kept pace with rising costs. The unfortunate reality, however, is that it does not. Financial aid with respect to time is not nearly enough to affect the nature of cost increases. Certainly for many it provides a meaningful offset now, but over the course of multiple years, it will not be able to affect the way in which costs to students increase. This leaves us with very literally a “snowball effect” that can easily get out of hand. Or in our case, more out of hand than it already was.

To inject some reality into the situation, consider the following: this model continues, even under the lowest tuition increases we’ve seen from President Cornwell, in 10 years a year at Wooster will cost $73,223. Cost will break the $100,000 barrier in 19 years, and in 30 years (when many current students may have kids in college) a year at Wooster will cost $147,455.

In case you haven’t already guessed, my point here is that the model Wooster has been using for most of its recent history cannot continue much further. The irony here is that a school so hell-bent on doing a good thing for the world through environmental sustainability that it seems to have willingly ignored financial sustainability in favor of competing with wealthy schools and bringing more money to campus. However, I hope that most people would agree that the model of Wooster’s total cost shown here is unsustainable.

That means the set of questions left behind is clear. What will break this model? When will people begin to say “this much money and four years at Wooster is not the best way to educate myself over the next four years?” Whatever the answers may be, some group of people at some point will force the model to change. It could be parents in a decade, or it could be students and alumni right now.