Exponential Growth

Middlebury College’s president got some press a while ago for capping the increase in tuition. Specifically, any tuition increases were capped at 1% over the Consumer Price Index, the standard measure of inflation in the US.

I’m not sure if whomever proposed this doesn’t understand exponential growth, or if Middlebury’s president didn’t understand it, or if he thinks that we don’t understand it, but I do, and let me explain it to you. Most of my data comes from Middlebury’s website, or comes directly or indirectly from the census bureau.

Middlebury’s total cost in 2010 was $50,400. This is a “comprehensive fee” that includes tuition, room, board, fees, and so forth. I’m going to assume that they won’t sneakily put massive increases into things other than tuition.

The median household income in the US in 2010 was $49,445.

The average rate of inflation in the US is 3.16%, averaging since 1958. Median household income grew at 0.04% over inflation since 1989. Naturally, these things fluctuate a lot as the market goes up and down, but those are the averages.

We can use this average to estimate the future tuition at Middlebury, and the future median income in the US. Here’s a graph.

Tuition forecast graph

If Middlebury’s tuition increases at their capped amount, the cost of going to school there will pass $100,000 per year in about 2027-28. This would be fine if we were all making $150,000 per year, but as you can see, we’re not.

More instructive, perhaps, is the gap between median income and tuition:

Tuition Gap

You can see that by 2040, tuition at Middlebury will cost about 35% more than the median household in the US makes per year.

Sadly I don’t have good data for the amount of financial aid available and how that changes by year, but unless it grows at more than 1% over the inflation rate, it’s not going to help.

It is a truism in science that exponential growth can’t continue forever. Eventually the graph turns either cyclic or logistic, and the growth stops. Inflation is a special case; it can keep going forever because we can just revalue the currency to take some zeroes off the end of the bills, as Mexico did with the “new peso” in 1993. When something’s cost regularly increases at more than the rate of inflation, it will eventually need to stop because no one will be able to pay for it.

Exponential growth is a real killer. Middlebury’s plan is better than the average college’s increase. The average for four-year schools is about twice the inflation rate, which would lead to a massive disparity of 160% by 2040. However, it still doesn’t genuinely make the school more affordable.

The only way to make your school more affordable is to have your tuition increase at less than the rate of inflation. Anything more is still exponential growth.

(Note: After this was posted I edited a few items for clarity.)

About Colin Fredericks

By day I help to create online courses at HarvardX. By night I write roleplaying games.

Posted on December 21, 2011, in Uncategorized and tagged , . Bookmark the permalink. Leave a comment.

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