# If price increases and quantity remains the same can we infer that demand is perfectly inelastic?

My college tutor told me that demand for college admission at our institute is price inelastic. She says so, because, in the past 20 years, price of college education at our institute has increased, but the number of students hasn't decreased. Does this really mean that college admission at our institute is price inelastic? Or is there a way I can counter that?

We know for a fact that supply is perfectly price inelastic. Each school typically has a quota -- some rough estimate of the number of students it wishes to enroll.

And every year, there are many who are able and willing to pay the full price of the good (a spot in the school) but are nonetheless not admitted.

Example. For decades, a school has consistently offered 10,000 seats to each cohort. Demand though has consistently risen so that price has also risen. However, we cannot infer anything about the slope of D (i.e. whether demand is price inelastic).

That demand is also price inelastic may very well be true, but cannot be inferred simply from the fact that the number of students hasn't decreased.

Another important consideration/complication is price discrimination. Through financial aid, US universities practice what amounts to near perfect price discrimination, making many students pay as much as they can bear. So, while the sticker price has risen greatly, the actual price paid by many students may not have risen as much.

My college tutor told me that demand for college admission at our institute is price inelastic.

Does this really mean that college admission at our institute is price inelastic?

That is not necessarily accurate. For instance, there could be excess demand so that a more expensive tuition makes no difference in enrollment because the wealthier students still outnumber the spots available in college.

Price inelasticity of demand of this college conveys the notion that a student generally does not care about tuition increases: he will enroll in this college anyway. But in reality, if there are options (that is, other colleges) from where to choose, most likely there are substitution dynamics at play even if the end result is that all spots in this college are filled up. Indeed, those wealthier students might be substituting their otherwise preferred and costlier college by enrolling in this one if their first option becomes unaffordable just like this college became unaffordable to other students.

It might actually be quite elastic but income has risen just enough to compensate for the increase in tuitions! It also might be the case that demand is high enough so that the amount of available spots is fully met at any reasonable price.

A priori, one just can't guarantee that the demand curve for higher education is inelastic based on the observation that over 20 years prices have risen without a significant decrease in demand. A lot can change in 20 years and one can't simply assume all things were held constant during the period.