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.