Is the market for university education perfectly competitive?

Nowhere near perfectly competitive!

It's not exactly contestable first of all: you need licenses, permits, whatever else you may need for setting up an educational institution! Hiring professors and academics will be hard as the top universities with the most 'market power' are able to get the best ones. So there goes equal access to resources.

There is also the fact that the top universities have recognition, 'brand value' and thus are able to differentiate themselves from other, average universities. So technically the 'goods' - courses are homogeneous but as they have different modules, and are delivered in different ways in each university, it's not homogeneous.

In terms of AR = MR and being a price taker, I suppose the universities are to some extent forced to take market price, although this is mainly down to the government placing price caps on their tuition fees. However, some are even exempt from this if I think their teaching standards or research quality is above a benchmark?

ALSO - there isn't perfect information or knowledge for firms and consumers, for common sense reasons.

In my opinion, the closest you may be able to get to perfectly competitive market is maybe farmers/agriculture or foreign exchange markets, maybe stock markets but again there are strong arguments as to why they aren't.

But, perfect competition is used as a benchmark in theoretical economics to compare against real life markets and see how they can improve or what they 'lack' such as allocative efficiency etc.

Very good information! Thank you for the help!