The movie concept is the general idea. You will write down your
idea in a form similar to a short story. The treatment isn't a "tease"
so you will write the entire story from beginning to end, leaving
nothing out. The reader should understand the whole concept (or
idea) after reading. You will include all of the major beats of the story
and the major obstacles, reversals, barriers that affect those beats.

It can be short - a few paragraphs - or it can be be several pages.
The more you can demonstrate your talent for weaving a good tale
without resorting to overwriting, the better. It's rare for a treatment
to have any dialogue, so in that aspect it's very different from a short
story. But you want to to be entertaining and engaging.

=============================================
The aim of an argument or discussion should not be victory, but progress.
Joseph Joubert, essayist (1754-1824)

If I may ask, if you're applying for graduate school, that implies you have an undergrad degree. So, if we are to give you better advice, perhaps you can tell us what graduate program you're applying to, and what your undergrad is.

Usually, a grad program requires you to provide a 2-page essay.

Read, "Selling Your Story in 60 Seconds" by Michael Hauge. Essentially, a pitch is what you are submitting. Good Luck!

Filmmakers, resources, and equipment for barter.
http://www.bizindie.com
Practical Networking for the Entertainment Industry. Free!

I'm not sure I have ever heard of anything called "movie concept". Those who know what it is, how is it different from the "film treatment", and the "film outline"?

I would come up with an idea, then read this book. "Save the cat" will give you everything you need. It was very helpful to me, and I wholeheartedly recommend it.

"Bullies aren't bulletproof"