Apple can absolutely compete - it's just a question of Apple's current interest in being in the Education space. The Education space is good PR, but it's NOT good for making money. This is something Apple has learned from years of supporting the Education market. Google has made headway into the Education space, not because of the cost (at least it doesn't play as big of a role as people might think), but because of the overall support the company has provided (including infrastructure [cloud services, bandwidth], software [suite of tools for students and educators], content/resources, and hardware partners) - Apple is not built, in it's current form, to compete with that level of commitment (especially being STILL a primarily hardware focused company - all of their software and services are designed to sell hardware). What's Google getting out of it? The same thing Google always gets - data.
Even if Apple came out with a cheaper iPad and some educational software tools, it's not going to be able to compete with what Google has brought to the game for Education. Even Microsoft, who has recently made a showing of support for education, knows that it's fighting Apple for Google's left over scraps.
Having said all of that, it's not to say Apple should give up. There will always be spaces for Apple to play. While Google is big, it's not invulnerable. Google has a lot to offer, but it's also less attractive in some respects (such as data and privacy concerns). Not to mention, there are still a lot of educators who PREFER Apple over Google and that DOES count when making decisions (acceptance is a big deal, but not usually enough to stop or change large contracts).
Apple can still win big in Personal Education - i.e. by not focusing on large governing bodies, but instead on individuals. Some of this is evidenced by their "Today at Apple" and "iTunes U". Individual Education is going to become a BIG space over the next few years - we'll start to see more of a focus on enriching individuals as companies start expanding those offerings. Microsoft already has a big leap ahead in this space with their purchase of LinkedIn (which had purchsed Lynda.com).