Cheap microscopes often produce images that have colored edges. why?

Because of the lens

Explanation:

The lens have a problem and it's the same that the atmosphere offers, if you look at the moon in the night while a cloud is close (it looks better on full moon) you can see an aura wrapping the moon, that happens because the clouds in the atmosphere divide the light and make that aura. The same happens with the lens of some microscopes, that's why the most expensive microscopes are avoiding the use of lens.