Sure, I read it all. $200 is pretty cheap too.
On the other hand, $400-500 is also cheap, but that's their business
Well, since I work in the industry, I just like to point out that a logo is not just something you have on a website. It's your company soul so to say. The face outwards. We usually charge our customers depending on how long time it takes and how established the firm is.
An example offer on your firm (that's roughly calculated) we'd charge about $1000. Since you get the logo from a kind of "competition" you don't buy a finished solution. Time will go into sorting the logos, choosing the logo and so on.
Besides, it'll probably have to be extremely high-res or vector-based (you got to think of your image as a company).
Well, if I have misunderstood your "logo-compo" and it's a "only-for-the-web-no-conformity-here" - My bad