I am also aware that LW and MIRI are bothered by RationalWiki.
I was a little bit at first, but then I tried clicking "random page" a few times to get a sense of what RationalWiki is like as a whole. Other than stubs, every page I landed on contained an attack of some sort. Being upset about a RationalWiki entry being unfair and negative is... like being upset about Ambrose Bierce's The Devil's Dictionary being linguistically inaccurate. It doesn't really matter and that's not really what they do.
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I think it is semantics that depend on your assumptions:
http://www.investopedia.com/terms/e/economicrent.asp
Profits are economic rent are the same in a lot of instances. If all markets were perfect their would be neither profit nor economic rent. Can you think of a situation where profit is not economic rent?
When you talk about perfectly competitive markets having no profit, you're probably thinking of the term "economic profit". The sort of profit everyone usually thinks of is revenue minus cost, which is called accounting profit by economists so as to distinguish it from economic profit. Also economists are really bad at naming things. Economic profit is revenue-costs-opportunity costs.
In perfect competition, firms do make accounting profit, but they don't make economic profit.
Thanks for posting your model here and getting involved in the discussion. It's always good to be able to discuss these things publicly because I'm sure many people are learning a lot from it.