The letter seems reasonable enough to me, though I'm not sure my counter would've been my limit. That is, if you wanted 110, you might've asked for a bit more -- 115, say -- in order to settle on what you actually wanted. Your letter is quite sincere, but you also don't mention what the problems are: in this forum, you've told us the commute is a concern, but you don't mention it in your letter. What if they stayed at $100, and said you could work at home, say, four days a month? There are probably other counter-offers along that line, and maybe even other lines where common ground can be found. Had you thought of calling HR and negotiating over the phone instead of writing?