The rule USED to be "Make a reasonable offer up-front." The candidate may accept it, reject it outright, or attempt to negotiate, but their initial offer will tell you a lot about how serious they are about hiring you.
This offer isn't reasonable. It isn't even close.
They KNOW what you're currently getting. They KNOW they're in an expensive area, and you currently aren't.
Companies that are really good to work for don't lowball their offers. Even the companies that are doing really cool stuff understand that they have to pay at least the going rates for their people, because their competition WILL pay going rates.
Also, recognize that, should you take this job, your raises will be based on your hiring salary.
Unless you are willing to accept continuing abject poverty as a condition of employment, this is one offer you should walk away from.
Enderland commented: "1) You have no idea if this is an offer which isn't reasonable, 2) wtf does "abject poverty" have anything to do with the situation, 3) how does the company offering KNOW what they currently make?, 4) how do you KNOW the asker is making market rate anyways?, and lastly, 5) they aren't asking "should I walk away" they are asking how to respond, so you completely miss the point of the question." His comment deserves a longer answer than I can make in a counter-comment.
To address his points in logical order, rather than physical:
3) Every hiring process I have ever seen or heard about in the last forty years or so included disclosure of the candidate's current salary and salary history. There are several reasons for this, the simplest being that it gives you an idea of whether the candidate is ROUGHLY qualified (you generally don't hire a$20K/year clerk for a $80K/year executive job). It also prevents you from unknowingly offering the candidate LESS than he is currently making, which would be a waste of time.
Obviously, the current salary is only valid in context of his current location. However, his current location was on his resume and his job application form. They know where he is now.
2) If he is reasonably compensated in his current town, and he moves to a town with DOUBLE the cost of living, he's going to be hurting come payday. Alternatively, it may be that he's "making out like a bandit" in his current job, and he would be then much closer to "just making ends meet" in the new town. Accounting 101: "Dollars in pocket = dollars in - dollars out." "Abject poverty" may have been an exaggeration, but there is such a thing as poetic license.
4) There are three possibilities: A. The original poster is currently underpaid. B. The original poster is currently paid market rate. C. The original poster is currently overpaid. I chose to assume that he was not overpaid. At that point, he is either underpaid or being paid market rate. If he's underpaid in his home town, the odds are that he will be REALLY underpaid in a more expensive market.
1) "Reasonable" is, of course, subjective. Every serious offer, where "serious" meant "we do want to hire this guy", that I have ever seen or heard of included at least a 5% "courtesy bump" in the salary, based on the candidate's current salary (see point 3, above). The offer on the table is an actual dollar match, not a bump, with a significant penalty baked in because of the cost-of-living disparity. Where I come from, this is a pay cut. Further, because of the SIGNIFICANT disparity in cost of living, this is effectively a LARGE pay cut. I see that as unreasonable.
To extend it a bit, for those who think he should counter-offer: Prospective employers do in fact have some amount of negotiating leeway, and, in SOME cases, will consider counteroffers. HOWEVER, they usually don't have 50% or more leeway. When they offer, say, $100,000/year, that usually doesn't mean they're easily willing to go as high as $150,000/year. In the case at hand, for the candidate to break even on cost of living, he needs a 50% bump on his current salary to go to TheirTown: anything less is an effective pay cut. To create negotiating room, he's going to have to ask for considerably more than 50%, to have a hope of them settling at what he needs. If he's currently getting, say $70K, and he needs at least $105K to break even on cost of living, he's going to have to counter with somewhere around $140K, and it is highly unlikely that they have THAT much negotiating leeway.
5) To clarify, my answer was that his response should be to decline the offer and walk away. I don't see any upside in attempting to negotiate a reasonable offer, given that they appear to be starting so far apart.