Lets go one step further - don't tell them where you're (going to) live. Now what can they do? Guess? Because really its no more your employer's business than what car you drive or your kids' names.
Although I agree with the basic premises - equal pay for equal work, employee should get the benefits of lower cost of living - I think it is the employer's business in more ways than one. Taxes, time zone, internet connection - many things could come into play. Not to mention the golden handcuffs it could create if the employee is drastically overpaid for their local market.
Ok I'm agreeable to tell the employer what time zone I'm in, but that's about it. The rest I'll tell HR after I'm hired, so they can fill in their forms.