I will avoid any mention of fairness since employment negotiations seldom have anything to do with fairness. You (we, me, us) are all commodities that our employers purchase.
Having said that, your employer offering you a "good, local wage" implies that they feel the position could be filled in the local labor market. My question (to myself but they need to provide information to answer) is "Why would they be willing to import skills if the position could be filled locally?" If there is a compelling reason why they feel they cannot fill the position locally, then local labor wage levels are really not relevant. The choice is what do you feel its worth and how does that compare to the other candidates whom they would consider moving into the position. If they feel they could fill the position locally I would question their decision to move someone down since the the success of that is every bit as risky as sourcing a local, unknown talent.
If the purpose is for the reason of career development, you have to weight your future earning potential (which is significant with a successful international management experience) and taking a short term(?) earning set back. Once again, if they value you this much, why would they be trying to discount you?
As for international assignment in general, going into a management situation on a temporary (2-3 years) basis has its own set of challenges. You may find issues are perfectly comfortable waiting you out for 2-3 years. Add the fact that no one anywhere like when a foreigner comes in to manage them, and that training, organizational learning, and process improvement all work on a timetable quite differently from country to country. I am on the 5th year of a 2-year temporary assignment. Things really didn't click until those working for me, and I, saw my assignment move from temporary to permanent.
If you don't like the lifestyle and your new work environment and the challenges both bring, no level of compensation will make it better. The opposite also applies.