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In Avengers: Age of Ultron, we get this exchange between Captain America (Steve Rogers) and Falcon (Sam Wilson):
Sam Wilson: Found a place in Brookyln yet?
Steve Rogers: I don't think I can afford a place in Brooklyn.
As CinemaSins points out, this seems unlikely.
Wait…you're a celebrity working in a highly-funded secret government agency, and you can't afford a place in Brookyln? What, are they paying you in 1940s money?
He raises a good point. SHIELD is pretty well-funded (they can afford lots of cutting edge tech). Steve has some money (otherwise he wouldn't be able to look for a place to live), so SHIELD must be paying him a salary. And that salary is surely generous given that he is one of their top agents. If nothing else, I would expect him to at least get salary equivalent to some of the top paid military personnel.
And even if that wasn't enough, as a celebrity (with his own museum!), surely Captain America could make money from public appearances (e.g. museum events, late night talk show, first pitch at a baseball game).
So why does Captain America not have the money to buy an apartment in Brookyln?