If we do that then we would be trusting that tool, which doesn't look right to me. (I don't think that SF is 138% more expensive than Miami, FL.) Let's put whatever we make, knowing that it's just an approximation.
By the way, I'd rather live in an expensive city making proportionally more money, because my savings would also be proportionally larger, and when you're buying a plane ticket to Europe online or a pair of shoes at Zappos, they don't check your zip code to give you a price.
I live in San Francisco and it is probably 138% more expensive than Miami, FL. A cheapo 1br in the city runs around $1200 a month. Nice places cost $1500-2500 a month. I'm paying $2k a month myself but it's a really nice place w a Golden Gate Bridge, Alcatraz, and city view. How much are places in Miami?
That's only "renting" and prices are not too far off in Miami based on your numbers (a place equivalent to yours in Miami I would say cost "maybe" a little less). How about food, clothe, transportation? Are those things also more than twice more expensive? No way. For example, you can live without a car in SF because public transportation there is decent. In Miami you need a car as you need your legs.
And I'm not even considering the benefits that a globalized world brings to "expensive" cities. In other words, if we assume that everything is 138% more expensive in SF then savings will also be 138% larger and, in the "equivalence equation", you have to factor in the purchasing power of San Franciscans in markets outside SF and Miami, otherwise you'd be saying something of the sorts of: To maintain your standard of living when you move to SF from Miami you need to make 138% more money (and by the way, you'll get a 20 days vacation in Spain for free).
To be honest, you can usually shop better in large cities than you can in small ones. Flights are cheaper, you have more specialized discount stores, the amount of competition is higher. Big box pricing is also fairly consistent country wide. You'll find 'levi signature' jeans for $10 on clearance in the Mountain View Target and in the Austin Target.
As someone that moved to the bay area from Miami 6 years ago 138% sounds about right to me. Comparing apples to apples you would need to compare Biscayne, Coconut Grove, Coral Gables in Miami to SF. Those neighborhoods are $1,000 to $2,000 a month.
As someone making the move from Miami to SF I can give some approximations that are hopefully time-accurate. Brickell/Downtown/South Beach/Grove 1BR prices are in the $1200-1600 range down here now for a now standard pad. You can of course go much higher, but not much cheaper (cheapest I've seen is $1100, a total steal these days). I myself have paid $1250 or so the last few years, however the building I just left in Brickell now has 1BRs starting at $1400. Demand has certainly moved the price needle up in the cooler parts of town here. For a similar looking place in SF I'm looking at the $1800-$2000 range in similarly cool parts of town. I could of course venture out to the Richmond and save/get more space but that's the same anywhere. In keeping apples to apples I'm comparing the Miami areas above to Nob Hill/Russian Hill/North Beach/Marina/Pac Heights/Inner Richmond areas. If I'm off in the SF comparisons someone please DO let me know. :)
By the way, I'd rather live in an expensive city making proportionally more money, because my savings would also be proportionally larger, and when you're buying a plane ticket to Europe online or a pair of shoes at Zappos, they don't check your zip code to give you a price.