When is a dollar not worth a dollar?

Joseph and I have been putting up a number of post on compensation recently (many inspired directly or indirectly by Felix Salmon), but there is something important that's been left out of the discussion both here and on the other blogs I've been reading on the subject:

Some dollars are worth more than others.

Having bounced back and forth from statistician to teacher to entrepreneur over the years, I've seen plenty of large fluctuations in income and I've developed a pretty good idea of what it costs to live comfortably as a single person in various cities.

In LA the cutoff is somewhere around thirty thousand. For that money you can get a decent apartment in pleasant neighborhood and still have enough income left over both to meet your basic needs and to get out and have some fun. (LA is one of the world's great cheap-eats towns)

If you go from mid-thirties to mid-nineties (which I did at one point), you will see a significant change in your lifestyle but it is nothing compared to the change you'll feel if you go from the mid thirties to the low twenties. Below thirty you start facing some ugly compromises. You may have to move to a rough part of town, Food becomes a larger part of your budget. Costs associated with work (wardrobe, transportation) remain annoyingly constant. Going out with friends becomes a great luxury (it's hard to convince the bartender to sell you two-thirds of a beer)

This discrepancy in lifestyle suggests the need for a different metric. Here's an example. To make the numbers come out even, let's talk about three incomes: 21K, 30K, 90K with our hypothetical Angeleno starting in the middle. In both absolute (60K) and relative terms (200%) the jump to the top tier dwarfs the jump to the bottom (9K/30%) but in impact on quality of life, the exact opposite holds.

What does all this mean? For one thing, it means that expected value and marginal changes are not the right tools to look at compensation, at least not in the way we normally use them. It means that the problem requires more of a piecewise approach.