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Incentive isn't u'(x), it's more like u'(x)/u(x). Scaling u''(x) doesn't change inequality anyway (as defined by measurements of u(b)/u(a) or the Gini index) s
by SamReidHughes 11y ago
Incentive isn't u'(x), it's more like u'(x)/u(x).
Scaling u''(x) doesn't change inequality anyway (as defined by measurements of u(b)/u(a) or the Gini index) so it's a poor stand-in for the kind of convexity people are complaining about.
- yummyfajitas 11y agoThe incentive is how much your utility increases - between state B and state A, that's u(B)-u(A) = u'(h)(B-A). Take limits and you get to u'(x) for marginal estimates. Inequality is most definitely NOT defined by ratios of a utility function. The convexity of the OP was in the utility function; he seemed to believe that convexity of reward (and hence of utility, assuming u(reward) is monotonic) would only increase the reward for those at the top.
- SamReidHughes 11y agoMaybe you should have made clear in your post, then, that u is utility, not income. If u is utility and v is income, then v'(x)/v(x) ~ u'(x), more or less. Most measures of inequality involve dollar ratios, which seem to correspond to differences in utility, or at least to self-reported happiness.