⁵Jensen’s inequality (Jensen 1906) states that for any strictly concave function u defined on a random variable X with expected value E(x), we get u(E(x)) > E(u(x)). In social welfare theory, this means that, for any concave individual utility, the average welfare of an egalitarian distribution is always higher than the average welfare obtained through any other distribution of the same total amount of resources. In the example above Jensen’s inequality refers to the distribution of urban amenities across cities a and b.