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Given a bounded open subset Ω of R d and two positive weight functions f and g, the Cheeger sets of Ω are the subdomains C of finite perimeter of Ω that maximize the ratio C f (x) dx ∂ * C g(x) dH d−1. Existence of Cheeger sets is a well-known fact. Uniqueness is a more delicate issue and is not true in general (although it holds when Ω is convex and f ≡ g(More)
Following the recent analysis of Lucas and Rossi-Hansberg [10], we study the equilibrium structure of cities. By adopting a different (monetary) specification of commuting costs, we are able to prove the existence of equilibrium in more general situations: non-circular cities, or multi-sectorial production. The main mathematical tool in this paper is the(More)
Typical welfare and inequality measures are required to be Lorenz consistent which guarantees that inequality decreases and welfare increases as a result of a progressive transfer. We explore the implications for welfare and inequality measurement of substituting the weaker absolute differentials, deprivation and satisfaction quasi-orderings for the Lorenz(More)
We consider a problem of derivatives design under asymmetry of information: the principal sells a contingent claim to an agent, the type of whom he does not know. More precisely, the principal designs a contingent claim and prices it for each possible agent type, in such a way that each agent picks the contingent claim and pays the price that the principal(More)