Opportunity-based other-regarding preferences in general equilibrium: existence

We consider a pure exchange economy with a finite number of goods and households. Following the path-breaking paper by Kranich, we introduce two differences with respect to the standard model: (i) each household utility function depends not only on her own consumption but also on other households’ welfare, measured by wealth; then, other-regarding preferences are based on other households opportunities; (ii) households are allowed to promise transfers to other households and the promises are bound to be honored. We provide a proof of existence of equilibria, solving several problems which are not addressed by the paper by Kranich. We present a robust example of non-existence of equilibria if the crucial assumption of an upper bound on transfers is violated. As a mathematical by-product of our analysis, we give easy-to- check conditions that ensure that commonly used constraint set-valued functions satisfy properties that are needed to apply standard existence theorems.