Relative wealth, status-seeking, and catching-up
We show that, if relative wealth appears in the utility function, for example due to status seeking, then under certain conditions on the curvature of the utility function and the production function, the poor will eventually catch up with the rich. We give sufficient conditions for the final distribution of wealth to be independent of the initial distribution, and conditions for saddlepoint stability in a two-class model. Nous démontrons que si l'utilité est une fonction de la richesse relative, peut-être à cause de la recherche du standing, alors, sous certaines hypothèses concernant la courbature de la fonction d'utilité et de la fonction de production, les gens pauvres peuvent rattraper les gens riches. Nous donnons des conditions suffisantes pour que la distribution de richesse finale soit indépendante de la distribution initiale, ainsi que les conditions suffisantes pour la stabilité au sens du point de selle.
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