Walras and dividends equilibrium with possibly satiated consumers

The main contribution of the paper is to provide a weaker nonsatiation assumption than the one commonly used in the literature to ensure the existence of competitive equilibrium. Our assumption allows for satiation points inside the set of individually feasible consumptions, provided that the consumer has satiation points available to him outside this set. As a result, we show the concept of equilibrium with dividends [see Aumann, R.J., Drèze, J.H., 1986. Values of markets with satiation or fixed prices. Econometrica 54, 1271–1318; Mas-Collel, A., 1992. Equilibrium theory with possibly satiated preferences. In: Majumdar, M. (Ed.), Equilibrium and Dynamics: Proceedings of the Essays in Honour of David Gale. MacMillan, London, pp. 201–213] is pertinent only when the set of satiation points is included in the set of individually feasible consumptions. Our economic motivation stems from the fact that in decentralized markets, increasing the incomes of consumers through dividends, if it is possible, is costly since it involves the intervention of a social planner. Then, we show, in particular, how in securities markets our weak nonsatiation assumption is satisfied by Werner [Werner, J., 1987. Arbitrage and the existence of competitive equilibrium. Econometrica 55, 1403–1418] assumption.