Competitive Equilibria in Economies with Multiple Divisible and Indivisible Commodities and No Money

A general equilibrium model is considered with multiple divisible and multiple indivisible commodities.In models with indivisibles it is always assumed that an indivisible commodity, called money, is present that is used to transfer the value of certain amounts of indivisible goods.For these economies with a finite number of divisible and indivisible goods and money and without producers it is well understood that a general equilibrium exists if the individual demands and supplies for the indivisibele goods belong to a same class of discrete convexity.In this paper we a model with multiple divisible and multiple undivisible commodities, in which none of the divisible goods may serve as money.Moreover, there are a finite number of producers owning a non-increasing returns to scale technology.One of the producesrs is assumed to have a linear production technology in order to produce divisible goods. Individual endowments being sufficienly large for production and discrete convexity guarantees the existence of a competitive equilibrium.