Competitive equilibria in economies with multiple divisible and indivisible commodities and without money

A general equilibrium model is considered with multiple divisible and multiple indivisible commodities. In models with indivisibles it is typically assumed that an indivisible commodity, called money, is present that is needed to transfer the value of amounts of indivisible goods. For economies with divisible and indivisible goods and money and without producers it is well understood in the literature that a general equilibrium exists if the individual demands and supplies for the indivisible goods all belong to the same class of discrete convexity. In this paper we consider economies with multiple divisible and multiple indivisible commodities, but without money as one specific commodity for value transfer. Moreover, we allow for one or more producers that own a nonincreasing returns to scale technology. However, one of the producers has a production technology which is linear in producing divisible goods. In this way the composite of the divisible goods takes over the role of money in the model. Individual endowments being large enough for production together with discrete convexity guarantees the existence of a competitive equilibrium using Kakutani’s fixed point theorem.