Competitive Equilibria in Economies with Multiple Divisible and Multiple Divisible Commodities

In this paper we consider a general equilibrium model with a finite number of divisible and indivisible commodities.In models with indivisibilities it is typically assumed that there is only one perfectly divisible good, which serves as money.The presence of money in the model is used to transfer the value of certain amounts of indivisible goods.For such economies with one divisible commodity Danilov et al. showed the existence of a general equilibrium if the individual demands and supplies belong to a same class of discrete convexity.For economies with multiple divisible goods and money van der Laan et al. proved existence of a general equilibrium if the divisible goods are produced out of money using a linear production technology and no other producers are present in the model.In the models to be presented in this paper we allow for multiple divisible commodities and a finite number of producers with non-increasing returns to scale technologies.Convexity is replaced by pseudoconvexity, while the indivisible parts of individual demands and supply should belong to some class of discrete convexity.In the first model money is present.Money is strictly desired by the consumers like in the other models, is indispensable for production and enough money should be present in the economy.To guarantee existence of a general equilibrium individual demands and supplies should be products of divisible and indivisible parts.In the second model there is no money, but at least one linear production technology is present in order to produce the divisible goods.Individual endowments being sufficienly large for production guarantee the existence of a competitive equilibrium.