Existence and welfare properties of equilibrium in an exchange economy with multiple divisible and indivisible commodities and linear production technologies (Q1601454)

The authors consider an exchange economy with a finite number of divisible commodities, indivisible goods, linear production technologies and a finite number of agents. It is assumed that each agent initially owns one indivisible object and a certain amount of one of the divisible commodities, say, commodity zero, and that each agent can demand any amount of each of the divisible commodities, but demands at most one indivisible object. Commodity zero is served as labor or capital and is used as input to produce the other divisible commodities. It is proved that there exists a competitive equilibrium in the economy provided the utility functions representing preferences of agents are weakly monotonic on both commodity zero and the indivisible commodities and are continuous on the divisible commodities, and if each agent initially owns in some sense a sufficient amount of commodity zero. The usual convexity assumption is not required here. By imposing strong monotonicity of the utility on commodity zero it is shown that any competitive equilibrium is in the core of the economy and therefore the first theorem of welfare holds. Finally, the second welfare theorem stating that any Pareto efficient allocation satisfying some condition can be sustained by a competitive equilibrium allocation for some well-chosen redistribution of the total initial endowments is obtained.