Existence and Welfare Properties of Equilibrium in an Exchange Economy with Multiple Divisible and Indivisible Commodities and Linear Production Technologies
Existence and Welfare Properties of Equilibrium in an Exchange Economy with Multiple Divisible and Indivisible Commodities and Linear Production Technologies
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多种可分割和不可分割商品及线性生产技术的交换经济中均衡的存在性和福利性质
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发表时间：
2002
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通讯作者：
Zaifu Yang
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作者：
G. Laan;Dolf Talman;Zaifu Yang
本文考虑一类具有有限数量可分商品、线性生产技术、不可分商品和有限数量代理人的经济。这一类中有几个著名的经济体，它们以不可分割的商品和货币为特例。结果表明，如果效用函数在可分商品上是连续的，且在可分商品中的一种和所有不可分商品上都是弱单调的，如果每个代理人最初拥有足够数量的可分商品中的一种，并且如果生产部门的“无生产无投入”假设成立，则该类中任何经济都存在竞争均衡。这里不需要通常的凸性假设。此外，通过对一种可分商品施加强单调性，我们表明任何竞争均衡都位于经济的核心，因此福利第一定理也成立。我们进一步得到了第二个福利定理，证明在一定条件下，对于总初始禀赋的一些精心选择的再分配，竞争均衡分配可以维持帕累托有效分配。
In this paper we consider a class of economies with a finite number of divisible commodities, linear production technologies, and indivisible goods, and a finite number of agents. This class contains several well-known economies with indivisible goods and money as special cases. It is shown that if the utility functions are continuous on the divisible commodities and are weakly monotonic both on one of the divisible commodities and on all the indivisible commodities, if each agent initially owns a sufficient amount of one of the divisible commodities, and if a "no-production-without-input"-like assumption on production sector holds, then there exists a competitive equilibrium for any economy in this class. The usual convexity assumption is not needed here. Furthermore, by imposing strong monotonicity on one of the divisible commodities we show that any competitive equilibrium is in the core of the economy and therefore the first theorem of welfare also holds. We further obtain a second welfare theorem stating that under some condtions a Pareto efficient allocation can be sustained by a competitive equilibrium allocation for some well-chosen redistribution of the total initial endowments.