Walrasian均衡价格的单值性：一种固定偏好禀赋再分配构造
Monodromy of Walrasian Equilibrium Prices: A Fixed-Preference Endowment-Redistribution Construction
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中文总结 AI 辅助
本文构造固定偏好下仅变动禀赋的闭路径，证明三种及以上商品时Walrasian均衡价格沿环可能不返回自身，揭示局部正则性不足以保证全局路径无关性。
中文摘要 AI 辅助
假设一个经济体沿着基本面的闭路径连续移动，并精确地返回到其初始状态。沿着该路径连续跟踪的正则Walrasian均衡价格未必返回到其自身。对于每种商品数量$L\ge3$，我们构造了一个封闭的单参数纯交换经济族，其中所有偏好都是固定的，只有三个个体禀赋变化，且总资源保持不变。沿着该环，两个正则均衡价格分支被交换，而第三个分支返回到自身；在终点，每个经济原始变量都精确地回到初始状态。该构造最多使用$2L+2$个消费者。我们还提供了一个精确实现，最多使用$2L$个消费者，其中所有禀赋固定且只有一个偏好变化；这两个族生成相同的总超额需求。关键的实现问题是参数化的：经典的总体实现结果保证在每个固定参数值处存在一个经济，但不保证实现原始变量的连续环。我们显式地构造了这样一个环。由此产生的单值性在足够小的$C^1$扰动下是结构稳定的。对于一或两种商品，这是不可能的，使得三种商品成为尖锐阈值。因此，局部正则性保证了局部连续性，但不保证均衡分支的全局路径无关同一性，这对多重性下的全局比较静态和基于连续性的均衡选择具有意义。
英文摘要
Suppose an economy moves continuously along a closed path of fundamentals and returns exactly to its initial state. A regular Walrasian equilibrium price followed continuously along that path need not return to itself. For every number of commodities $L\ge3$, we construct a closed one-parameter family of pure-exchange economies in which all preferences are fixed, only three individual endowments vary, and aggregate resources remain constant. Along the loop, two regular equilibrium-price branches are exchanged while a third returns to itself; at the end, every economic primitive is exactly as it was initially. The construction uses at most $2L+2$ consumers. We also provide an exact realization with at most $2L$ consumers in which all endowments are fixed and only one preference varies; the two families generate identical aggregate excess demand. The key realization problem is parametric: classical aggregate-realization results guarantee an economy at each fixed parameter value, but not a continuous loop of realizing primitives. We construct such a loop explicitly. The resulting monodromy is structurally stable under sufficiently small $C^1$ perturbations. It is impossible with one or two commodities, making three commodities the sharp threshold. Thus local regularity guarantees local continuation but not a globally path-independent identity of an equilibrium branch, with implications for global comparative statics under multiplicity and for equilibrium selection based on continuation.
发表机构
- Università di Cagliari（卡利亚里大学）
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