Monodromy of Walrasian Equilibrium Prices: A Fixed-Preference Endowment-Redistribution Construction

2026-09-18

AI Summary

研究解决了在经济基础循环变动下瓦尔拉斯均衡价格不回归原点的问题，通过构建固定偏好和再分配禀赋的模型，揭示了三商品是该现象发生的临界点。

Abstract

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.

Problem

• Walrasian equilibrium
• monodromy
• endowment redistribution
• fixed preferences
• commodity threshold

Innovation

• Walrasian Equilibrium
• Monodromy
• Endowment-Redistribution
• Structural Stability