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

Andrea Loi and Stefano Matta

Papers from arXiv.org

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.

Date: 2026-09
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