The Invisible Hand as an Emergent Property

Giorgio Fabbri, Davide Fiaschi and Cristiano Ricci
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Davide Fiaschi: Universtiy of Pisa, Dipartimento di Economia e Management, Pisa, Italy
Cristiano Ricci: Universtiy of Pisa, Dipartimento di Economia e Management, Pisa, Italy

No 2025013, LIDAM Discussion Papers IRES from Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES)

Abstract: We develop a multi-sector competitive economy where firms reallocate across sectors under myopic profit-seeking behaviour and quadratic reallocation costs. The dynamic path, formalised as a gradient flow in Wasserstein space, unfolds as a sequence of short-run competitive equilibria converging to a globally stable long-run competitive equilibrium. Two emergent properties arise: (i) decentralised and uncoordinated decisions of consumers and firms can be interpreted as solving a sequence of optimisation problems on aggregate consumption, which increases monotonically along the path; (ii) the long-run competitive equilibrium is efficient, as the distribution of firms maximises aggregate consumption and profit rates are equalised across sectors. These results are robust to extensions such as asymmetric preferences, labour immobility, and mild intrasectoral externalities, though they may fail under fixed reallocation costs. Using EU firm-level data (2018–2023), we find convergence in sectoral profit rates but not in labour productivity, indicating limited labour mobility. We also document moderate substitutability among goods, small intrasectoral externalities, and no significant fixed reallocation costs.

Keywords: out-of-equilibrium dynamics; positive general equilibrium theory; multi-sector economy; myopic firms; firm heterogeneity; intra-industry reallocation; Wasserstein space; gradient flow (search for similar items in EconPapers)
JEL-codes: C61 C62 D24 D50 D92 (search for similar items in EconPapers)
Date: 2025-09-08
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