The Invisible Hand as an Emergent Property

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.