Abstract:

This paper develops a dynamic industry model within a general equilibrium framework to examine the effects of intra-industry reallocation on aggregate behavior. The analysis focuses on scenarios where, in the short run, sectoral factor returns are not necessarily equal due to the presence of temporarily immobile factors. Specifically, the paper adapts Sonnenschein (1982) to an economy composed of short-sighted competitive firms and workers who move across sectors in response to differential factor returns under quadratic movement costs. 

We demonstrate that the macrodynamics of the system can be represented as a gradient flow. Consequently, the dynamics of firm sectoral distribution—i.e., the sequence of short-run general equilibria—can be interpreted as a sequence of instantaneous aggregate optimizations. In the continuous-time limit, this process is characterized by a partial differential equation. We establish the existence, global stability, and efficiency of the long-run equilibrium under varying conditions of consumer preferences, technology, and labor mobility. Furthermore, we analyze the properties of the convergence path, which reveals specific dynamic aggregate efficiency, even when it arises from the uncoordinated actions of individual firms. 

When only quadratic movement costs are present, the economy converges to a unique long-run equilibrium, regardless of the initial distribution of firms. In this equilibrium, sectoral profit rates are equalized, and the distribution of firms across sectors reflects sectoral productivity (and sectoral labor allocation, in cases of labor immobility). Conversely, when fixed movement costs are introduced, an infinite number of equilibria can emerge, with the specific outcome heavily influenced by initial conditions, sectoral profits, and productivity levels. Additionally, the presence of increasing returns driven by intra-sectoral positive externalities amplifies initial productivity differentials, whereas congestion effects or negative pecuniary externalities counteract these disparities .

Joint work with Davide Fiaschi et Cristiano Ricci

Location:

Room Malinvaud, CEPS University of Val d'Essonne
Boulevard François Mitterrand, 91025, Evry