Convergence to Long-Run Equilibrium - On some Recent Variations of the Pure Cross-Dual Model

In some recent works on the dynamics of capitalistic competition Duménil and Lévy proposed two ways to overcome the problem of instability of long-run equilibrium in cross-dual models of gravitation: in the first one a different notion of rate of profit, the "realised" rate of profit is supposed to drive capitalists' investment decisions; in the second one the goal is pursued by introducing a direct adjustment of output in response to imbalances between demand and supply. In the present paper we argue that both these procedures rise a logical problem, concerning capitalists' behaviour and their information set, and we present a re-formulation of the model that avoids it.