Structural Change and Economic Dynamics 10 (1999) 225 – 237 Convergence to long-run equilibrium — On some recent variations of the ‘pure’ cross-dual model Enrico Bellino * Uniersita ` Cattolica del Sacro Cuore, Largo Gemelli, 1, 20123 -Milano, Italy Accepted 21 April 1998 Abstract In some recent works on the dynamics of capitalistic competition Dume ´nil and Le ´vy 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. © 1999 Elsevier Science B.V. All rights reserved. JEL classification: D46; D50; E11 Keywords: Capitalistic competition; Gravitation; Long-run equilibrium; Market prices; Natu- ral prices 1. Introduction In some recent works, Dume ´nil and Le ´vy proposed two ways of overcoming the problem of local instability of long-run equilibrium in cross-dual gravitation models. The first method is based on the use of a particular notion of rate of profit, the ‘realized’ rate of profit, on which capitalists base their investment decisions. This notion, being based on actually cashed returns, appears most appropriate to * Tel: +39 272 342693; fax: +39 272 342406; e-mail: ebellino@mi.unicatt.it 0954-349X/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII S0954-349X(98)00042-3