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For many years, the idea prevailed that it was impossible to model the classical analysis of competition and to obtain the results put forward by the classics: the existence and stability of a long-term equilibrium with an evenly distributed rate of profit among industries. This widely held view was due, in particular, to the work of H. Nikaido. In 1983, we presented a first model demonstrating the relevance of the classical analysis. A meeting in 1984 in Paris on the topic of "Gravitation", played a decisive role in the destruction of the negative a priori conception of the irrelevance of the classical view. A set of models were presented which transformed the general contention.

The purpose of this article is to describe a more elaborated model than those of 1983 and 1984 mentioned above. Three industries are considered. One important specificity of this model is that it includes a treatment of fixed capital. The first purpose of the present article is to provide the analytic treatment of the local stability of the classical long-term equilibrium in this framework. Then, the stability of long-term equilibrium in this model is illustrated using computer simulation. The notion of a "classical" short-term equilibrium is introduced.

G. Duménil, D. Lévy, "The Analytics of the Competitive Process in a Fixed Capital Environment", 1989, The Manchester School, Vol. LVII(1), pp. 34-57.

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