ABSTRACT OF PAPER
Title: An Analytical Foundation of the Classical Idea of Long-Period Price with Differential Profit Rates
Author: D'Agata Antonio, Mori Kenji
The modern analysis of classical long-period price configurations is characterized by the systematic use of the assumption of uniform profit rate. The uniformity of the profit rate has been intuitively explained as the consequence of the assumption of free competition, that is of free capital mobility across industries. In fact, according to the traditional interpretation, if this condition is satisfied, then producers will move their capital across sectors until a uniform profit rate is attained. This approach has two shortcomings: first, it is a partial way of formalizing the classical idea of competition conceived as free capital movement across sectors. In fact, classical economists expressly recognize in their works the persistence of differential profit rates even in the long run due not only to “barriers to entry”, which hamper free movement of capital, but also to specific behavior of producers determining their investment decision in sectors. Second, because by continuing to justify the assumption of profit rate uniformity on the ground of an informal notion of free competition, the literature precludes the way to constructing a rigorous theory of the classical view of price formation being able to explain the uniformity of profit rates. This state of affairs clearly calls for the development of models in which the classical view of long-period price formation is developed in a rigorous way and which is compatible with differential profit rates. The aim of this paper is just to propose a contribution along this direction. More specifically, by following Smith and Ricardo’s view concerning the possibility of differential profit rates even with free mobility of capital due to factors affecting producers‘ investment decision, we develop a multisectoral model which allows to select a subset of the feasible profit rate set supporting long period configurations. Our model is also able to spell out precise conditions which must hold to necessarily have uniformity of the profit rates in the long period as well as conditions excluding the possibility of existence of a long period configuration with uniform profit rates. The paper is organized as follows. First, we shall briefly describe Smith and Ricardo’s view concerning the factors determining differential profit rates. We emphasize that according to them it is possible to have differential profit rates even with free mobility of capital. Second, we formalize this view in a two sectoral model and provides some results concerning the set of long period profit rate vectors. Finally, we generalize the model to the n-sector case.
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