On the Determination of the Return to Capital when there is no Exogenous Ownership in Firms
This paper addresses the issue of the determination of return to capital when there is no exogenous ownership in firms. Hahn and Solow have proposed a notion of equilibrium for this setting and we consider this notion from a partial equilibrium point of view (i.e. under the assumption that the rate of return to capital is given). We present a study of the notion of compatible and perfectly compatible capital stocks with a given rate of return. A capital stock is compatible with a given rate of return if it yields a gross operating surplus per unit of capital equal to this rate of return. Perfectly compatible capital stocks are capitals which are compatible and which maximize “pure profit”, i.e. the difference between profit and the product of the rate of return times the capital stocks. Our assumptions encompass but are not reduced to the standard case where production sets exhibit constant returns to scales. Several examples of independent interest are presented. The results of this paper could be useful in the study of small open economies, or in a general equilibrium setting (with the usual assumption that firms are symmetric).
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