The Long-run Behaviour of the Patinkin Model

In this paper I present conditions under which the long-run-stock equilibrium in Patinkin's general equilibrium model exists, is unique and is globally stable. These conditions are basically that all goods are weak gross substitutes and non-inferior. The model is developed in Patinkin (1965); Archibald and Lipsey (1958) were, I think, the first writers to study its long-run properties. The demonstration of the proposition is a straightforward application of Morishima's (1964) generalizations of the Perron-Frobenius theorems. Actually, the analysis applies to a somewhat wider class of models than Patinkin's, since the properties of his model which we use are those concerning the homogeneity of the demand and excess-demand functions. It is clear that these properties will be true of other money models as well. I make no particular defence of this model against, for example, the criticisms of Hahn (1965) and Clower (1967). However, the properties of it that I use are standard assumptions in expositions of neoclassical monetary theory (see also Friedman, 1969, and Samuelson, 1968). For that reason alone it seems worthwhile to investigate its long-run behaviour since it is only in the long run that the principal results of that theory hold

Economics · Economic theories and models · Economic Theory and Institutions · Economic Theory and Policy

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