The structure and stability of competitive dynamical systems

In recent neoclassically and classically oriented literature on competitive processes several models have been presented which work not only with the ‘law of demand’ but also with the ‘law of profitability’. In such dynamical models a cross-dual process is stylized in which price changes are initiated by imbalances in supply and demand and changes of outputs are caused by profitability differentials. Such cross-dual dynamics can now be found in neoclassical tradition (Morishima 1976, 1977; Mas–Colell 1974, 1986) and in classical tradition. In classical tradition the analysis of such a cross-dual adjustment process was initiated particularly by some recent publications of Nikaido (1978, 1983, 1985) who questioned the stability of classical competition. In comparison to his results it is the purpose of this article to show that the classical approach to the dynamics of competition may be able to produce stability results which are of at least comparable interest to those of neoclassical stability theory.

Classical and Neoclassical Competitive Adjustment Processes

The authors consider an otherwise conventional monetary growth model in which spatial separation and limited communication create a transactions role for currency, and stochastic relocation gives rise to financial intermediaries. In this framework they consider how changes in fiscal and monetary policy, and in reserve requirements, affect inflation, capital formation, and nominal interest rates. There is also considerable scope for multiple equilibria; the authors show how reserve requirements that never bind along actual equilibrium paths can play an important role in avoiding undesirable equilibria. Finally, they demonstrate that changes in (apparently) nonbinding reserve requirements can have significant, real effects. Coauthors are Mark G. Guzman, Elisabeth Huybens, and Bruce D. Smith. Copyright 1997 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Monetary, Fiscal, and Reserve Requirement Policy in a Simple Monetary Growth Model

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The "saddlepoint property" and the structure of dynamic heterogeneous capital good models

The invariance principle and income-wealth conservation laws: Application of Lie groups and related transformations

C. CATON and K. SHELL University of Pennsylvania The basic result of Hahn's seminal contribution to the descriptive theory of hetero- geneous capital accumulation [2] is that the short-run-perfect-foresight balanced-growth equilibrium is a saddlepoint in the space of capital-labour ratios and capital goods prices. In the context of a special model, Shell and Stiglitz [5] show further that on paths not tending to balanced growth, price ratios become zero (or infinite) in finite time. If machines are freely disposable, asset markets cannot be in equilibrium on such " errant " trajectories. A recent paper by Atkinson [1] has pointed out some very special features of the Shell-Stiglitz technology, casting some doubt on the generality of the conclusions. In the present paper, we investigate the " Hahn problem " in the context of a more regular model of production, the " quarter-circle" technology employed by Samuelson in his study of joint production [4]. As in the previous studies, we find that the unique balanced-growth equilibrium is a saddlepoint, and on paths not tending to balanced growth the price ratio becomes zero or infinite in finite time. 1. THE MODEL As in [5], we study a one-sector, two-capital model in which a homogeneous output, Y, is produced by the cooperation of labour, L, machines of the first kind, K1, and machines of the second kind, K2. Assuming constant returns-to-scale and denoting quantities per unit labour by lower case letters, the production relation can be written as y = f(kl, k2). For ease of analysis we assume that the production function is linear in logarithms, so

C. Caton

Papers

An Exercise in the Theory of Heterogeneous Capital Accumulation