Knowledge that Transforms

The comparative static effects of increased uncertainty in standard two-period models of consumer and producer behavior under uncertainty have been shown in [10 and 11] to be complex. Two principal objectives of this paper are: (i) to describe some assumptions, forms of risk independence, about preferences and technologies, that simplify the behavioral effects of increased variability; and (ii) to characterize the preferences and technologies that are consistent with risk independence. The theory of duality plays an important part in the analysis.

However, his example is based on an extreme assumption that the capitalists' propensity to consume, c, is unity. If, like Marx, we instead assume that c 0. To show this we use the generalized von Neumann model [2, 3], of which Petri's example is no more than a special case with c = 1. Assume c 0. By the two Lemmas to the Generalized Fundamental Marxian theorem [1], we know that e > 0 implies IrW > 0 and gC implies e > 0. Hence e > 0 rr > 0 ro > 0 gO > 0. Conversely 7r°> 0 g° > Ogc > 0 e>0O. Thus e>0 0 O. Thus, provided the capitalists save at least a part of their incomes for accumulation, the Generalized Fundamental Marxian Theorem holds not only for the warranted rate of profit and the capacity rate of growth but also for the equilibrium rate of profit and rate of balanced growth.

Lung-Fei Lee, G. S. Maddala, R. P. Trost, Asymptotic Covariance Matrices of Two-Stage Probit and Two-Stage Tobit Methods for Simultaneous Equations Models with Selectivity, Econometrica, Vol. 48, No. 2 (Mar., 1980), pp. 491-503

[In this paper we prove a global index theorem for general equilibrium models with activity analysis production technologies. We begin by constructing a single-valued function whose fixed points are equivalent to the equilibria of such a model. We then associate each fixed point with an index that is an integer determined by the local properties of this function at that point. The global index theorem makes a statement about the sum of all the indices of equilibria that implies conditions sufficient for uniqueness of equilibrium.]

[This paper is concerned with linear models. In this context it gives a necessary and sufficient condition for equality of two generalized least squares estimators of any subset of the parameters. The result is applied to many kinds of problems: the Frisch-Waugh problem, equality of OLS and GLS estimators, equality of the single equation GLS and the overall GLS estimators in seemingly unrelated regressions, equality of partial and overall 3SLS, lineartransformation of a linear model, superfluous observations, and mixed estimation.]