Knowledge that Transforms

[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.]

[This paper provides a generalization of Sen's poverty measure. The generalization is motivated by the failure of Sen's poverty measure to satisfy some transfer-sensitivity axioms proposed in this paper. A numerical method of computing the alternative poverty measures is provided along with an illustration based on the data from the Australian household expenditure survey carried out during 1974.]

This paper presents a decomposition of the total effect of a change in a quantity constraint on the money income constant conditional demand function into an income compensated substitution effect and a pure income effect. The substitution effect is shown to be equivalent to the Hicks substitute-complement relation while the income effect is shown to depend directly on the extent of over- or under-supply of the constrained good. The Tobin-Houthakker results on rationing constraints can be generalized in an intuitive manner to cases of non-optimal values of the constraint when the two goods involved are: (1) Hicks substitutes, the constrained good is over-supplied and the unconstrained good is a normal good; or, (2) Hicks complements, the constrained good is under-supplied and the unconstrained good is a normal good. In the case of substitutes and under-supply or complements and over-supply, the sign of the Hicks substicute-complement relation is not sufficient to determine the sign of the partial derivative of interest. Several applications of the theoretical results are also presented.