Homothetic functions revisited

Summary. This paper examines the proposition that homotheticity is equivalent to the property that (e.g., in the context of a production function) the marginal rate of substitution is constant along any ray from the origin. This claim is made in many places, but hitherto the prerequisites have not been stated explicitly. In the present contribution it is demonstrated that an additional condition is required for the claim to hold. We present a theorem that achieves equivalence by also assuming ‘nowhere ray constancy’. It turns out that this condition is implied by assumptions often made, e.g., in production theory. Further, a complete characterization is given of the class of functions that satisfy ray constant marginal rates of substitution or, somewhat more generally, a condition of ray parallel gradients. In addition to homothetic functions this class contains functions homogeneous of degree 0 (i.e., ray constant) and functions which are homothetic in disjoint regions separated by regions of ray constancy. Received: November 5, 1999; revised version: October 31, 2000     

Equivalence between welfare and entropy approaches to residential location

An optimization model for residential location in an urban area is presented. As the objective, a welfare measure is considered which is derived as aggregated expected utility based on utility-maximizing individual behaviour. The utilities include travel costs for work trips as well as a measure of the disutility with high-density living. The problem of finding a welfare maximizing housing allocation is shown to be equivalent to an entropy maximizing problem provided that a certain condition is met. By considering a dual formulation, a computationally more expedient problem is obtained. The model approach is illustrated by a few applications to the Stockholm region.     

A Transition Cost Rationale for Transition of the Firm within the Family

Small Business Economics - This paper is about the transition of ownership of shares in small and medium-sized enterprises (SMEs) within the family (i.e. from parents to children). In spite of the...