The Debreu Gap Lemma and some generalizations

In this paper we study the Debreu Gap Lemma and its generalizations to totally ordered sets more general than (R, less than or equal to). We explain why it is important in economics to study utility functions which may not be real-valued and we build the foundations of a theory of continuity of such generalized utility functions. (C) 2004 Published by Elsevier B.V.

Uniqueness for boundary value problems for second order finite difference equations

We establish maximum principles for second order difference equations and apply them to obtain uniqueness for solutions of some boundary value problems.

Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

Conventional detection methodology is limiting our ability to understand the roles and functions of fine roots

We lack a thorough conceptual and functional understanding of fine roots. Studies that have focused on estimating the quantity of fine roots provide evidence that they dominate overall plant root length. We need a standard procedure to quantify root length/biomass that takes proper account of fine roots. Here we investigated the extent to which root length/biomass may be underestimated using conventional methodology, and examined the technical reasons that could explain such underestimation. Our discussion is based on original X-ray-based measurements and on a literature review spanning more than six decades. We present evidence that root-length recovery depends strongly on the observation scale/spatial resolution at which measurements are carried out; and that observation scales/resolutions adequate for fine root detection have an adverse impact on the processing times required to obtain precise estimates. We conclude that fine roots are the major component of root systems of most (if not all) annual and perennial plants. Hence plant root systems could be much longer, and probably include more biomass, than is widely accepted.

Output price subsidies in a stochastic world

This article studies the comparative statics of output subsidies for firms, with monotonic preferences over costs and returns, that face price and production uncertainty. The modeling of deficiency payments, support-price schemes, and stochastic supply shifts in a state-space framework is discussed. It is shown how these notions can be used, via a simple application of Shephard's lemma, to analyze input-demand shifts once comparative-static results for supply are available. A range of comparative-static results for supply are then developed and discussed.