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.

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.

The production of male of-only offspring in beef cattle - a proof of principle project

The Australian beef industry places the greatest value in bulls, in comparison to cows, for prime beef production. Male carcasses can be sold for a larger profit due to their increased muscle mass. This project aims to demonstrate the feasibility of producing male animals that can sire male only offspring, through a transgenic approach in mice that could later be translated into livestock production systems. The mouse Sry (Sex determining region on the Y) gene has been shown to provide the initiating molecular signal leading to male sex determination in mammals. Sry has also been shown to cause sex reversal in XX mice transgenic for the gene. In this project Sry will be targeted to a locus not subject to X-inactivation on the X chromosome of XY mice. These mice will be bred to determine how the transgene is passed on, to determine expression of the transgene, and to assess its activity in causing XX sex reversal. The male mice transgenic for the Sry gene on their X chromosome will be produced using tetraploid aggregation, which in a single step produces 100% ES cell derived embryos. The same target locus can later be used to introduce the bovine SRY gene onto the X chromosome of bovidae species and using germ cell transplantation produce sex reversed animals. This would bypass the need for expensive chimera crosses and provide farmers with a stud bull capable of producing only sons.