Student Financial Aid:The Roles of Loans and Grants (Working Paper 37)

This paper addresses the roles of loans and grants as forms of student financial aid. It begins with a simple choice model where individuals decide to pursue post-secondary studies if i) the net benefits of doing so are positive and ii) no financing or liquidity constraints stand in their way. The effects of loans and grants on these two elements of the schooling decision are then discussed. It is argued that based on equity, efficiency, and fiscal considerations, loans are generally best suited for helping those who want to go but face financing constraints, whereas grants are more appropriate for increasing the incentives for individuals from disadvantaged backgrounds to further their studies. Loan subsidies, which make loans part-loan and part-grant, are also discussed, including how they might be used to address “debt aversion”. Given that subsidised loans have a grant (subsidy) element, while grants help overcome the credit constraints upon which loans are targeted, the paper then attempts to establish some general rules for providing loans, for subsidising the loans awarded, and for giving “pure” grants. It concludes with an application of these principles in the form of a recent proposal for reforming the student financial system in Canada. *

An impulsive differential equation model for Marek's disease

Many dynamical processes are subject to abrupt changes in state. Often these perturbations can be periodic and of short duration relative to the evolving process. These types of phenomena are described well by what are referred to as impulsive differential equations, systems of differential equations coupled with discrete mappings in state space. In this thesis we employ impulsive differential equations to model disease transmission within an industrial livestock barn. In particular we focus on the poultry industry and a viral disease of poultry called Marek's disease. This system lends itself well to impulsive differential equations. Entire cohorts of poultry are introduced and removed from a barn concurrently. Additionally, Marek's disease is transmitted indirectly and the viral particles can survive outside the host for weeks. Therefore, depopulating, cleaning, and restocking of the barn are integral factors in modelling disease transmission and can be completely captured by the impulsive component of the model. Our model allows us to investigate how modern broiler farm practices can make disease elimination difficult or impossible to achieve. It also enables us to investigate factors that may contribute to virulence evolution. Our model suggests that by decrease the cohort duration or by decreasing the flock density, Marek's disease can be eliminated from a barn with no increase in cleaning effort. Unfortunately our model also suggests that these practices will lead to disease evolution towards greater virulence. Additionally, our model suggests that if intensive cleaning between cohorts does not rid the barn of disease, it may drive evolution and cause the disease to become more virulent.