Rod Nillsen

This work has its origins in a proposal from the West Report (1998) on higher education in Australia. The West Report considered possible changes to the monies allocated to universities on the basis of research. One method of doing this, and its implications, were discussed by David Phillips in an article in The Australian newspaper (July 1, 1998, page 41). The work mentioned below was carried out in response to the David Phillips article, with the idea of using simple mathematics to clarify some of the issues. The talk and the papers below consider the issues as an abstract resource allocation problem. Using simple mathematics, the situation is analysed in somewhat more generality than in the article of Phillips, and the qualitative implications assessed. There is also a discussion of how, depending upon the circumstances, the parameters of the general procedure may be adjusted to avoid unacceptable outcomes, or to achieve ones considered desirable. You can download the following:

• An application of functions of the form (ax+b)/(cx+d) to modelling a problem of resource allocation, being slides of a talk given at the Mathematics Teachers' Day held at the University of Wollongong on June 27, 2006.
  
• Impacts on resource allocations when the relative importance of allocation criteria is changed ". a paper developing some of the ideas of the talk given at the Teachers' Day, including discussion of the distinctive contribution mathematical thinking potentially can make to the analysis of general social problems and policy.
  
• A version of the shorter paper "An application of elementary functions to a resource allocation problem " which will appear in the Australian Senior Mathematics Journal
  
• A copy of the newspaper article by David Phillips, in which he discusses some of the specific implications of some proposals in the West Report. I am grateful to David Phillips for giving permission to make his article available on this site.
• A copy of The West Report.
  

The formulation of resource allocation problems in general mathematical terms potentially provides a greater understanding of the strengths and deficiencies of particular procedures and an appreciation of possible alternatives. In Australian public policy, mathematics is generally seen as a secondary tool for data accumulation and associated arithmetical calculations. It is hoped that these papers may serve to show the potential for mathematical thinking to contribute to obtaining broad, qualitative insights into questions of public policy.

A controversial issue in Australia is the use of general taxpayer funds to provide subsidies for private or independent schools. (Note that in the UK these schools are called public schools). The Government often mentions that its policies save the taxpayer money, because subsidizing pupils going to private schools is cheaper than paying the full cost for those pupils to go to a government school. In 2005 the then Minster, Brendan Nelson, stated that Government policy saved taxpayers $4 billion per year. A talk based on this issue was given to mathematics school teachers at the University of Wollongong in June 2005. The basic question addressed in the talk was: is the current Government subsidy at a level that maximizes taxpayer savings? The accuracy of any conclusions depend upon the validity of the mathematical formulation of the problem, but the analysis is suggestive that the saving of public funds in this area of policy is an incidental effect of policy, rather than its main purpose. For example, under the assumptions , and if we further assume that 10% of pupils would go to independent schools even if there were no Government subsidy, the Government could save $1,252 million more than it does under current policy.

You can download the following:

• A short non-mathematical article (about 750 words) on this issue, originally submitted to a newspaper but unpublished
  
• Slides of the talk given to the school teachers
  
• A version of the paper "An application of quadratic functions to Australian Government policy on funding schools" which will appear in the Australian Senior Mathematics Journal
  

A purpose in giving the talk and writing the paper was to show how high school level mathematics could be used to clarify issues of public policy and controversy. The aim was also to illustrate mathematics as a way of thinking , not simply as a set of rules for calculation, and as a potential tool for sustained investigation of public issues at the high school level.

The analysis assumes a linear model for demand in relation to the subsidy, and this leads to a quadratic function for the savings in terms of the subsidy offered. However, high school mathematics discusses how to calculate the maximum value of a quadratic and where the maximum is attained. There are connections with the "Laffer curve", a mathematical curve (presumed quadratic) used in the USA under President Ronald Reagan as a reason for adjusting the tax rate.

Rod Nillsen, February 2007

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