Publication Details

This article will originally appear as Nillsen, R, An application of quadratic functions to Australian Government policy on funding schools, Australian Senior Mathematics Journal, Australian Association of Mathematics Teachers, 2006 (in press). Journal information available here.


In the Sydney Morning Herald newspaper of 23rd March 2005 the economics writer Ross Gittins argued that the funding arrangements for private schools in Australia positively encourage parents to move their children from the state system to the private system. The Federal minister, Dr Brendan Nelson, responded by saying that the policy of subsidising pupils who go to a private school results in taxpayer savings of $4 billion. However, the minister's response did not address the extent to which more funds could possibly be saved by having a different subsidy from the one currently offered by the government. Now, there are two conflicting factors in offering subsidies to private school pupils. On the one hand, the greater the subsidy per pupil, the more pupils will enroll in private schools. On the other hand, the greater the subsidy per pupil the less money will be saved each time a pupil enrolls in a private school. How do these factors balance out, and where would an optimal subsidy occur? The problem is closely related to other problems of optimisation that arise in business, industry and public policy. Mathematically, the problem can be modelled, at the level of school mathematics, by means of a quadratic function that describes how the savings to the taxpayer change as the subsidy changes. Further details are on the author’s website at http://www.uow.edu.au/~nillsen