Xavier A, (2003)

‘Hospital Competition, GP Fundholders and Waiting Times in the UK Internal Market: the Case of Elective Surgery’

International Journal of Health Care Finance & Economics 3, pp. 25-51

A theoretical paper, aiming to model demand for and supply of NHS elective surgery using a “modified Hotelling” framework.
Xavier uses a duopoly model in which two NHS hospitals are located at opposite ends of a road. There are N potential patients, uniformly distributed along this road, and 2 GPs, each of whom has half the patients situated at each point on the road.
Fundholding is modelled by assuming that one GP on ‘the road’ becomes a GP fundholder (GPFH) while the other remains a cost-insensitive Health Authority funded GP. The cost-sensitive GPFH is no longer a perfect agent for his patients, as he takes referral cost as well as waiting times into account when making decisions.
GPFHs will pay a price for care that exceeds hospital marginal cost.
If GPFHs pay more than marginal costs, their patients will have zero waiting time. (Because at any given level of supply, raising the price paid by GPFH patients and decreasing waiting times leaves production costs unchanged but raises revenue, making the hospital better off.)
Health Authorities in Xavier’s model pay less for care than GPFHs, and less than hospital marginal costs, but their patients face positive waiting times.