Public and Private Health Care Financing with Alternate Public Rationing Rules

We develop a model to analyze alternative health care financing arrangements. Health care is demanded by individuals varying in income and severity of illness. There is a limited supply of health care resources used to treat individuals, causing some individuals to go untreated. We examine outcomes under full public finance, full private finance, and mixed, parallel public and private finance under two rationing rules for the public sector: needs-based rationing and random rationing. Insurers (both public and private) must bid to obtain the necessary health care resources to treat their beneficiaries. While public insurer's ability-to-pay is limited by its (fixed) budget; the private insurers willingness-to-pay reflects the individuals' willingness-to-pay for care. When permitted, the private sector supplies supplementary health care to those willing and able to pay. We find that the introduction of a private sector diverts treatment from relatively poor to relatively rich individuals. Moreover, if the public system allocates care according to need, then the average severity of the untreated is higher in a mixed system than in a pure public system. While we can unambiguously sign most comparative static effects for a general set of distribution functions, an analysis of the relationship between public sector rationing and the scope for a private health insurance market requires distributional assumptions. For a bivariate uniform distribution function we find that the private health insurance market is smaller when the public sector rations according to need as compared to random allocation of health care.