Price adjustment in the hospital sector

Prospective payment systems are currently used in many OECD countries, where hospitals are paid a fixed price for each patient treated. We develop a theoretical model to analyse the properties of the optimal fixed prices to be paid to hospitals when no lump-sum transfers are allowed and when the price can differ across providers to reflect observable exogenous differences in costs (for example land, building and staff costs). We find that: a) when the marginal benefit from treatment is decreasing and the cost function is the (commonly used) power function, the optimal price adjustment for hospitals with higher costs is positive but partial; if the marginal benefit from treatment is constant, then the price is identical across providers; b) if the cost function is exponential, then the price adjustment is positive even when the marginal benefit from treatment is constant; c) the optimal price is lower when lump-sum transfers are not allowed, compared to when they are allowed; d) higher inequality aversion of the purchaser is associated with an increase in the price for the high-cost providers and a reduction in the price of the low-cost providers.