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Pricing Policies When Patients are Heterogeneous: A Welfare Analysis

In this paper we use a simple theoretical model to compare alternative regulation regimes for the reimbursement of medical innovations when responses to a new treatment (effectiveness) are heterogeneous within the eligible population. We study two dimensions: i) efficiency in selecting sub-groups of patients for which the new technology is reimbursed, ii) distribution of rent between firm and payer. We show that when rational behaviour of profit maximizing firms is taken into account stratified cost-effectiveness analysis and marginal value based prices lead to the same equilibrium, which is efficient only if the population is sufficiently homogeneous. Inefficiency arises because some patients that should be treated are not. On the other hand, prices based on the average value may allow for an efficient solution even when heterogeneity is large. With limited heterogeneity efficiency may be achieved even if part of the rent is retained by the payer. We show that stratified cost-effectiveness analysis is an optimal policy for the payer under the constraint that the price is set by the firm, who knows that the payer will define the number of patients to reimburse in order to maximize total net benefit. However, this policy is only efficient from the societal perspective when the eligible population is sufficiently homogeneous. When heterogeneity is substantial, the number of patients treated is inefficiently low. On the other hand, average value based prices always allow for an efficient solution, provided that some conditions are satisfied. These conditions imply that the fraction of rent that needs to be left to the firm to achieve efficiency is non-decreasing in the degree of heterogeneity in effectiveness.