Many health-care systems use provider payment as an instrument to ensure an efficient and equitable delivery of care. Capitation-based payment schemes are popular because they contain costs. However, they are known to lead to underprovision of care, especially to high-need patients. Using a laboratory experiment, we test whether the availability of resources affects providers’ response to a capitation-based scheme. We find that the relative underprovision of care to high-need patients exists both when providers are resource abundant and constrained. Next, we introduce two different versions of the scheme and test whether they incentivize providers to take better care of high-need patients. One scheme ring-fences part of the capitation payment to a fixed physician salary, whilst the other scheme differentiates payments based on patients’ expected need of care. We find that high-need patients gain the most from a fixed provider salary under resource abundance, but find no difference in gains between patient types under resource constraint. Our results also show that differentiation of capitation makes providers take relatively better care of patients linked to an above average payment compared to a below average payment, regardless of resource constraints. Our findings suggest that both the design of the scheme and the market condition affect providers’ patient prioritization under capitation.