Tax/subsidy and capacity decisions in a two-tier health system with welfare redistributive objective

We study the tax/subsidy and capacity decisions of the public sector in a two-tier health system with a welfare redistributive objective. Public care is considered as a public provision of private goods and can be used to achieve welfare redistribution. The public sector is financed through general taxation, offering free but delayed service. The private sector offers delay-free service at a price. Patients choose between public and private care to maximize their expected net surplus. The system planner assigns weights to patients with different delay sensitivities, with the objective of maximizing the total weighted patient welfare by choosing the tax/subsidy and capacity decisions. We show that if the system planner treats all patients equally, she tends to imposes a lower tax on or provide a higher subsidy to private care. In the case of equal weight, the larger the capacity of the public sector, the more the tax/subsidy policy can improve the total patient welfare. If the planner is more concerned about the welfare of patients with low delay sensitivities, she should subsidize private care only when the capacity of the public sector exceeds a threshold. The subsidy is then used to induce patients with high delay sensitivities to seek private care. With more patients being served in the private sector, the total cost incurred in the public sector is lowered, and so is the general tax burden borne by patients with low delay sensitivities. In the case of unequal weight, the tax/subsidy policy results in a larger welfare improvement when the public sector has either a small or a large capacity. Finally, we discuss the capacity decision of the public sector given a fixed tax/subsidy.