Topping up or opting out? The optimal design of public provision schemes

There is extensive public provision of private goods in all developed countries. The public provision scheme is often designed so that individuals can opt out, but not top up (supplement) the publicly provided quantity/quality. Using an optimal income tax/public provision model we derive the respective conditions under which a public provision scheme should allow or forbid supplementing. Disregarding administrative costs, a system where individuals are not allowed to top up is optimal if the demand for the publicly provided good increases in the amount of leisure available, while a scheme allowing individuals to top up is warranted if the demand decreases with the amount of leisure.