Optimal Redistribution With Productive Social Services

We analyze the optimality of alternative mechanisms of public provision of private goods affecting the productive capacity of households (e.g. education, health-care) rather than directly their welfare. Opting out mechanisms - often considered a tool to focus social expenditure - are proven to be welfare improving under the assumption that the provided good is not a substitute of households' exogenous productive capacity (say, inherited wealth). Conversely, when publicly provided goods are substitute of inherited productive capacity, topping up mechanisms prove more efficient.