This paper revisits the problem of optimal public good (or public bad) provision under optimal non-linear income taxes, where the main methodological novelty is that we allow for heterogeneity in preferences and exposure to the public good, by using a modern interpretation of the perturbation approach. This generalization is shown to have crucial implications for the optimal provision rule, and in particular with respect to distributional concerns. The optimal provision rule is shown to deviate from the Samuelson rule in relation to the differences between cross-section and individual income elasticities of the marginal willingness to pay for the public good. This implies that, contrary to the conventional view, it is often optimal to take distributional concerns into account also in cost-benefit analysis, and thus not to delegate such concerns solely to the tax and transfer system.

Applied welfare analysis relies on willingness-to-pay estimates. When the government provides goods that are non-rival or non-excludable, however, willingness to pay is hard to elicit. We characterize a local direct mechanism that truthfully elicits status-quo marginal willingness to pay under general preferences. Allowing arbitrary welfare weights and policy costs that include fiscal externalities generated by mechanism transfers, we characterize the welfare-maximizing local public-good reform at each report profile. The reform is locally incentive compatible when its implemented weighted marginal value of public funds exceeds the welfare cost of raising a public dollar through the residual financing margin. Otherwise, characterizing the constrained second-best mechanism requires additional analysis.

The idea of lifetime taxation was introduced by Vickrey (1939) because fluctuating

incomes are taxed more than constant flows of income under progressive taxation. In

this paper I put this idea in a Mirrleesian framework of optimal non-linear taxation to

evaluate whether taxation of lifetime income improves social welfare compared to period taxation. Optimal non-linear taxes for period and lifetime taxation are derived using the perturbation approach. A simple two-period model with an exogenous two-dimensional heterogeneity in ability is used to study the equity-efficiency trade-off under lifetime taxation. I find that, for standard social-welfare functions, the idea of Vickrey (1939) no longer holds with optimal non-linear taxes, since marginal taxes tend to be declining in income. The resulting optimal period tax is close to linear in income, which implies equal taxes conditional on lifetime income. This explains why gains of moving to lifetime taxation in the numerical simulation are small.

This paper examines the optimal income tax threshold, a topic that has received limited attention in existing literature. I show that the optimal non-linear tax threshold varies across income levels. Analysis of the social planner’s problem reveals that, as income rises, the optimal threshold is shaped by three forces: (i) a mechanical effect, whereby the threshold should be higher (lower) when a large share of individuals is located above (at) the relevant tax bracket; (ii) weaker income effects on labor supply, which push the threshold upward; and (iii) distributional considerations, which push the optimal threshold downward. Simulations calibrated with empirically plausible parameters indicate that the optimal threshold declines with income and becomes very low for high-income earners. I derive the optimal aggregate threshold implied by government optimization. I find that income tax thresholds in developed countries are higher than optimal for high-income earners and lower than optimal for the population as a whole.