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.

Understanding marginal willingness to pay for public-good reforms is important for empirical welfare analysis because standard reduced-form approaches may miss key fiscal and incentive constraints. We study how to elicit individuals’ marginal willingness to pay for public-good reforms when preferences exhibit income effects and social welfare weights may differ across people. Our starting point is a local reform problem around the status quo in which the planner chooses changes in public-good provision and taxes subject to incentive compatibility and exact budget balance. The analysis shows that recovering taxes from reported marginal willingness to pay is feasible only if the implied payment schedules satisfy a set of tight consistency conditions. This creates a central tension between truthful revelation, exact implementation, and fiscal feasibility. More broadly, the project develops a framework for thinking about how to elicit marginal willingness to pay for public goods and closely related publicly financed policies.

The idea of lifetime taxation was introduced by Vickrey (1939) since fluctuating incomes are taxed more than constant flows of income under progressive taxation. In this paper I put this idea in a 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 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.