Optimal Taxation of Indistinguishable Activities

Optimal tax policy frequently prescribes different tax treatments for activities that are difficult in practice for tax administrators to distinguish, such as expenditures undertaken for business versus personal purposes. We study the optimal design of income tax deductions for such expenditures under the assumption that a common deduction rate must be applied to both forms of the expenditure. The Pareto optimal common deduction turns on the relative compensated spending response for each margin, weighted by the income tax wedge. We also characterize the welfare gain from distinguishing between the two expenditure forms as a harmonic mean of the compensated responses. We illustrate both results with an application to air travel expenses.