The marginal cost of raising tax revenue and redistributing income

We present analytic formulas for calculating marginal welfare costs when taxes are levied against the wages of a heterogeneous population of households and marginal tax revenue finances either the supply of a public good or lump-sum transfers. The formulas are applied to explain the wide discrepancy between estimates of marginal welfare costs for redistribution previously obtained through computer simulation procedures. Our calculations reveal that these procedures introduced lump-sum transfers that were not specified as part of the reforms to be simulated, but explain most of the differences between their estimates. We also show that welfare cost estimates are quite sensitive to the elasticity of labor supply with respect to exhaustive public spending.