The paper studies an economy with H households, N + 1 commodities, and M fixed factors with commodity taxes and government expenditures on goods and services. The first and second order directional derivatives of a certain weighted sum of utility functions with respect to any direction of tax change are calculated. The resulting measure of deadweight loss, due essentially to Boiteux, is contrasted with a measure based on Debreu's coefficient of resource utilization as well as with the more familiar measure of loss due to Hotelling and Harberger. The basic analytical technique used is the usual comparative statistics analysis, except that duality theory is used to simplify the computations.