Failure of integrability is shown to cause path-dependence of willingness-to-pay measures of welfare change. Using the linear expenditure system, effects of failure of integrability are negligible (substantial) for estimating income (price) elasticities. For single price changes, Hausman's approach to calculating willingness to pay from ordinary demands becomes subject to excessive errors of estimation. For multiple price changes, calculations of willingness to pay become path dependent. The empirical approach of Vartia to calculation of willingness to pay for multiple price changes thus involves an arbitrary choice of path. Furthermore, the Willig results justifying consumer surplus approximation fail.