This paper presents evidence that consumers underreact to taxes that are not salient and characterizes the welfare consequences of tax policies when agents make such optimization errors. The empirical evidence is based on two complementary strategies. First, we conducted an experiment at a grocery store posting tax inclusive prices for 750 products subject to sales tax for a three week period. Scanner data show that this intervention reduced demand for the treated products by 8 percent. Second, we find that state-level increases in excise taxes (which are included in posted prices) reduce alcohol consumption significantly more than increases in sales taxes (which are added at the register and are hence less salient). We develop simple, empirically implementable formulas for the incidence and efficiency costs of taxation that account for salience effects as well as other optimization errors. Contrary to conventional wisdom, the formulas imply that the economic incidence of a tax depends on its statutory incidence and that a tax can create deadweight loss even if it induces no change in demand. Our method of welfare analysis yields robust results because it does not require specification of a positive theory for why agents fail to optimize with respect to tax policies.