  To determine the welfare implications of price changes in demand data, we
introduce a revealed preference relation over prices. We show that the absence
of cycles in this relation characterizes a consumer who trades off the utility
of consumption against the disutility of expenditure. Our model can be applied
whenever a consumer's demand over a strict subset of all available goods is
being analyzed; it can also be extended to settings with discrete goods and
nonlinear prices. To illustrate its use, we apply our model to a single-agent
data set and to a data set with repeated cross-sections. We develop a novel
test of linear hypotheses on partially identified parameters to estimate the
proportion of the population who are revealed better off due to a price change
in the latter application. This new technique can be used for nonparametric
counterfactual analysis more broadly.
