With the aim of determining the welfare implications of price change in
consumption data, we introduce a revealed preference relation over prices. We
show that an absence of cycles in this preference relation characterizes a
model of demand where consumers trade-off the utility of consumption against
the disutility of expenditure. This model is appropriate whenever a consumer's
demand over a {\em strict} subset of all available goods is being analyzed. For
the random utility extension of the model, we devise nonparametric statistical
procedures for testing and welfare comparisons. The latter requires the
development of novel tests of linear hypotheses for partially identified
parameters. In doing so, we provide new algorithms for the calculation and
statistical inference in nonparametric counterfactual analysis for a general
partially identified model. Our applications on national household expenditure
data provide support for the model and yield informative bounds concerning
welfare rankings across different prices.Comment: 53 page
