The Generalised Axiom of Revealed Preferences (GARP) allows for testing utility maximisation when choices and prices are observed (Afriat’s Theorem, Afriat, 1967). Under the hypothesis of utility maximisation, any bundle chosen under some budget must be preferred to all other bundles affordable under that budget. GARP, and therefore utility maximisation, is violated if one bundle is revealed preferred to another bundle, which is in turn revealed strictly preferred to the first bundle.
Varian (1988) shows that one can only test for GARP if all prices and goods chosen by a decision maker are observed. If only choices for a subset of goods are observed, the unobserved demand can make any bundle unaffordable under all other budgets, which means one cannot draw conclusions about preference relations. Typical consumer demand datasets do not have data on all goods consumed, which means that the utility maximisation hypothesis cannot be falsified.
Lab experiments would seem to be a solution, as the choices made by subjects can be fully observed in the lab. However, the choice task in the lab may not be the actual choice that subjects face. A subject may, for example, plan to buy noodles after the experiment ends when choosing to consume an apple in the lab, while planning to later buy an orange when choosing to consume a sandwich in the lab. Thus, demand is still not observed for all goods.
We show that despite this, one can still test for GARP in an experiment as long as prices and wealth outside the lab do not change during the experiment, a condition which is typically satisfied. If wealth does not change, then any bundle which is affordable in the experiment must remain affordable when outside consumption may be part of the consumption choice. This holds even if it is not exactly known what this outside consumption is. Hence, testing for GARP under lab conditions is equivalent to testing for GARP for the complete choice problem.
van Bruggen, P., & Heufer, J. (2017). Afriat in the lab. Journal of Economic Theory, 169, 546-550