Paul Samuelson pp 193-227 | Cite as

# Samuelson’s Approach to Revealed Preference Theory: Some Recent Advances

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## Abstract

Since Paul Samuelson introduced the theory of revealed preference, it has become one of the most important concepts in economics. This chapter surveys some recent contributions in the revealed preference literature. We depart from Afriat’s theorem, which provides the conditions for a data set to be consistent with the utility maximization hypothesis. We provide and motivate a new condition, which we call the Varian inequalities. The advantage of the Varian inequalities is that they can be formulated as a set of mixed integer linear inequalities, which are linear in the quantity and price data. We show how the Varian inequalities can be used to derive revealed preference tests for weak separability and show how they can be used to formulate tests of the collective household model. Finally, we discuss measurement errors in the observed data and measures of goodness-of-fit, power, and predictive success.

## Keywords

Afriat’s theorem collective household model GARP mixed integer linear programming revealed preference Varian inequalities weak separability## Notes

### Acknowledgements

Thomas Demuynck acknowledges financial support by the Fonds de la Recherche Scientifique-FNRS under grant nr F.4516.18. Per Hjertstrand acknowledges financial support from Jan Wallander och Tom Hedelius stiftelse, Marcus och Marianne Wallenbergs stiftelse and Johan och Jakob Söderbergs stiftelse.

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