Center for Economic Research, Department of Economics, University of Minnesota
We prove that the Strong Axiom of Revealed Preference tests the existence of
a strictly quasiconcave (in fact, continuous, generically Coo, strictly concave, and
strictly monotone) utility function generating finitely many demand observations.
This sharpens earlier results of Afriat, Diewert, and Varian that tested
("nonparametrically") the existence of a piecewise linear utility function that could
only weakly generate those demand observations. When observed demand is also
invertible, we show that the rationalizing can be done in a Coo way, thus extending a
result of Chiappori and Rochet from compact sets to all of Rn.
For finite data sets, one implication of our result is that even some weak types
of rational behavior - maximization of pseudotransitive or semitransitive
preferences -- are observationally equivalent to maximization of continuous, strictly
concave, and strictly monotone utility functions.
Matzkin, R.L. and Richter, M.K., (1987), "Testing Strictly Concave Rationality", Discussion Paper No. 239, Center for Economic Research, Department of Economics, University of Minnesota.
Matzkin, Rosa L.; Richter, Marcel K..
Testing Strictly Concave Rationality.
Center for Economic Research, Department of Economics, University of Minnesota.
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