Rational Agents Might Be Overweight, Underweight, or the Physiologically Optimal Weight

Abstract

Levy (2002) and Dragone (2009) showed that rational agents tend to become overweight. Their result is shown to be equivalent to a seemingly innocuous assumption placed on the instantaneous utility function. It is also shown that their models can rationalize agents who are underweight, or even the physiologically optimal weight, in a steady state. These deductions follow from a more complete characterization of the steady state solutions of their rational eating models, in which three general inequalities are shown to hold in a steady state and an equivalence among the signs of four steady state expressions is demonstrated.