Rational eating: can it lead to overweightness or underweightness?

Although a deviation from the physiologically optimal weight increases the probability of dying, the steady state for an expected lifetime-utility maximiser is a state of overweightness. However, even a small initial deviation from this rationally stationary weight is followed by explosive oscillations. These oscillations might lead to severe and chronic underweightness in a late stage of life. In the presence of socio-cultural norms of appearance, the rationally stationary weight of fat people is lower than otherwise and the rationally stationary weight of lean people is greater than otherwise.