The mathematical formula used to predict economic behavior for 40 years is completely wrong for anyone on the brink of bankruptcy.
The standard Euler equality assumes that people make smooth, rational choices about their future spending. This fails near the point of financial ruin because the value of survival becomes the only thing that matters. People in desperate situations behave in ways that the old math describes as irrational or puzzling. When a person is about to lose everything, they stop following the rules of standard dynamic optimization. Replacing the old formula with an inequality that accounts for ruin explains decades of mysterious economic data.
Euler Equalities Near Ruin
SSRN · 6466958
The Euler equality is the first-order condition of every dynamic optimization problem, and in the consumption setting, it is valid on a subset of the state space. Near ruin, it stops being the right first-order condition. When ruin is irreversible and insurance is insufficient, the first-order conditions split into equalities far from ruin and inequalities near it. The gap is the value of survival. Far from ruin, the textbook holds, and a household satisfies orthogonality, adjusts buffers and co