Cass criterion

The Cass criterion, also known as the Malinvaud–Cass criterion, is a central result in theory of overlapping generations models in economics. It is named after David Cass.¹²

A major feature which sets overlapping generations models in economics apart from the standard model with a finite number of infinitely lived individuals is that the First Welfare Theorem might not hold—that is, competitive equilibria may be not be Pareto optimal.

If ${\displaystyle p_{t}}$ represents the vector of Arrow–Debreu commodity prices prevailing in period ${\displaystyle t}$ and if

${\displaystyle \sum _{t=0}^{\infty }{\frac {1}{\|p_{t}\|}}<\infty ,}$

then a competitive equilibrium allocation is inefficient.³