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.^[1][2]

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 $p_t$ represents the vector of Arrow–Debreu commodity prices prevailing in period $t$ and if

$\sum_{t=0}^{\infty} \frac{1}{\| p_t \| } < \infty$.

then a competitive equilibrium allocation is inefficient.^[3]

References

1. Cass, David (1972), "On capital overaccumulation in the aggregative neoclassical model of economic growth: a complete characterization", Journal of Economic Theory 4 (2): 200–223, doi:10.1016/0022-0531(72)90149-4
2. Balasko, Yves; Shell, Karl (1980), "The overlapping generations model, I: the case of pure exchange without money", Journal of Economic Theory 23 (3): 281–306, doi:10.1016/0022-0531(80)90013-7