# Cass criterion

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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 ${\displaystyle p_{t}}$ 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]

## 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
3. ^ Farmer, Roger E. A. (1999). The Macroeconomics of Self-fulfilling Prophecies. MIT Press. p. 132.