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 [math]\displaystyle{ p_t }[/math] represents the vector of Arrow–Debreu commodity prices prevailing in period [math]\displaystyle{ t }[/math] and if

[math]\displaystyle{ \sum_{t=0}^{\infty} \frac{1}{\| p_t \| } \lt \infty , }[/math]

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. ISBN 9780262062039. https://books.google.com/books?id=fYmOO_jdGUYC&pg=PA132.

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