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

${\displaystyle {\displaystyle \sum _{t=0}^{\mathrm{\infty }}}\frac{1}{\Vert p_t\Vert }<\mathrm{\infty },}$

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

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