# 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 model](/source/overlapping_generations_model)s in [economics](/source/economics). It is named after [David Cass](/source/David_Cass).<ref name="Cass72">{{citation | last1 = Cass| first1 = David | year=1972 |title= On capital overaccumulation in the aggregative neoclassical model of economic growth: a complete characterization | journal =[Journal of Economic Theory](/source/Journal_of_Economic_Theory) | volume = 4| pages = 200–223 | doi = 10.1016/0022-0531(72)90149-4 | issue = 2}}</ref><ref name="BalaskoShell80">{{citation | last1 = Balasko | first1 = Yves| author-link=Yves Balasko| last2 = Shell| first2 = Karl | author-link2= Karl Shell | year=1980|title= The overlapping generations model, I: the case of pure exchange without money | journal =[Journal of Economic Theory](/source/Journal_of_Economic_Theory) | volume = 23| pages = 281–306 | doi = 10.1016/0022-0531(80)90013-7 | issue = 3}}</ref>

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](/source/First_Welfare_Theorem) might not hold—that is, [competitive equilibria](/source/competitive_equilibrium) may be not be [Pareto optimal](/source/Pareto_optimal).

If <math>p_t</math> represents the vector of [Arrow–Debreu](/source/Arrow%E2%80%93Debreu) [commodity](/source/Good_(economics_and_accounting)) prices prevailing in period <math>t</math> and if

:<math>\sum_{t=0}^{\infty} \frac{1}{\| p_t \| } < \infty ,</math>	

then a [competitive equilibrium](/source/competitive_equilibrium) allocation is [inefficient](/source/Pareto_efficiency).<ref>{{cite book |first=Roger E. A. |last=Farmer |title=The Macroeconomics of Self-fulfilling Prophecies |publisher=MIT Press |year=1999 |page=132 |url=https://books.google.com/books?id=fYmOO_jdGUYC&pg=PA132 |isbn=9780262062039 }}</ref>

== References ==
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Category:Economics and time

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