nonempty coalition, even a coalition of one. Consequently, if nobody has any endowment, and yet contains some "free lunch" , then (assuming preferences are monotonic) every household would like to take all of for itself, and consequently there exists *no* core state. Intuitively, the picture of the world is a committee of selfish people, vetoing any plan that doesn't give the entire free lunch to itself. The limit to growth: Consider a society with 2 commodities. One is "labor" and another is "food". Households have only labor as endowment, but they only consume food. The looks like a ramp with a flat top. So, putting in 0-1 thousand hours of labor produces 0-1 thousand kg of food, linearly, but any more labor produces no food. Now suppose each household is endowed with 1 thousand hours of labor. It's clear that every household would immediately block every other household, since it's always better for one to use the entire for itself. Main results (Debreu and Scarf, 1963) In Debreu and Scarf's paper, they defined a particular way to approach an infinitely large economy, by "replicating households". That is, for any positive integer , define an economy where there are households that have exactly the same consumption possibility set and preference as household . Let stand for the consumption plan of the -th replicate of household . Define a plan to be equitable iff for any and . In general, a state would be quite complex, treating each replicate differently. However, core states are significantly simpler: they are equitable, treating every replicate equally. Consequently, when studying core states, it is sufficient to consider one consumption plan for each type of households. Now, define to be the set of all core states for the economy with replicates per household. It is clear that , so we may define the limit set of core states . We have seen that contains the set of market equilibria for the original economy. The converse is true under minor additional assumption: The assumption that is a polygonal cone, or every has nonempty interior, is necessary to avoid the technical issue of "quasi-equilibrium". Without the assumption, we can only prove that is contained in the set of quasi-equilibria. Accounting for nonconvexity The assumption that production possibility sets are convex is a strong constraint, as it implies that there is no economy of scale. Similarly, we may consider nonconvex