## Optimality in infinite horizon economies |

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a-efficient applications approximating family Arrow-Debreu model assume Axiom bijective birth process canonical market structure Chapter closed commodity space concept condition consider consumer consumption model consumption set contradiction converges convex sets corresponding criterion defined Definition 7.1 discounted utility divergent economies over market equilibrium Example 3.6 feasible allocation feasible program finite economy finite number finite set finite subset Gaussian curvature implies improving sequence induces inefficient inequality interpretation introduced Lemma Let C,M Let E=(S Let f,C,M liminf many-goods models market morphism measure of curvature model with support one-good models overlapping generations model p z p z Pareto optimal allocation preferred sets price system problem production model production sets properties pseudo-closed reader reduced model associated relation Section semi-independent semigroup simple morphism subsemigroup Suppose t)teN Theorem 3.9 units of measurement vector welfare economics