Efficiency and prices in economies of overlapping generations
In a general economy of overlapping generations, I introduce a notion of uniform inefficiency, corresponding to the occurrence of a Pareto improvement with a small uniform destruction of resources [G. Debreu, The coefficient of resource utilization, Econometrica 19 (1951) 273-292]. I provide a necessary and sufficient condition for uniform inefficiency in terms of prices at a competitive equilibrium: an allocation is uniformly inefficient if and only if the relative price of the aggregate endowment in a given period into the aggregate endowment up to that period does not vanish over periods of trade, a sort of Modified Cass Criterion [D. Cass, On capital overaccumulation in the aggregative neoclassical model of economic growth: a complete characterization, J. Econ. Theory 4 (1972) 200-223]. Minimal assumptions on fundamentals are needed for such a complete characterization. Furthermore, proofs reduce to simple and short direct arguments. Finally, I verify that uniform inefficiency is preserved under perturbations, a property that might fail for the canonical notion of inefficiency. Remarkably, an allocation is uniformly inefficient if and only if a non-vanishing redistribution, like a social security mechanism, is welfare improving.
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- Balasko, Yves & Shell, Karl, 1980. "The overlapping-generations model, I: The case of pure exchange without money," Journal of Economic Theory, Elsevier, vol. 23(3), pages 281-306, December.
- Geanakoplos, John D. & Polemarchakis, Heraklis M., 1991. "Overlapping generations," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 35, pages 1899-1960 Elsevier.
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- Geanakoplos, J. & Polemarchakis, H., 1991. "Overlapping generations," CORE Discussion Papers 1991031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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