Growth in Economies with Non Convexities: Sunspots and Lottery Equilibria

We investigate the relation between lotteries and sunspot allocations in a dynamic economy where the utility functions are not concave. In an intertemporal competitive economy, the household consumption set is identified with the set of lotteries, while in the intertemporal sunspot economy it is the...

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Bibliographic Details
Published in:Economic theory 2004-10, Vol.24 (3), p.701-726
Main Authors: Rustichini, Aldo, Siconolfi, Paolo
Format: Article
Language:English
Subjects:
Allocative efficiency
Commodities
Competition
Consumer economics
Consumption
Economic efficiency
Economic growth
Economic inelasticity
Economic models
Economic theory
Economics
Equilibrium
Expected utility
Family economics
General economic equilibrium
Households
Lotteries
Pareto optimum
Probability distribution
Production functions
Studies
Sunspots
Utility functions
Welfare economics
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Summary:We investigate the relation between lotteries and sunspot allocations in a dynamic economy where the utility functions are not concave. In an intertemporal competitive economy, the household consumption set is identified with the set of lotteries, while in the intertemporal sunspot economy it is the set of measurable allocations in the given probability space of sunspots. Sunspot intertemporal equilibria whenever they exist are efficient, independently of the sunspot space specification. If feasibility is, at each point in time, a restriction over the average value of the lotteries, competitive equilibrium prices are linear in basic commodities and intertemporal sunspot and competitive equilibria are equivalent. Two models have this feature: Large economies and economies with semi-linear technologies. We provide examples showing that in general, intertemporal competitive equilibrium prices are non-linear in basic commodities and, hence, intertemporal sunspot equilibria do not exist. The competitive static equilibrium allocations are stationary, intertemporal equilibrium allocations, but the static sunspot equilibria need not to be stationary, intertemporal sunspot equilibria. We construct examples of non-convex economies with indeterminate and Pareto ranked static sunspot equilibrium allocations associated to distinct specifications of the sunspot probability space.
ISSN:0938-2259
1432-0479
DOI:10.1007/s00199-004-0509-1