Equilibrium Prices When the Sunspot Variable Is Continuous

Garratt, Rod; Keister, Todd; Qin, Cheng Zhong; Shell, Karl

doi:10.1006/jeth.1999.2634

Cited by 16 publications

(36 citation statements)

References 20 publications

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“…Our unique result in Theorem 15 is an application of Corollary 1.12 in Clarke et al (1988, pp.186) and a result in Yotrutani (1978). The reason why we can obtain a unique Euler solution of (9) is largely due to the fact that V (·) is 10 This condition is automatically satisfied in our context, since each market order is always bounded by    …”

Section: Figure 1 An Euler Price Iterative Processmentioning

confidence: 96%

Walrasian equilibrium in an exchange economy with indivisibilities

Ma¹,

Nie²

2003

Mathematical Social Sciences

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may AbstractThis paper studies an exchange economy with indivisibilities. Our main goal is to see if a price system can function well in an economy (e.g., an economy with complementary preferences) that does not have a Walrasian equilibrium. We study the price adjustment processes governed by the Euler iterative scheme. We show that in an economy that has a Walrasian equilibrium, our price adjustment processes have a common uniform limit that is unique and converges to a Walrasian equilibrium price vector in finite time. Surprisingly, in an economy that does not have a Walrasian equilibrium, our price adjustment processes also have a common uniform limit that is unique and converges to a market equilibrium price vector in finite time. Moreover, market equilibrium prices coincide with Walrasian equilibrium ones in an economy that has a Walrasian equilibrium. Further, there are no prices other than the Walrasian or market equilibrium ones that have such a property of global stability.

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Section: Figure 1 An Euler Price Iterative Processmentioning

confidence: 96%

Walrasian equilibrium in an exchange economy with indivisibilities

Ma¹,

Nie²

2003

Mathematical Social Sciences

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“…When each lottery induces a (compatible) sunspot allocation, lotteries and sunspot allocations are equivalent. Garret, Kreister, Qui and Shell [5] show that equivalence is achieved by any "continuous randomizing device" 1 . When the probability space of extrinsic uncertainty is not rich enough, sunspot equilibrium allocations, if they exist, may be Pareto suboptimal.…”

Section: Competitive Equilibria and Sunspot Equilibriamentioning

confidence: 99%

“…2 However, when the extrinsic uncertainty space is ([0, 1), B, L), under fairly general assumptions, every sunspot equilibrium allocation induces an equilibrium lottery allocation. If equilibrium allocations of the lottery economy are supported by linear prices, the viceversa is also true, ( [5] and [6]). This equivalence result is based on the assumed existence of sunspot equilibria and, equivalently, of lottery equilibria supported by linear prices.…”

Section: Competitive Equilibria and Sunspot Equilibriamentioning

confidence: 99%

“…Hence, feasibility is just a restriction on the average value of the lotteries. Thus, in large economies lottery and sunspot equilibrium allocations are equivalent, [8] and [5].…”

Section: Competitive Equilibria and Sunspot Equilibriamentioning

confidence: 99%

“…We identify the set of sunspots with the interval [0, 1), their probability with the Lebesgue measure L and we allow for different specifications of the σ−algebra,B, withB ⊂ B, the Borel sets over the interval [0, 1).As shown in [5], ([0, 1), B, L) (or any probability space isomorphic to it) accomplishes desideratum 1), in the following precise sense: Let C be a Borel subset of Y and observe thatŷ [5], in Lemma 4, proves that for each β ∈ M 1,+ (Y ), there areŷ ∈ Y ([0, 1), B) such thatŷ ∼ β and viceversa. Also, by the same argument, for each given sunspot space (Ω, A,σ) and each y ∈ Y (Ω, A) there existsŷ * ∈ Y ([0, 1), B, L) such thatŷ * ∼ŷ.…”

Section: Sunspot and Lottery Allocationsmentioning

confidence: 99%

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Growth in economies with non convexities: sunspots and lottery equilibria

Rustichini

Siconolfi

2004

Economic Theory

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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. Copyright Springer-Verlag Berlin/Heidelberg 2004Lottery equilibria, Sunspot Equilibria, Non-convexities.,

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A Characterization of Robust Sunspot Equilibria

Garratt¹,

Keister²

2002

Journal of Economic Theory

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In nonconvex environments, a sunspot equilibrium can sometimes be destroyed by the introduction of new extrinsic information. We provide a simple test for determining whether or not a particular equilibrium survives, or is robust to, all possible re…nements of the state space. We use this test to provide a characterization of the set of robust sunspot-equilibrium allocations of a given economy: it is equivalent to the set of equilibrium allocations of the associated lottery economy. ¤ We thank Huberto Ennis, Aditya Goenka, the associate editor and a referee for providing useful comments. We especially thank Karl Shell for helpful comments and advice.

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Equilibrium Prices When the Sunspot Variable Is Continuous

Cited by 16 publications

References 20 publications

Walrasian equilibrium in an exchange economy with indivisibilities

Walrasian equilibrium in an exchange economy with indivisibilities

Growth in economies with non convexities: sunspots and lottery equilibria

A Characterization of Robust Sunspot Equilibria

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