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Social Choice and Welfare

Erschienen in:

26.03.2015

A Hurwicz type result in a model with public good production

verfasst von: Mridu Prabal Goswami, Arunava Sen, Sonal Yadav

Erschienen in: Social Choice and Welfare | Ausgabe 4/2015

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Abstract

A classic result in the theory of incentive compatibility is Hurwicz (Decision and organization: a volume in honor of Jacob Marschak, 1972). The paper showed that strategy-proof (SP), Pareto-efficient and individually rational social choice functions do not exist in two-good, two-agent exchange economies. This result has been extended in several ways, for instance, to arbitrary numbers of agents and goods and to restricted domains. In this paper, we extend the result to economies with production. We consider a two-good economy with a single public good that can be produced from a private good according to a convex cost function. Agents have initial endowments of the private good. We show that SP, Pareto-efficient, individually-rational and continuous social choice functions do not exist in this environment. Pareto-efficiency, individual rationality and continuity axioms apply only to a “small” domain of preferences parametrized by a real number.

Vorheriger Artikel Impossibility theorems are modified and unified

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See Serizawa (2002), Serizawa and Weymark (2003), Nicoló (2004), Serizawa (2006), Zhou (1991), Goswami et al. (2014), Barberà and Jackson (1995) and Hashimoto (2008).

See Goswami (2013) and Barberà and Jackson (1995).

In their model, although production of the public good does not appear explicitly, it can be embedded without loss of generality in a model with endowments and a linear production technology.

The no-exploitation condition can be regarded as weak. However our model and assumptions allow for the possibility of its violation. On the other hand, we impose a continuity assumption albeit on a specific sub-domain. Our results are therefore independent of (Serizawa (1996)and Deb and Ohseto (1999)).

See Satterthwaite and Sonnenschein (1981), Serizawa (1996), Barberà and Jackson (1995) and Goswami et al. (2014).

We would like to the thank the Associate Editor for bringing this to our attention.

These preferences have the single-crossing property; see Goswami et al. (2014) and Goswami (2013). They clearly satisfy properties (a), (b) and (c) above and therefore belong to \({{\mathcal {R}}}\).

The absolute value of the slope of \(IC(\theta _i,b)\) at point \(b\) is strictly greater than the absolute value of the slope of \(L(a,b)\).

\(\text {Int}\ S\) denotes the interior of set \(S\).

\(L(d^{\prime },c)\) is downward sloping since \(d^{\prime }\) is chosen such that the level of public good at \(d^{\prime }\) is strictly greater than \(M\) which is the level of public good at \(c\). Also the level of private good at \(d^{\prime }\) is strictly less than the level of private good at \(c\).

Note that if Curve \(A\) is vertical, then our claim is trivially true.

Note that in this case, condition (iv) of Lemma 3 is satisfied trivially because \(L(e,h)\) is upward sloping.

The domain \({\mathcal {D}}\) is a single-crossing domain. These properties hold generally for such domains—for details see Goswami (2013).

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Titel: A Hurwicz type result in a model with public good production
verfasst von: Mridu Prabal Goswami
Arunava Sen
Sonal Yadav
Publikationsdatum: 26.03.2015
Verlag: Springer Berlin Heidelberg
Erschienen in: Social Choice and Welfare / Ausgabe 4/2015
Print ISSN: 0176-1714
Elektronische ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-015-0888-1

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