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Social Choice and Welfare

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26-03-2015

A Hurwicz type result in a model with public good production

Authors: Mridu Prabal Goswami, Arunava Sen, Sonal Yadav

Published in: Social Choice and Welfare | Issue 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.

previous article 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).

Barberà S, Jackson M (1995) Strategy-proof exchange. Econometrica 63:51–87CrossRef

Beviá C, Corchón L (1995) On the generic impossibility of truthful behavior: a simple approach. Econ Theory 6:365–371CrossRef

Campbell DE, Truchon M (1988) Boundary optima and the theory of public goods supply. J Pub Econ 35:241–249CrossRef

Corchón LC, Rueda-Llano J (2008) Differentiable strategy-proof mechanisms for private and public goods in domains that are not necessarily large or quasi-linear. Rev Econ Des 12:279–291

Deb R, Ohseto S (1999) Strategy-proof and individually rational social choice functions for public good economies: a note. Econ Theory 14:685–689CrossRef

Goswami MP (2013) Non fixed-price trading rules in single-crossing classical exchange economies. Soc Choice Welf 44:1–34

Goswami MP, Mitra M, Sen A (2014) Strategy proofness and Pareto efficiency in quasilinear exchange economies. Theor Econ 9:361–381CrossRef

Hashimoto K (2008) Strategy-proofness versus efficiency on the Cobb-Douglas domain of exchange economies. Soc Choice Welf 31:457–473CrossRef

Hurwicz L (1972) On informationally decentralized systems. In: McGuire CB, Radner Roy (eds) Decision and organization: a volume in honor of Jacob Marschak. North-Holland, Amsterdam

Hurwicz L, Walker M (1990) On the generic nonoptimality of dominant-strategy allocation mechanisms: a general theorem that includes pure exchange economies. Econometrica 58:683–704CrossRef

Jackson MO (2003) Mechanism theory. Optimization andoperations. In: Derigs U (ed) Encyclopedia of life support systems. EOLSS, Oxford

Moulin H (1980) On strategy-proofness and single peakedness. Pub Choice 35:437–455CrossRef

Nicoló A (2004) Efficiency and truthfulness with Leontief preferences. A note on two-agent, two-good economies. Rev Econ Des 8:373–382

Rudin W (1976) Principles of mathematical analysis, vol 3. McGraw-Hill, New York

Saporiti A (2009) Strategy-proofness and single-crossing. Theor Econ 4:127–163

Satterthwaite MA, Sonnenschein H (1981) Strategy-proof allocation mechanisms at differentiable points. Rev Econ Stud 48(4):587–597CrossRef

Serizawa S (1996) Strategy-proof and individually rational social choice functions for public good economies. Econ Theory 7:501–512CrossRef

Serizawa S (2002) Inefficiency of strategy-proof rules for pure exchange economies. J Econ Theory 106:219–241CrossRef

Serizawa S (2006) Pairwise strategy-proofness and self-enforcing manipulation. Soc Choice Welf 26:305–331CrossRef

Serizawa S, Weymark JA (2003) Efficient strategy-proof exchange and minimum consumption guarantees. J Econ Theory 109:246–263CrossRef

Tian G (1996) On the existence of optimal truth-dominant mechanisms. Econ Lett 53:17–24CrossRef

Weymark JA (2011) A unified approach to strategy-proofness for single-peaked preferences. SERIEs 2:529–550CrossRef

Zhou L (1991) Inefficiency of strategy-proof allocation mechanisms in pure exchange economies. Soc Choice Welf 8:247–254CrossRef

Title: A Hurwicz type result in a model with public good production
Authors: Mridu Prabal Goswami
Arunava Sen
Sonal Yadav
Publication date: 26-03-2015
Publisher: Springer Berlin Heidelberg
Published in: Social Choice and Welfare / Issue 4/2015
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-015-0888-1

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