Abstract
We construct a complete space of smooth strictly convex preferences defined over commodities and monetary transfers. Our model extends the classical one in that preferences are strictly monotone in monetary transfers, but need not be monotone in all commodities. We thereby provide a natural framework for performing genericity analyses in situations involving inventory costs or decisions under risk. The constructed space of preferences is contractible, which allows for a natural aggregation procedure in collective decision situations.
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Notes
To be fair, much of classical demand theory can be developed by relying on the weaker local-nonsatiation assumption; yet strict monotonicity appears to be the rule in applications. The implications of nonmonotone preferences for the existence and efficiency of competitive equilibria have been examined by Polemarchakis and Siconolfi (1993), among others. However, they take individual preferences as given and do not provide a framework for genericity analysis.
Notice, in that respect, that, when the state space is infinite, conducting a genericity analysis in the finite-dimensional space of portfolio choices is mathematically much simpler than doing so in the infinite-dimensional space of state-contingent consumption choices.
It should be noted that A4 does not follow from A1 if V is a proper subset of \(\mathbb {R}^{\ell +1}\); indeed, in this case, \(\succeq \) can be closed relative to \(V \times V\), though its upper contour sets are adherent to the boundary of V in \(\mathbb {R}^{\ell +1}\) and are thus not closed relative to \(\mathbb {R} ^{\ell +1}\).
Conversely, negative contributions to collective goods can, in the presence of altruistic concerns, come at a personal cost in the form of guilt or shame. For instance, if we interpret q in Fig. 2 as the individual’s contribution to a collective good, then, for any fixed level of t, he equally loses from contributing too little, \(q= q_1^- + \varepsilon \), as from contributing too much, \(q= q_1^+ - \varepsilon \). A4 implies that both situations involve prohibitive costs as \(\varepsilon >0\) converges to zero.
See Spanier (1966) for precise definitions of these terms.
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We thank the editor and two anonymous referees for very thoughtful and detailed comments. We also thank Michel Le Breton and Jérôme Renault for extremely valuable feedback.
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Attar, A., Mariotti, T. & Salanié, F. On a class of smooth preferences. Econ Theory Bull 7, 37–57 (2019). https://doi.org/10.1007/s40505-018-0142-y
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DOI: https://doi.org/10.1007/s40505-018-0142-y