Testing Consumer Rationality using Perfect Graphs and Oriented Discs

Given a consumer data-set, the axioms of revealed preference proffer a binary test for rational behaviour. A natural (non-binary) measure of the degree of rationality exhibited by the consumer is the minimum number of data points whose removal induces a rationalisable data-set.We study the computational complexity of the resultant consumer rationality problem in this paper. This problem is, in the worst case, equivalent (in terms of approximation) to the directed feedback vertex set problem. Our main result is to obtain an exact threshold on the number of commodities that separates easy cases and hard cases. Specifically, for two-commodity markets the consumer rationality problem is polynomial time solvable; we prove this via a reduction to the vertex cover problem on perfect graphs. For three-commodity markets, however, the problem is NP-complete; we prove thisusing a reduction from planar 3-SAT that is based upon oriented-disc drawings

Stochastic Dominance and Nonparametric Comparative Revealed Risk Aversion

It is shown how to test revealed preference data on choices under uncertainty for consistency with first and second order stochastic dominance (FSD or SSD). The axiom derived for SSD is a necessary and sufficient condition for risk aversion. If an investor is risk averse, stochastic dominance relations can be combined with revealed preference relations to recover a larger part of an investor's preference. Interpersonal comparison between investors can be based on intersections of revealed preferred and worse sets. Using a variant of Yaari's (1969) defi nition of more risk averse than, it is shown that it is sufficient to compare only the revealed preference relations of two investors. This makes the approach operational given a finite set of observations. The central rationalisability theorem provides strong support for this approach to comparative risk aversion. The entire analysis is kept completely nonparametric and can be used as an alternative or complement to parametric approaches and as a robustness check. The approach is illustrated with an application to experimental data of by Choi et al. (2007). Most subjects come close to SSD-rationality, and most subjects are comparable with each other. The distribution of risk attitudes in the population can be described by comparing subjects' choices with any given preference, which is also illustrated.Dieser Artikel zeigt zunächst, wie Daten zu Entscheidungen unter Unsicherheit auf Konsistenz mit stochastischer Dominanz in erster und zweiter Ordnung (FSD bzw. SSD) getestet werden können. Wenn ein Investor SSD-rational ist, können die SSD-Relation und die offenbarte Präferenzrelation kombiniert werden, um einen größeren Teil der Präferenzen des Investors zu rekonstruieren. Interpersonelle Vergleiche zwischen Investoren können auf Basis von Schnittmengen der Besser- und Schlechtermengen der Investoren vorgenommen werden. Basierend auf Yaaris (1969) risikoaverser als-Relation wird gezeigt, dass ein Vergleich der endlichen offenbarten Präferenzrelationen hinreichend ist; der Ansatz ist daher operational. Die Analyse ist vollständig nichtparametrisch und kann als Alternative oder Ergänzung zu parametrischen Ansätzen und als Robustheitsprüfung angewandt werden. Der Ansatz wird mit experimentellen Daten von Choi et al. (2007) illustriert. Die meisten Probanden kommen SSD-Rationalität sehr nahe und sind miteinander vergleichbar. Die Verteilung von Riskoeinstellungen kann durch den Vergleich der Probanden mit jeder beliebigen Präferenz beschrieben werden, was ebenfalls illustriert wird

A Geometric Measure for the Violation of Utility Maximization

Revealed Preference offers nonparametric tests for whether consumption observations can be rationalized by a utility function. If a consumer is inconsistent with GARP, we might need a measure for the severity of inconsistency. One widely used measure is the Afriat efficiency index (AEI). We propose a new measure based on the extent to which the indifference surfaces intersect the budget hyperplanes. The measure is intuitively appealing and, as a cutoff-rule evaluated by Monte Carlo experiments, performs very well compared to the AEI. The results suggest that the new measure is better suited to capture small deviations from utility maximation

In Vino Veritas: The Economics of Drinking

It is argued that drug consumption, most commonly alcohol drinking, can be a technology to give up some control over one's actions and words. It can be employed by trustworthy players to reveal their type. Similarly alcohol can function as a social lubricant and faciliate type revelation in conversations. It is shown that both separating and pooling equilibria can exist; as opposed to the classic results in the literature, a pooling equilibrium is still informative. Drugs which allow a gradual loss of control by appropriate doses and for which moderate consumption is not addictive are particularly suitable because the consumption can be easily observed and reciprocated and is unlikely to occur out of the social context. There is a tradeoff between the efficiency gains due to the signaling effect and the loss of productivity associated with intoxication. Long run evolutionary equilibria of the type distribution are considered. If coordination on an exclusive technology is efficient, social norms or laws can raise efficiency by legalizing only one drug

Crime, Inequality, and the Private Provision of Security

In a high-crime environment with many high-income citizens, private security companies which offer protection against crime can flourish. In this article crime is modelled as a game where richer victims yield a higher return on crime, but with decreasing returns to crime as more criminals choose crime to supplement their income. Private security providers offer protection against crime and face Cournot competition. The model allows for the analysis of market clearing prices for effort against crime. Among the implications of the model are that rising inequality will lead to more expenditure on protection against crime, and that the upper income classes are suffering from the same or lower crime density than the middle income class. Taking into account the response of criminals and victims, rising inequality can actually lead to less crime if either (i) the legal income opportunity of the marginal criminal increases or (ii) marginal utility from income decreases and richer individuals spend a higher proportion of their income on protection (i.e. protection is a superior good). Often the middle class suffers from higher crime densities as inequality increases, as the increased spending on protection by the upper class (i) shifts crime to the middle class and (ii) increases market prices for protection, leaving the middle class with less affordable protection against crime. Emigration of the middle class can then further increase inequality. This highlights the importance of taking into account the response of individuals against crime and shows that the link between inequality and crime is a complex one.In diesem Artikel wird Kriminalität als Spiel modelliert, in welchem wohlhabenere Opfer mehr Gewinn erbringen; dieser Gewinn nimmt aber ab, je mehr Kriminelle sich auf wohlhabene Opfer konzentrieren. Private Sicherheitsdienstleister bieten Schutz gegen Kriminalität an und stehen im Cournot-Wettbewerb miteinander. Das Modell erlaubt die Untersuchung markträumender Preise für Sicherheitsdienstleistungen. Das Modell impliziert unter anderem, dass steigende Ungleichheit der Einkommensverteilung zu höheren Ausgaben für Sicherheitsdienstleistungen führt, und dass die oberen Einkommensschichten unter dem gleichen oder sogar geringeren Maß an Kriminalität leiden als mittlere Einkommensschichten. Es zeigt sich, dass steigende Ungleichheit Kriminalität sogar reduzieren kann, wenn (i) legale Einkommensmöglichkeiten des marginalen Kriminellen steigen und/oder (ii) der Grenznutzen des Einkommens abnimmt und wohlhabendere Individuen einen höheren Anteil ihres Einkommens für (superiore) Sicherheitsdienstleistungen ausgeben. Mittlere Einkommensschichten können bei steigender Ungleichheit unter mehr Kriminalität leiden, da steigende Ausgaben für Sicherheit durch höhere Einkommensschichten (i) Kriminalität auf niedrigere Einkommensschichten verlagern und (ii) den Marktpreis für Sicherheitsdienstleistungen erhöhen. Emigration der mittleren Einkommensschichten kann dann zu einem weiteren Anstieg der Ungleichheit führen

A detailed chemical kinetic modeling, ignition delay time and jet-stirred reactor study of methanol oxidation

A shock tube (ST) and a rapid compression machine (RCM) have been used to measure new ignition delay times for methanol oxidation over a wide range of pressures (2-50 atm) and equivalence ratios (0.5, 1.0, and 2.0). These measurements include dilute and fuel/'air' conditions (1.5-21.9% methanol), over a temperature range of 820-1650 K. The new data has been compared to previously published studies and provides insight into internal combustion engine relevant conditions which are previously un-studied at pressures of 10, 30, 40 and 50 atm. In addition to these ignition delay times, species concentrations have also been measured using a jet-stirred reactor (JSR). In these experiments methanol concentrations of 2000 and 4000 ppm were used at equivalence ratios of 0.2-2.0, at pressures of 1-20 atm, and in the temperature range of 800-1200 K with residence times varying from 0.05-2.00 s. The newly measured experimental data was used to develop a new detailed chemical kinetic model (Mech15.34). This model was also validated using available literature data. The new model is capable of predicting all of the validation data with reasonable accuracy, with some discrepancy in predicting formaldehyde in the JSR data. All of this, results in a robustly validated and accurate, new detailed chemical kinetic model. (C) 2015 The Combustion Institute. Published by Elsevier Inc. All rights reserved.Ultan Burke and Alexander Heufer would like to acknowledge the financial support from the Irish Research Council (IRC). Wayne Metcalfe and Sinead Burke would like to acknowledge the financial support of Saudi Aramco.peer-reviewed2018-01-2