1,736 research outputs found
When does aggregation reduce uncertainty aversion?
We study the problem of uncertainty sharing within a household: "risk sharing," in a context of Knightian uncertainty. A household shares uncertain prospects using a social welfare function. We characterize the social welfare functions such that the household is collectively less averse to uncertainty than each member, and satises the Pareto principle and an independence axiom. We single out the sum of certainty equivalents as the unique member of this family which provides quasiconcave rankings over risk-free allocations
Profit maximization and supermodular technology
A dataset is a list of observed factor inputs and prices for a technology; profits and production levels are unobserved. We obtain necessary and sufficient conditions for a dataset to be consistent with profit maximization under a monotone and concave revenue based on the notion of cyclic monotonicity. Our result implies that monotonicity and concavity cannot be tested, and that one cannot decide if a firm is competitive based on factor demands. We also introduce a condition, cyclic supermodularity, which is both necessary and sufficient for data to be consistent with a supermodular technology. Cyclic supermodularity provides a test for complementarity of production factors
Ordinal notions of submodularity
We consider several ordinal formulations of submodularity, defined for arbitrary binary relations on lattices. Two of these formulations are essentially due to Kreps [Kreps, D.M., 1979. A representation theorem for “Preference for Flexibility”. Econometrica 47 (3), 565–578] and one is a weakening of a notion due to Milgrom and Shannon [Milgrom, P., Shannon, C., 1994. Monotone comparative statics. Econometrica 62 (1), 157–180]. We show that any reflexive binary relation satisfying either of Kreps’s definitions also satisfies Milgrom and Shannon’s definition, and that any transitive and monotonic binary relation satisfying the Milgrom and Shannon’s condition satisfies both of Kreps’s conditions
Spherical Preferences
We introduce and study the property of orthogonal independence, a restricted
additivity axiom applying when alternatives are orthogonal. The axiom requires
that the preference for one marginal change over another should be maintained
after each marginal change has been shifted in a direction that is orthogonal
to both.
We show that continuous preferences satisfy orthogonal independence if and
only if they are spherical: their indifference curves are spheres with the same
center, with preference being "monotone" either away or towards the center.
Spherical preferences include linear preferences as a special (limiting) case.
We discuss different applications to economic and political environments. Our
result delivers Euclidean preferences in models of spatial voting, quadratic
welfare aggregation in social choice, and expected utility in models of choice
under uncertainty
Supermodularity and preferences
We uncover the complete ordinal implications of supermodularity on finite lattices under the assumption of weak monotonicity. In this environment, we show that supermodularity is ordinally equivalent to the notion of quasisupermodularity introduced by Milgrom and Shannon. We conclude that supermodularity is a weak property, in the sense that many preferences have a supermodular representation
On behavioral complementarity and its implications
We study the behavioral definition of complementary goods: if the price of one good increases, demand for a complementary good must decrease. We obtain its full implications for observable demand behavior (its testable implications), and for the consumer's underlying preferences. We characterize those data sets which can be generated by rational preferences exhibiting complementarities. The class of preferences that generate demand complements has Leontief and Cobb–Douglas as its as extreme members
The Axiomatic Structure of Empirical Content
In this paper, we provide a formal framework for studying the empirical content of a given theory. We define the falsifiable closure of a theory to be the least weakening of the theory that makes only falsifiable claims. The falsifiable closure is our notion of empirical content. We prove that the empirical content of a theory can be exactly captured by a certain kind of axiomatization, one that uses axioms which are universal negations of conjunctions of atomic formulas. The falsifiable closure operator has the structure of a topological closure, which has implications, for example, for the behavior of joint vis a vis single hypotheses.
The ideas here are useful for understanding theories whose empirical content is well-understood (for example, we apply our framework to revealed preference theory, and Afriat's theorem), but they can also be applied to theories with no known axiomatization. We present an application to the theory of multiple selves, with a fixed finite set of selves and where selves are aggregated according to a neutral rule satisfying independence of irrelevant alternatives. We show that multiple selves theories are fully falsifiable, in the sense that they are equivalent to their empirical content
Inefficiency
We introduce an ordinal model of efficiency measurement. Our primitive is a notion of efficiency that is comparative, but not cardinal or absolute. In this framework, we postulate axioms that we believe an ordinal efficiency measure should satisfy. Primary among these are choice consistency and planning consistency, which guide the measurement of efficiency in a firm with access to multiple technologies. Other axioms include symmetry, which states that the names of commodities do not matter, scale-invariance, which says that units of measurement of commodities does not matter, and strong monotonicity, which states that efficiency should decrease if the inputs and outputs remain static when the technology becomes unambiguously more efficient. These axioms characterize a unique ordinal efficiency measure which is represented by the coefficient of resource utilization. By replacing symmetry (the weakest of our axioms) with a very mild continuity condition, we obtain a family of path-based measures.Efficiency Measurement, Coefficient of Resource Utilization, Ordinal, Choice Consistency, Planning Consistency, Path-based
Imaging individual barium atoms in solid xenon by scanning of a focused laser for use in the nEXO experiment
2019 Spring.Includes bibliographical references.Neutrinoless double beta decay (0νββ) is a non-standard model decay process in which two simultaneous beta decays occur, with no emission of neutrinos. This decay is of great interest. If observed, it will demonstrate that the neutrino and anti-neutrino are not distinct. This decay also violates lepton number conservation, a requirement for some theories seeking to explain the matter-antimatter asymmetry of the universe. A measurement of the decay half-life will also give information on the absolute mass scale of the neutrinos. EXO-200 and nEXO use liquid xenon (LXe) time projection chambers (TPC) to search for 0νββ decay. EXO-200 first observed two neutrino double beta decay (2νββ) in xenon-136, the rarest decay ever observed. A low background measurement is vital to maximizing sensitivity to the 0νββ decay mode, yet to be observed. In this dissertation, research and development of a technique for positive identification of the barium-136 daughter (barium tagging) is presented. It is desirable to incorporate barium tagging into the future nEXO detector, as it provides discrimination against all background except for the 2νββ decay mode. The scheme being developed in this work involves extraction of the barium daughter in solid xenon with a cryogenic probe, followed by matrix-isolation fluorescence spectroscopy to tag the barium atom. This work focuses on the detection of individual barium atoms in a prepared solid xenon sample. Single atom sensitivity has been achieved, and a method for imaging of individual atoms by scanning of a focused laser has been demonstrated
On Behavioral Complementarity and its Implications
We study the behavioral denition of complementary goods: if the price of one good increases, demand for a complementary good must decrease. We obtain its full implications for observable demand behavior (its testable implications), and for the consumer's underlying preferences. We characterize those data sets which can be generated by rational preferences exhibiting complementarities. In a model in which income results from selling an endowment (as in general equilibrium models of exchange economies), the notion is surprisingly strong and is essentially equivalent to Leontief preferences. In the model of nominal income, the notion describes a class of preferences whose extreme cases are Leontief and Cobb-Douglas respectively.Afriat's Theorem, Weak Axiom of Revealed Preference, Complementary goods.
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