Preference-Theoretic Weak Complementarity: Getting More with Less

A preference-theoretic characterization of weak complementarity is provided based on an explicit representation of revealed preference. Weak complementarity is defined in terms of the observable property of nonessentiality and the unobservable property of no existence value. Preference-theoretic characterizations of these properties facilitate a precision and intuition that is not generally available within the existing calculus-based literature. An exact welfare measure is specified that does not require a continuous nonmarket good or monotonic preference on the nonmarket good, and which can be easily generalized to accommodate infinite choke prices. It is shown that no existence value can be rejected by revealed preference, contradicting a widely stated assertion within the literature. Even though no existence value is unobservable, it does require an observable condition that is nontrivial with three or more market goods.

A Revealed Preference Feasibility Condition for Weak Complementarity

It is widely reported in the literature that it is not possible to test nonmarket good preference restrictions against revealed preference. While it is clearly impossible to affirm any particular preference restriction as being “true,” it is possible to show that a preference restriction is not feasible. A revealed preference feasibility test for weak complementarity is presented here. With weak complementarity defined by the observable property of nonessentiality and the unobservable property of no-existencevalue, the latter is the actual preference restriction. It is shown that no-existencevalue is feasible if and only if an observable revealed preference condition of “singlepreference” is satisfied. This strong revealed preference condition is nontrivial when there are two or more market goods in addition to the weak complement. With simple Samuelsonian revealed preference we can falsify single-preference and thereby reject weak complementarity. Stone-Geary numeric examples are included to demonstrate these and other results.

Falsifying the “Goodness” of Nonmarket Goods with Revealed Preference

Some assert that it is impossible to test preference restrictions against revealed preference. The “goodness” preference restriction simply assumes that one value of a nonmarket good is preferred over another other with any fixed commodity consumption. This paper uses a preference-theoretic methodology to show how goodness can be falsified by revealed preference for compensation-based welfare analysis. When goodness is not directly falsifiable, it is still possible to use revealed preference to set lower bounds on goodness that may be so implausible as to provide an indirect falsification of goodness. In addition to potential application of these techniques with real-world problems, the principal contribution of this paper is demonstrating that it is possible to test nonmarket good preference restrictions using only revealed preference. This paper also illustrates the possible contributions of preference-theoretic methodology in a literature that is dominated by the discussion of calculus-based techniques.

A Preference-Theoretic Methodology for Nonmarket Goods

A methodology for nonmarket goods is presented based on preference algebra and set theory that allows us to specify exactly when preference assumptions such as weak complementarity can be tested against revealed preference information. Revealed preference is insufficient for welfare analysis involving state preference variables such as nonmarket goods. The preference and set-theoretic structure presented here is specifically designed to characterize the minimal additional preference information necessary for exact welfare analysis, and also provides a common basis for specifying the many context-specific methods that have been proposed for closing the information gap (whether or not they provide this minimal information). The paper closes with examples demonstrating how this structure can be used as a methodology for working with assumptions about preference structure, focusing on when such assumptions can be tested against revealed preference. This includes an extended examination of weak complementarity and related issues, followed by five shorter examples including two types of repackaging for price indices and the new and disappearing goods problem.

Low pressure gas flow analysis through an effusive inlet using mass spectrometry

A mass spectrometric method for analyzing flow past and through an effusive inlet designed for use on the tethered satellite and other entering vehicles is discussed. Source stream concentrations of species in a gaseous mixture are determined using a calibration of measured mass spectral intensities versus source stream pressure for standard gas mixtures and pure gases. Concentrations are shown to be accurate within experimental error. Theoretical explanations for observed mass discrimination effects as they relate to the various flow situations in the effusive inlet and the experimental apparatus are discussed

On the imaginary parts of chromatic root

While much attention has been directed to the maximum modulus and maximum real part of chromatic roots of graphs of order $n$ (that is, with $n$ vertices), relatively little is known about the maximum imaginary part of such graphs. We prove that the maximum imaginary part can grow linearly in the order of the graph. We also show that for any fixed $p \in (0,1)$, almost every random graph $G$ in the Erd\"os-R\'enyi model has a non-real root.Comment: 4 figure