Bargaining Solutions as Social Compromises

A bargaining solution is a social compromise if it is metrically rationalizable, i.e., if it has an optimum (depending on the situation, smallest or largest) distance from some reference point. We explore the workability and the limits of metric rationalization in bargaining theory where compromising is a core issue. We demonstrate that many well-known bargaining solutions are social compromises with respect to reasonable metrics. In the metric approach, bargaining solutions can be grounded in axioms on how society measures differences between utility allocations. Using this approach, we provide an axiomatic characterization for the class of social compromises that are based on p-norms and for the attending bargaining solutions. We further show that bargaining solutions which satisfy Pareto Optimality and Individual Rationality can always be metrically rationalized.     

The circular and time reversal tests reconsidered in economic price index theory

In this paper, a generalized definition of the well known economic price index is used to derive some similarities and dissimilarities between statistical and economic price index theory. The relationships between statistical and economic index numbers are analyzed by means of two tests taken from axiomatic (statistical) approaches which can also be formulated in an economic context.     

A note on the true factorial price index-addendum to a note by Balk

In this note we show that for more than one good the true factorial price index is exact only for Leontief-type, fixed coefficients utility functions.     

Progressive taxation and redistributive taxation: Different labels for the same product?

The paper examines different approaches to measure tax progressivity. In particular the distributional aspect of taxation is considered in some depth. For each member of a parametric class of inequality concepts, including more than only the relative and the absolute view of inequality, a necessary and sufficient condition for a tax function to be inequality reducing with respect to this concept for all admissible pre-tax income distributions is derived, both in strong and weak form. Only three very natural properties are required to prove this result: each tax liability is less than the corresponding pre-tax income, taxation does not reverse ranks on the income scale, and inequality is reduced if a rich gives to a poor such that they do not interchange their ranks. A definition of tax progressivity based on the shown equivalence is suggested. It is demonstrated that inequality reducing taxation is equivalent to progressive taxation in the sense of an increasing average tax rate if and only if the concept of relative inequality is used.An early version of this paper was presented at the seminar on Distributive Justice and Inequality at the Wissenschaftskolleg, Berlin, May 20–24, 1986. Some of the material contained previously circulated under the heading Generalized concepts of tax progression and inequality reduction.The author is indebted to Peter Lambert whose survey of tax progressivity inspired the present analysis incredibly. James Foster, John Weymark, and two anonymous referees provided helpful comments. Remaining errors and omissions are all mine.