Linear Inequality Concepts and Social Welfare

The paper presents an abstract definition of linear inequality concepts leading to linearly invariant inequality measures and characterizes the class of linear concepts completely. Two general methods of deriving ethical measures are proposed. They imply an Atkinson-Kolm-Sen index and a new dual index reflecting the inequality of living standard. Then all separable social welfare orderings which generate linearly invariant measures are characterized. The measures are presented and their general properties discussed. Dual measures prove to be additively decomposable. Linear welfare orderings defined on rank-ordered income vectors are examined. They are consistent with all linear inequality and yield an inequality ordering for every concept.inequality concept, ethical inequality measures, decomposability, social welfare

Measures of downside risk

The paper characterizes a family of downside risk measures. They depend on a target value and a parameter reflecting the attitude towards downside risk. The indicators are probability weighted -order means of possible shortfalls. They form a subclass of the measures intro¬duced by Stone (1973) and are related to the measures proposed by Fishburn (1977). The axiomatization is based on some properties which are desirable and appropriate for the measurement of risk.

Extending the cost function: A simple method of modeling environmental regulation

The paper shows that a variety of different scenarios in environmental economics can be modeled by one abstract concept, an extended cost function, which takes into account a firm's technological and regulatory constraints. It satisfies the usual properties of a cost function and reasonable properties with respect to the regulatory parameter. An extended cost function represents a simple unified approach which does not depend on the specific form of regulation and the way emissions are modeled.

On the definition of nonessentiality

Nonessentiality of a good is often used in welfare economics, cost-benefit analysis and applied work. Various definitions of this property are presented in the literature on public and environmental economics. This note clarifies their relationship.Preferences, nonessentiality

The Difficulty of Income Redistribution with Labour Supply

Two common principles in distributional analysis are that (i) a progressive transfer moves the Lorenz curve upwards, and (ii) progressive [neutral] taxation reduces [leaves unchanged] inequality. In order to establish these results it is currently assumed that the distribution of income is exogenously given. The relevance of these results is therefore limited in practice where incomes are determined by the working decisions of the agents in the economy. Considering a simple economy with two goods and two agents we indicate sufficient conditions for inequality in net income to decrease as a result of rich to poor transfers or progressive taxation. By means of simple examples we show that, when one incorporates labour supply responses, the fulfillment of these conditions is highly hypothetical and that everything can happen.Endogenous labour supply

Inequality reducing taxation reconsidered

The paper investigates inequality reducing taxation for various inequality views. Using the general definition of an inequality concept (Ebert (2004)) corresponding definitions of Lorenz dominance, inequality reduction and measures of tax progression are provided. The framework allows us to simplify and clarify the different approaches found in the literature, to extend this analysis, and to present brief and transparent proofs

The decomposition of inequality reconsidered: Weakly decomposable measures

The paper characterizes the class of weakly decomposable (aggregable) inequality measures which satisfy a new (weak) decomposition (and agregation) property. These measures can be decomposed into the sum of the usual within-group and a between-group term which is based on the inequality between all pairs of individuals belonging to the groups involved. The measures therfore depend on the inequality index for two-person distributions and are proportional to the total sum of the inequality values between all pairs of individuals. Extending Gini's mean difference, the Gini coefficient, and the variance of logarithms we characterize three families of measures. By choosing other basic measures furhter (families of) weakly decomposable measures can be defined

The social evaluation of income distribution: An assessment based on happiness surveys

The paper investigates how the income distribution affects the subjective well-being of society. Starting from the concept of a social welfare function defined on income distributions it assesses the preference for equality in European countries. It examines how mean income and the distribution of income in a country (measured by an appropriate inequality measure) determine the subjective well-being of its inhabitants which is identified with social welfare. This issue is addressed under alternative assumptions concerning the adjustment of needs due to differences in household size. The results derived are relevant for the design and monitoring of redistribution policies

Inequality and Envy

Using a simple axiomatic structure we characterise two classes ofinequality indices - absolute and relative - that take into account "envy"in the income distribution. The concept of envy incorporated hereconcerns the distance of each person's income from his or herimmediately richer neighbour. This is shown to be similar to justiceconcepts based on income relativities.Inequality, envy, transfer principle.