Johann K. Brunner

Transition from a pay-as-you-go to a fully funded pension system: The case of differing individuals and intragenerational fairness

In recent contributions to the theory of public pension systems it was argued that a Pareto-improving transition from an established unfunded pension system to a funded one is possible. This result is derived in an overlapping-generations model with identical individuals. In the present study an extended model, with differing individuals, of an intragenerationally fair unfunded pension scheme is introduced. Within this more realistic framework it is shown that, in general, a Pareto-improving transition to a funded system is not possible, because any instrument applied for the financing of pensions in the phase of transition involves intragenerational redistribution.

Optimum taxation of bequests in a model with initial wealth

We formulate an optimal�?taxation model where parents leave bequests to their descendants for altruistic reasons. In contrast to the standard model, individuals differ not only in earning abilities, but also in initial (inherited) wealth. In this model, a redistributive motive for an inheritance tax – which is equivalent to a uniform tax on all expenditures – arises, given that initial wealth increases with earning abilities. The introduction of the inheritance tax either increases intertemporal social welfare or has an ambiguous effect, depending on whether the external effect related to altruism is accounted for in the social objective.

Optimum Taxation of Life Annuities

The market for private life annuities is characterised by adverse selection; that is, contracts offer lower than fair payoffs to individuals with low life expectancy. Moreover, longevity and income have been found to be positively correlated. We formulate an optimum income taxation model that incorporates these facts and discuss the conditions under which a linear tax on annuity payoffs, which raises more revenues from long-living individuals than from short-living, can serve as an instrument for redistribution. Further, we consider a nonlinear tax on annuity payoffs, and find that it can be employed to correct the distortion of the rate of return caused by asymmetric information.

Adverse Selection in the Annuity Market When Payoffs Vary Over the Time of Retirement

This paper investigates the effect of adverse selection and price competition on the private annuity market in a model with two retirement periods. In this framework annuity companies can offer contracts with different payoffs over the periods of retirement. Varying the time structure of the payoffs affects annuity demand and welfare of individuals with low and high life expectancy in different ways. By this, annuity purchasers can be separated according to their survival probabilities. Our main finding is that a Nash-Cournot equilibrium may not exist; if one exists, it will be a separating equilibrium. On the other hand, even if a separating equilibrium does not exist, a Wilson pooling equilibrium exists.

Bargaining with reasonable aspirations

Consider bargaining situations with two persons, where both have a specific idea of what would be an equitable outcome. In case these ideas differ, a procedure is needed which leads to a compromise between the different views. In the present paper the axioms of restricted homogeneity and of relative monotonicity are introduced, each of which, together with other standard conditions, allows one to determine a solution for this class of bargaining problems. An extension of this solution to bargaining problems with more than two persons is formulated.

A note on the optimum income tax

Abstract This paper analyzes the optimum utilitarian income tax, with special attention given to the characterization of the lower end of the optimum tax function, in the case when the least qualified individuals do not work. Moreover, the positivity of the marginal tax rate throughout is shown to be a consequence of the desirability of redistribution of income or leisure, given the self-selection constraints and preferences fulfilling agent monotonicity and non-inferiority of leisure.

Optimal taxation of wealth transfers when bequests are motivated by joy of giving

Abstract Inherited wealth creates a second distinguishing characteristic of individuals, in addition to earning abilities. We incorporate this fact into a model of optimal labor-income taxation, with bequests motivated by joy of giving. We find that taxes on bequests or on inheritances allow further redistribution if, in the parent generation, initial wealth and earning abilities are positively related. However, these taxes distort the bequest decision and thus, the overall effect on social welfare is ambiguous. On the other hand, a tax on all expenditures of a generation (a uniform tax on consumption plus bequests) has the same redistributive effect as an inheritance tax but does not distort the bequest decision.

Piecewise linear optimization

Two methods for solving an optimization problem with piecewise linear, convex, and continuous objective function and linear restrictions are described. The first one represents a generalization of the ordinary Simplex-Algorithm by Dantzig, the second one an adaptation of the Reduced Gradient Method by P. Wolfe to the discussed problem. Contrary to the usually employed algorithms, both methods have the advantage of working without an increase of the number of variables or restrictions. An algorithmic presentation and deliberations on the appropriateness of different versions of the methods are provided.ZusammenfassungZwei Verfahren zur Lösung eines Optimierungsproblems mit stückweise linearer, konvexer und stetiger Zielfunktion und linearen Nebenbedingungen werden beschrieben. Das erste stellt eine Verallgemeinerung des gewöhnlichen Simplex-Algorithmus von Dantzig dar, das zweite eine Anpassung der Methode der Reduzierten Gradienten von P. Wolfe an das behandelte Problem. Beide Verfahren haben gegenüber den üblicherweise verwendeten Algorithmen den Vorteil, ohne Erhöhung der Zahl der Variablen oder Restriktionen zu arbeiten. Eine algorithmische Darstellung und Überlegungen zur Eignung verschiedener Versionen der Verfahren werden gegeben.

Die Erbschaftsteuer: Bestandteil eines optimalen Steuersystems?

Zusammenfassung: Die Erbschaftsteuer hat eine ausgeprägte Umverteilungswirkung. Zugleich belastet sie die Kapitalbildung von Eltern als Vorsorge für ihre Nachkommen. In diesem Überblicksartikel wird im Rahmen der Theorie der optimalen Besteuerung der normativen Frage nachgegangen, welche Stellung dieser Steuer in einem Steuersystem zukommen soll. Ihr Wohlfahrtseffekt hängt wesentlich vom Motiv für die Vermögensweitergabe ab, das in einer Reihe von – vor allem amerikanischen – empirischen Studien untersucht wurde. Außerdem ist von Bedeutung, in welchem Maß Unterschiede zwischen den Personen in der Analyse berücksichtigt werden; je umfassender dies geschieht, desto mehr kommt man zu der Erkenntnis, dass es sinnvoll ist, zur Erhebung des Steueraufkommens auch die Erbschaftsteuer einzusetzen. Schließlich werden in dem Beitrag auch einige weitere Aspekte wie die Interpretation der Erbschaftsteuer als Versicherung gegen Pflegeausgaben, die Behandlung der Unternehmensweitergabe und das Problem der Vermögenskonzentrationbesprochen.

A theorem on utilitarian redistribution

A theorem is presented which characterizes regions where the marginal utilities of most goods decrease with increasing utility, given non-inferiority of one good and a strictly concave utility function. An analysis of the optimum utilitarian tax rests on this result.