Georg Tillmann

Stability in a simple pure consumption loan model

Abstract We consider a simple overlapping generation model with outside money and one consumption good. A class of price expectation functions is characterized such that the Stationary Market Equilibrium is globally stable.

Cost-axiomatic regulatory pricing

Abstract The axioms of the Shapley value and semi-values of non-atomic games can be taken as the starting point for axioms on the relation between costs and prices of a regulated multiproduct monopoly. The price mechanisms that result from this system of axioms are called cost- axiomatic prices. This paper shows the applicability of such pricing to all cases of regulatory constraints that require revenue to be a given percentage of costs (including cost-plus regulation, break-even pricing or Amtraks 50% clause). Moreover, we show that all such price mechanisms, including a fairly general system of taxation or subsidization of consumers, are demand compatible if cost-axiomatic pricing leads to deficits or profits.

Existence and stability of rational expectation-equilibria in a simple overlapping generation model

Abstract We consider a simple overlapping generation model with outside money and one consumption good. For a big class of preference relations, it is shown that globally no self-fulfilling expectation exists (except the trivial one) if the information set contains only past and present prices. Even locally, positive results can be obtained for homothetic preferences only. To get asymptotic stability this class must be restricted again: The elasticity of substitution must be very small. The implications of this are very negative: A Learning process can never reach rationality.

Neid und Progressive Besteuerung

There is an increasing theoretical interest in envy free equitable allocations. It seems natural to extend the literature by explicitly introducing income taxation as instrument towards elimination or reduction of envy. Such an inclusion of the income tax has not been addressed to in the recent theoretical papers on envy free allocations. We use the Foley-Varian concepts of envy as this is the most advanced theory on the topic. The use of this approach allows us in a straightforward manner to show the conditions for the achievement of envy free allocations, and to elaborate the differences between aggregate envy and social welfare. Summarizing, our main results, are as follows: (a) An equitable allocation can be reached by a progressive income tax if we disregard all disincentive effects of taxation on labour supply. This income tax, however, must equalize all net incomes (!). If, on the other hand, people reduce their labour supply because of taxation, it is impossible to find an income tax which guarantees equitable net income allocations for all possible distributions of individual abilities. For an a priori fixed distribution of abilities an equitable allocation can be achieved by income taxation, but only by a tax that includes all people to stop working. (b) Ordinal aggregate measures of envy are never changed by income taxation as long as the tax does not alter that ranking of individuals which underlies the individual envy. This implies a general failure of ordinal envy measures as it is typically one of the axioms of income taxation not to change individual rankings. (c) Minimizing cardinal aggregate measures of envy is conceptually different from maximizing cardinal social welfare functions although the results might coincide. Progressivity of a linear income tax can be shown to be a sufficient condition for envy minimization if the individual envy and its social acceptance follow particular patterns.

Equity and Taxation

Much of the economics of taxation is concerned with the principle of Paretian efficiency which regards efficiency only but has nothing to say about distribution of welfare or equity. One way to resolve this problem is to hypothesize the existence of some additive Social Welfare Function where the weights reflect the distributional goals of the society. But this approach may be objected as it involves interpersonal utility comparisons. Moreover it may be interesting not only to study a general framework in which value judgements may be incorporated (as in a SWF) but also to study the economic consequences of some specific value judgements. This will be done here by using the concept of equitable and fair allocations initiated by Foley.

Fairness and Production

One of the most central concepts in welfare economics is Pareto efficiency. It is clear, however, that efficiency only is unsatisfactory from a distributional point of view. Therefore it should be complemented with an equity criterion, which should be ordinal, too, to avoid interpersonal utility comparisons which are the normal case in Bergsonian welfare functions. As already mentioned in the introduction this will be done in this first chapter. We will explore two interesting equity criteria, Foley fairness and wealth fairness, in more detail in the following.

Redistribution, Observability and Different Tax Systems

In this chapter we will totally dispense with normative criteria as used in chapter one to determine equitable and efficient allocations. Instead of we will scrutinize which allocations are attainable, or implementable at all, if different kinds of taxes are available. The scopes of redistribution provided by the different taxes are compared with each other. Again we start with finite economies and go over to continuum economies. We will confine ourselves to “first best redistribution” although we see very clearly that the exploration had to be expanded to include second best solutions, too. This chapter is therefore a necessary, yet only first step in comparing different tax systems.

Taxation as Insurance

In this chapter we go over from a deterministic to a stochastic environment. Output is a random variable whose distribution can be influenced by changing labour supply but the risk cannot be eliminated totally on an individual level. A caring government “acts as insurance company” using a taxation scheme as means for redistribution among the agents. We will characterize and compare the optimal tax schemes for several given welfare functions.

An Economists’ View of Equitable Taxation

A political philosopher and ail economist apparently approach any given topic in very different ways. The political philosopher wants to start from a very general approach including “human abilities… which are diverse and variable, which wax and wane with incentive structures and modes of human capital formation.” (p. 103) The economist is much more modest. For him progress in economic knowledge is a step by step procedure and he first wants to make clear the basic principles. So before dealing with abilities which wax and wane, one should deal with given abilities to get a feeling for the way in which abilities are relevant for income formation and taxation. Before including all possible effects of progressive taxation, one should carefully deal with different single aspects. Models, which make everything endogenous, have not brought very much progress in economic analysis. Economists have learned that small models are useful to achieve precise results on particular interrelationships, and this information can be used to evaluate more complex phenomena.

Existence of a Temporary Equilibrium in a Three-Commodity Model

We show existence of a Temporary Equilibrium in a three commodity model (consumption good, labour and money) if consumers have static expectations in the sense of Patinkin.