Michael Landsberger

Incentive generating state dependent penalty system: The case of income tax evasion

Abstract Penalty systems can very often be looked upon as corrective measures established in order to eliminate or reduce costly externalities generated by optimizing economic agents. Hence, penalties can be viewed as regulatory measures and their efficient structure should be of interest to economists. We propose a dynamic incentive generating penalty system which, if instituted, may reduce, at a given cost, the generation of undesirable externalities. The special case to which we refer is income tax evasion, although our scheme should be applicable to any kind of externalities, such as pollution of the environment, violation of antirust laws and others which are created by repititive actions of economic agents.

Co-monotone allocations, Bickel-Lehmann dispersion and the Arrow-Pratt measure of risk aversion

For every integrable allocation (X1,X2, ...,Xn) of a random endowmentY=Σi=1/nXi amongn agents, there is another allocation (X1*,X2*, ...,Xn*) such that for every 1≤i≤n,Xi* is a nondecreasing function ofY (or, (X1*,X2*, ...,Xn*) areco-monotone) andXi* dominatesXi by Second Degree Dominance.If (X1*,X2*, ...,Xn*) is a co-monotone allocation ofY=Σi=1/nXi*, then for every 1≤i≤n, Y is more dispersed thanXi* in the sense of the Bickel and Lehmann stochastic order.To illustrate the potential use of this concept in economics, consider insurance markets. It follows that unless the uninsured position is Bickel and Lehmann more dispersed than the insured position, the existing contract can be improved so as to raise the expected utility of both parties, regardless of their (concave) utility functions.

Demand for risky financial assets: A portfolio analysis

Abstract Demand for risky financial assets takes place in portfolio settings. The common stochastic orders applied in economics fail to rank demand for assets in such situations even for risk-averse investors. Therefore, the evaluation of the relative desirability of risky financial assets requires the establishment of new orders. We prove that if returns on risky assets are ordered by the monotone likelihood ratio order then dominating assets will be more desired by all investors with nondecreasing utility functions.

Lotteries, insurance, and star-shaped utility functions

Abstract Most agents insure against risks which entail large losses, but few insure against small losses. The fact that organized lotteries charge low ticket prices examplifies this spirit. This weakly risk averse behavior pattern seems to be well structured but is at variance with concavity. We derive axiomatically a class of utility functions, star-shaped, which accommodate these phenomena. Concavity yields risk aversion everywhere and decreasing marginal utility. Star-shaped utility functions exhibit risk aversion at some wealth positions, and average utility from any of these is a decreasing function of wealth.

A tale of two tails: An alternative characterization of comparative risk

A characterization of comparative risk, parallel to but more restrictive than the Rothschild-Stiglitz (1970) characterization, is developed. As in Rothschild and Stiglitz, we develop a four-way characterization that consists of generating processes (a noise condition and generation by a sequence of special mean-preserving spreads), integral conditions, and preferences. The building blocks of this new order, Mean-preserving increases in risk about ν, where ν is any constant, are mean-preserving spreads whose centers have a nonempty intersection. If this intersection contains the mean of the distribution, the induced order, or mean-preserving increase in risk about the mean, conveys a particularly meaningful notion of an increase in risk as a buildup of the tails of the distribution.

Participation in auctions

Participation (preparing offers) in auction and procurement games—e.g., bidding for spectrum rights or for control of corporations—is very costly, which calls for analyzing participation (no less than how to play the games) as part of equilibrium. The result is a model with bi-dimensional distribution of types (as in [Jackson, M.O., 1999. Nonexistence of equilibria in auctions with both private and common values. Mimeo. http://www.stanford.edu/~jacksonm/nonexist.pdf]) and endogenous distribution of participants. Players with low production but high participation costs may decide not to participate, forcing the auctioneer to pay higher-than-necessary prices. To mitigate this phenomenon, auctioneers may consider partially reimbursing participants for the costs they incur in preparing offers. Restricting attention to symmetric games, we prove that • The game we consider has a unique symmetric equilibrium, with and without the reimbursement mechanism.

Mean-preserving Portfolio Dominance

Consider risk-averse agents with utility functions U and V holding portfolios composed of the same two (risky and riskless) assets. Then, V is (Arrow) more risk averse if in all such portfolios V invests less in the risky asset. A natural extension of this analysis of attitudes towards risk to risk itself is to establish a relation between distributions which is necessary and sufficient to induce such investment patterns in the class of all risk-averse agents. This characterization is established in this paper for distributions with equal means. Second Degree Dominance performs a similar role for the notion of ‘more risk averse’ introduced by Pratt but it is too weak for the Arrow concept.

Allocative and distributional effects of a monopolistic cooperative firm in a capitalist economy

Abstract It is well known that labor-managed firms operating under socialism exhibit “bizarre” behavior with respect to their production strategy. We prove that under capitalism most of these distortions disappear, consequently, the production strategies of an entrepreneurial monopoly and of the labor-managed firm become indistinguishable. However, there appears an almost inherent instability in the distribution of profits. The degree of instability depends on the existence of some sort of supportive legislation. Thus, unlike under socialism, in a capitalistic economy the labor-managed firm may have an effect on the distribution of profits at most.

Correlated Signals Against Monotone Equilibria

We consider symmetric auctions that may be multi-unit, with multi-dimensional bids and correlated multi-dimensional signals. Payment and allocation mechanisms are quite arbitrary. There are n potential bidders and the process of submitting a bid involves cost, which may be random and may vary across bidders. The number of effective bidders is part of an equilibrium. In fact, our model addresses more general games of which auction games are a special case. However, given the importance of auctions in economic theory and their prevalence in reality, they can be considered as a perfect archetype of our model. We prove that if n is sufficiently large and signals behave in a burst mode (which appears to be rather typical under interdependence), there is no equilibrium supported by monotone strategies. Since results obtained in the auction literature rely on monotonicity of strategies, even very basic results, such as existence and uniqueness of a symmetric equilibrium, become open questions, even for single unit first price auctions. We establish some properties of equilibria. They seem very innocuous and yet, they have power in the sense that they are incompatible with monotone strategies.

Feasible Net Income Distributions Under Income Tax Evasion: An Equilibrium Analysis

We investigate how redistribution of income is affected by the fact that income is privately observed and agents may not be truthful in their reports to tax authorities. In response, the government establishes an audit mechanism with penalties. Adhering to a signaling equilibrium concept, we prove that agents resort to mixed strategies, which makes it difficult for tax authorities to identify the true types. The audit strategy has a cutoff property: all income declarations below the pivotal income are audited with a constant probability; other declarations are not audited. In spite of not necessarily being truthful, agents whose true income is below or equal to the pivotal income pay their liability and, consequently, the government is implementing the designated tax schedule for those agents. In equilibrium, penalties and tax corrections equal the audit cost. Consequently, the audit system does not contribute directly to revenues, and its role is restricted to supporting the equilibrium. Copyright 2000 by Blackwell Publishing Inc.