Avraham Beja

The Structure of the Cost of Capital under Uncertainty

In the analysis of models of competitive markets under uncertainty, different approaches can be distinguished. One approach, typically dealt with in welfare economics, is the specification of environmental conditions that are sufficient for the existence of equilibrium prices, with all the corollary implications for the efficiency of the competitive system. Prominent examples of this approach are the works of Arrow [2], Debreu [3] and Radner [12]. Another approach, typical to the analysis of capital markets, is concerned more with the structure of equilibrium prices, rather than their existence. Under this approach, basic interest lies in the implications of various given assumptions about the preferences of individuals (e.g. risk aversion) on the relationship between various properties of capital assets and their equilibrium prices, which are initially assumed to exist. Such studies extend from the classical investigations, such as Hicks [6] and Lutz [10], on the term to maturity of “riskless” capital assets, to recent ones concerned primarily with the issue of risk, such as Sharpe [13], Lintner [9], Hirshleifer [7,8] and others. 1 The present study represents an attempt at a slightly different approach. We postulate the existence of equilibrium prices for capital assets under uncertainty, and then proceed to analyze the properties implicit in their definition. It is shown that some results can be derived without recourse to the way individuals make decisions, their detailed preferences or their subjective assessments of probabilities. ∗ The author appreciates the must useful comments of two referees. 1 For example, see also Diamond [4], Green [5], and Myers [11] - all using the same ArrowDebreu framework of uncertainty used here.

Efficient Sampling by Artificial Attributes

Hypotheses about the fraction of items in a lot possessing a “specification attribute” X < L can be tested by generally sampling the variable X or directly sampling the attribute of interest. When the process variance is known, it is often more efficient to test against “compressed limits” for one or more “artificial” attributes X < La , X < Lb etc. This study discusses the efficient choice of one or two compressed limits. General guidelines for this choice are suggested, and then evaluated under many hypothetical test specifications. One compressed limit offered ~40% – 97% savings over direct attribute sampling; two limits allowed about 20% further savings.

Optimal Priority Assignment with Heterogeneous Waiting Costs

For an M/G/1 queuing system, this paper assumes (l) that the discipline is administratively constrained to a “head-of-the-line” rule with n classes, and (2) that priorities are centrally assigned to customers according to their individual cost per unit time spent in the system, or their individual service-time requirements, or both (as the available information may be), but independently of the state of the queue. Then optimal priority-assignment rules for the various information structures are characterized. When n = 2, the higher priority may always be optimally assigned to all customers who are “no worse than average” and with sufficiently high load to “practically all” customers.

Arrow and Gibbard-Satterthwaite revisited: Extended domains and shorter proofs

Abstract This short note offers some insights on Arrows theorem for social choice functions and the Gibbard-Satterthwaite theorem on the manipulatibility of voting schemes. At no cost in complexity, it extends these results by exploring the possibility that indifferences be admissible for some pairs of alternatives and not for others: the latter theorem is shown to apply under a larger class of domain conditions than the first. At the same time, the proposed proofs for the celebrated theorems (in their extended versions) are of independent interest, being much shorter and more transparent than previous proofs for the standard versions.

Finite and infinite complexity in axioms of rational choice or Sen's characterization of preference-compatibility cannot be improved

Abstract Axioms of rational choice are said to have “infinite complexity” if the consistency condition that they posit deals simultaneously not only with pairs, triples, or even arbitrarily large finite collections of decisions, but with infinite collections as well. This short note gives a proof that a characterization of the choice functions which are compatible with an underlying system of pairwise preferences must include an infinite complexity axiom, provided decision sets are not necessarily finite and the underlying preferences not necessarily a complete order.

Some Informational Aspects of Conservatism

Abstract When two value estimates are about equally likely, conservatism dictates reporting the less optimistic one (e.g. Lower of Cost or Market). We use an analytical model to investigate informational implications of this dictum, and identify types of environments where the conservative accounting treatment is more informative than a predetermined choice. The bias induced by the conservative choice is found to be adequately moderate, never excessive. It benefits users of the financial statements that take the reported figures at face value whenever upside errors are more costly (possibly only slightly more costly) than similar downside errors. Sophisticated users, who know how to give the reports the best possible interpretation, benefit from the lower variability, not from the bias. These latter benefits are least ambiguous when upside errors and downside errors are about equally costly.

Values for two-stage games: another view of the shapley axioms

This short study reports an application of the Shapley value axioms to a new concept of “two-stage games.” In these games, the formation of a coalition in the first stage entitles its members to play a prespecified cooperative game at the second stage. The original Shapley axioms have natural equivalents in the new framework, and we show the existence of (non-unique) values and semivalues for two stage games, analogous to those defined by the corresponding axioms for the conventional (one-stage) games. However, we also prove that all semivalues (hence, perforce, all values) must give patently unacceptable solutions for some “two-stage majority games” (where the members of a majority coalition play a conventional majority game). Our reservations about these prescribed values are related to Roths (1980) criticism of Shapleys “λ-transfer value” for non-transferable utility (NTU) games. But our analysis has wider scope than Roths example, and the argument that it offers appears to be more conclusive. The study also indicates how the values and semivalues for two-stage games can be naturally generalized to apply for “multi-stage games.”