An open expanding economy model

The authors extend the generalized von Neumann model they developed (with J. G. Kemeny) in 1956 to an open model by assuming that there are exogeneously determined export and import prices and that any amount can be exported or imported at these prices. The open model is then characterized by means of seven axioms. It is shown, by applying the theory of linear programming, that if four economically reasonable assumptions hold, the open model has at least one solution in which at least one good with positive export price is exported and at least one good with positive import price is imported. It is also shown that, in general, a continuum of expansion rates can be achieved by varying certain control variables. The choice of these expansion rates gives indirectly the choice of a suitable sub-economy and also determines the exports and imports of the economy. Other results and examples are discussed.     

NONPROLIFERATION POLICY CROSSROADS:

On October 1, 2008, Congress enacted a proposal that originated with President George W. Bush in 2005 to approve an unprecedented nuclear trade pact with India by removing a central pillar of US nonproliferation policy. Despite the numerous political challenges confronting the Bush administration, the initiative won strong bipartisan support, including votes from Democratic Senators Joseph Biden, Hillary Clinton, and Barack Obama. The four-year struggle to pass the controversial US-India nuclear trade agreement offers an exceptionally valuable case study. It demonstrates a classic tradeoff between the pursuit of broad multilateral goals such as nuclear nonproliferation and advancement of a specific bilateral relationship. It reveals enduring fault lines in executive branch relations with Congress. It vividly portrays challenges confronting proponents of a strong nonproliferation regime. This article is based on an analysis of the negotiating record and congressional deliberations, including interviews with key participants. It assesses the lessons learned and focuses on three principal questions: how did the agreement seek to advance US national security interests?; what were the essential elements of the prolonged state-of-the-art lobbying campaign to win approval from skeptics in Congress?; and what are the agreement's actual benefits—and costs—to future US nonproliferation efforts?     

Cost effectiveness of using a correlated variable in a complete inspection plan when inspection error is present

Due to advances in automated manufacturing systems and automatic inspection equipment, complete inspection (screening) has drawn increased attention recently and has become a widespread practice. Screening can be based on the performance variable of interest or on a variable which is correlated with the performance variable. Using a correlated variable as the screening variable is attractive when the inspection on the performance variable is destructive or costly. The purpose of this article is to illustrate both theoretically and empirically when a correlated variable rather than the performance variable should be used as the screening variable when inspection error is present.     

The advantage of deeper pockets in Silverman's game on intervals

Silverman's game on (1, B) × (1, B) was analyzed by R. J. Evans, who showed that optimal strategies exist (and found them) only on a set of measure zero in the parameter plane. We examine the corresponding game on (1, B) × (1, D) with D > B, and show that optimal strategies exist in about half the parameter plane. Optimal strategies and game value are obtained explicitly. © 1995 John Wiley & Sons, Inc.     

Assembly of systems having maximum reliability

The first problem considered in this paper is concerned with the assembly of independent components into parallel systems so as to maximize the expected number of systems that perform satisfactorily. Associated with each component is a probability of it performing successfully. It is shown that an optimal assembly is obtained if the reliability of each assembled system can be made equal. If such equality is not attainable, then bounds are given so that the maximum expected number of systems that perform satisfactorily will lie within these stated bounds; the bounds being a function of an arbitrarily chosen assembly. An improvement algorithm is also presented. A second problem treated is concerned with the optimal design of a system. Instead of assembling given units, there is an opportunity to “control” their quality, i.e., the manufacturer is able to fix the probability, p, of a unit performing successfully. However, his resources, are limited so that a constraint is imposed on these probabilities. For (1) series systems, (2) parallel systems, and (3) k out of n systems, results are obtained for finding the optimal p's which maximize the reliability of a single system, and which maximize the expected number of systems that perform satisfactorily out of a total assembly of J systems.