AN ANALYSIS OF THE DYNAMIC THEORY OF THE MULTI—PRODUCT FIRM USING THE CALCULUS OF VARIATIONS

The purpose of this paper is to present the theory of the multi-product firm in situations where the revenue function depends not only on the rate of output but also on changes in the rate of output, and, similarly, where the cost function depends on changes in the rate of factor utilization as well as the rate of their utilization. Since the analysis will utilize the calculus of variations, a general introduction to this technique is also presented. The model analyzed assumes perfect foresight and knowledge concerning the revenue, cost, and production functions, and the calculus of variations is used to derive the conditions for an extremum. The first section presents the mathematical model and the model of the firm, and the optimality conditions are discussed in the second section.     

MULTICRITERIA OPTIMIZATION: A GENERAL CHARACTERIZATION OF EFFICIENT SOLUTIONS*

In the context of deterministic multicriteria maximization, a Pareto optimal, nondominated, or efficient solution is a feasible solution for which an increase in value of any one criterion can only be achieved at the expense of a decrease in value of at least one other criterion. Without restrictions of convexity or continuity, it is shown that a solution is efficient if and only if it solves an optimization problem that bounds the various criteria values from below and maximizes a strictly increasing function of these several criteria values. Also included are discussions of previous work concerned with generating or characterizing the set of efficient solutions, and of the interactive approach for resolving multicriteria optimization problems. The final section argues that the paper's main result should not actually be used to generate the set of efficient solutions, relates this result to Simon's theory of satisficing, and then indicates why and how it can be used as the basis for interactive procedures with desirable characteristics.     

THE USE OF ARCS AND NODES FOR THE DETERMINATION OF CRITICAL PATHS IN PERT/CPM NETWORKS

The critical path in a PERT/CPM network is determined in various textbooks by finding the path with associated minimal slack for the network arcs or by finding the path with associated minimal slack for the network nodes. This paper points out that the use of nodes can result in a network path being incorrectly identified as a path of maximum length.     

ON PREDICTING COMPUTATIONAL TIME OF A BRANCH AND BOUND ALGORITHM FOR THE ASSIGNMENT OF FACILITIES

Experience with branch and bound algorithms indicates that computational time is a function of not only the size of the problem, but also the nature of the input data. This paper formulates statistically-based variables which describe certain characteristics of the input data and experimentally evaluates their ability to predict computational time for one branch and bound algorithm, the relative location of facilities or “plant layout” problem. Results suggest that the described experimental procedure may be useful for an a priori assessment of the computational difficulty of specific branch and bound problems.     

Interplay between Friends' Aggression and Friendship Quality in the Development of Child Aggression during the Early School Years

The aim of this study was to investigate the unique and combined role of friendship quality and friends' aggression in regard to the persistence of young children's physical aggression from kindergarten to grade 2. The sample included 1555 children (808 girls) assessed annually using teacher ratings. Two theoretical perspectives (i.e., the social learning and the social bonding perspectives) served as frameworks to guide the analyses and interpret the results. In line with the social learning perspective, friends' aggression was related to a significant increase in children's physical aggression. However, in line with the social bonding perspective, good friendship quality played both a compensatory and a protective role, by, respectively, reducing children's initial level of physical aggression and by mitigating, albeit marginally, the associations between friends' and children's physical aggression. These results suggest that fostering a positive relationship between friends in the early school years may decrease physical aggression even if the friends are aggressive.     

The impact of ethnicity on attitudes toward health care reform in New Mexico

Latinos tend to have significantly lower levels of access to general and top quality medical care than do non-Latino whites, and although disparities in access to health care have diminished for all other minority groups over time, they have widened for Latinos. Given these trends, current attempts to provide universal health care at both the national and state levels across the United States have large implications for the health status of Latinos. The objective of this analysis is to determine whether Latinos have different attitudes regarding health reform than non-Latino whites. Our data are from a statewide random digit dialing telephone survey of New Mexico residents, age 18 and older, conducted in the Fall of 2007. With a Latino population of 44% and ongoing health care reform efforts by the state legislature, New Mexico is an ideal location for this analysis. After controlling for a host of individual level factors, our findings suggest that while Latinos are less likely to identify health care as a salient state issue relative to the economy and crime, they are more likely than non-Latino whites to believe affordable health care programs are important. Finally, Latinos view employers, more than government or individuals, to be responsible for expanding health care coverage.     

The Politics of Hope and Despair: The Effect of Presidential Election Outcomes on Suicide Rates*

Objectives. This article examines the effect of election outcomes on suicide rates by combining the theory of social integration developed by Durkheim with the models of rational choice used in economics. Methods. Theory predicts that states with a greater percentage of residents who supported the losing candidate would tend to exhibit a relative increase in suicide rates. However, being around others who also supported the losing candidate may indicate a greater degree of social integration at the local level, thereby lowering relative suicide rates. We therefore use fixed‐effects regression of state suicide rates from 1981 to 2005 on state election outcomes during presidential elections to determine which effect is stronger. Results. We find that the local effect of social integration is dominant. The suicide rate when a state supports the losing candidate will tend to be lower than if the state had supported the winning candidate—4.6 percent lower for males and 5.3 percent lower for females. Conclusion. Social integration works at many levels; it not only affects suicide risk directly, but can mediate other shocks that influence suicide risk.