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A central question of many previous monetary studies has been the determination of the effects of various forces upon the actual supply of money in the economy. One of a number of competing monetary supply hypotheses (Brunner and Meltzer) has focused on the relationship between bank reserves and deposit creation. This theoretical structure was first suggested in earlier works by Phillips and Crick. Recent studies of similar nature, including those of Mellon and Orr, Morrison, and Brown and Lloyd, have employed the techniques of inventory theory to examine the factors influencing bank credit expansion. Similar inventory treatments of other cash balance and portfolio adjustment models are presented in the works of Baumol, Eppen and Fama, Lloyd, and Chitre. In the present paper, the effects of various forces on the optimal expansion of credit and the holding of reserves are investigated using the techniques of dynamic programming (see, for example, Bellman and Dreyfus). Discussed in the paper are the effects on bank credit expansion of uncertainty about reserve losses, various types of penalty costs, costs of adjustment, uncertain future interest rates, and of various institutional structures under which the bank must operate. This latter topic is important because of the Federal Reserve policy change of September 1968. Prior to that time, required reserves and actual reserves were computed over the same reserve period. Since that time, however, the required reserves in any period are known with certainty at the beginning of the period and depend upon deposit levels two periods earlier. For purposes of mathematical convenience, this latter structure is treated here as a one-period lag. [ABSTRACT FROM AUTHOR]

The model described in this paper was developed to provide guidance for price and promotion decisions in a consumer-goods division doing business in the United States marketplace. Demand is a dynamic function of price and promotion; the total market is divided into M interacting market segments that often have different needs and wants for the product and that can be sent different promotional messages; the segments usually have different price and promotion elasticities. For a given planning horizon, the model determines the optimal price to be charged in the M segments, the optimal promotional budget, and its allocation over the M segments. A convex programming formulation is utilized. The paper discusses the reality of the environment to be modeled, develops the model in relation to this reality, and then provides an empirical illustration of the model. [ABSTRACT FROM AUTHOR]

This paper is concerned with formulating, exploring and interpreting the uses and constructs which may be derived from a mathematical model of programming type which expresses more realistically than past efforts the actual conditions of current operations. It is an attempt to provide a means of attaining thereby an objective understanding of the implications of actual Federal Reserve liquidity policy on the actions and opportunities of banking institutions. The model presented corresponds to the problem of determining an optimal portfolio for an individual bank over several time periods in accordance with requirements laid down by bank examiners which are interpreted as defining limits within which the level of risk associated with the return on the portfolio is an acceptable one. The problem is transformed into an equivalent one offering advantages of analysis and of computation. Some methods of effective computation are explored. [ABSTRACT FROM AUTHOR]

Systems analysis has potential for many applications. But it has pitfalls in use as well. This paper discusses the operational context for the application of systems analysis to modernizing nations of the world. It also suggests some limitations of systems analysis in its indiscriminate use for this range of problems. [ABSTRACT FROM AUTHOR]

This paper examines real-time decision rules for a U.S. Air Force inventory system where items are repaired rather than "used up." The problem is to decide which user in the system has the greatest need for the newly available inventory items coming out of repair. The system is modeled as a Markov decision process and a heuristic rule is presented. This rule, the Transportation Time Look Ahead policy, is justified theoretically by showing that the rule is optimal for a modified model. Thus we have a theoretical justification of a decision rule in a large scale dynamic programming application. [ABSTRACT FROM AUTHOR]

The selection of appropriate product strategies by firms must account for the expected long-run returns from the market a firm contemplates entering, relative to the expected long-run returns from the market it is currently serving. These expected returns must also reflect the capabilities a firm has to implement this strategy and the resulting competitive situations it will face. The mathematical techniques of Markov processes and dynamic programming are used in this paper to develop an analytic framework which will select optimal product strategies for a firm that are consistent with its capabilities, that will meet its competitive situations, and that will maximize expected returns in the long run. This model is applied to a selected set of Michigan machine tool firms. The results indicate the general importance of total firm capabilities and the greater importance of management capability over the supporting capabilities in the selection of optimal product strategies. [ABSTRACT FROM AUTHOR]

This paper explores the implications of the theory of marginal cost pricing with regard to the regulation of Cable Antenna Television (CATV) systems. The chief concern is on optimal pricing and the various service dimensions of a CATV system, but the paper also deals with certain related topics, particularly that of optimal investment in the CATV industry. One difficulty in an analysis of this sort is the wide diversity of types of CATV systems, but this problem is handled by first discussing a relatively simple CATV system and then using this relatively simple analysis as a basis for investigating the pricing and investment implications of more complex systems and services. The analysis of efficiency is done with the welfare function, W = TR + S - C, where W is welfare, TR is total revenue, S is consumer's surplus, and C is total costs.

The article presents a response to an earlier article in the April 1956 issue of "The Journal of Marketing" from Professor Hans Brems, titled "Long-Run Automobile Demand." In that article, Professor Brems claimed that automobile output for the year 1955 exceeded demand and that it would be unwise to base long-run investment in plant on the current ratio of new car purchases. The author of this article takes issue with Professor Brems' claim, suggesting that his approach may be too simple and inadequate for long-run planning. The article summarizes Brems' formulation, presents an alternative formulation, and addresses long-run equilibrium adjustments and statistical derivation of the coefficients. The author claims that this model can also apply to other durable goods.

The article presents information on the new types of experimental design and the correspondingly appropriate statistical analysis which provide new promise for the scientific study of educational problems in the United States. Scientific facts may command interest because they are slightly used to describe something that has happened or an existing state of affairs. The main role of science is to examine the causes of events thereby leading to the formulation of general laws. An additional control designed to offer evidence of the influence of maturation, practice effects and other possible contributing factors consisted of a sixth grade group which had no classroom instruction in the content of a unit. The museum type of excursion was the only one of the four excursions in which a meaningful difference was found in favor of the control group, that is, the group which did not take the excursion.

The article presents a solution to a large-scale traveling-salesman problem which shows that a certain tour of 49 cities, one in each of the 48 states and Washington, D.C., has the shortest road distance. A brief history of the problem is provided. A city in each state including the District of Columbia was selected to try the optimal path method on a large problem. The devices in obtaining solutions include the use of undirected tours, the imposition of linear conditions to characterize the tours, the speeding up of the iterative process and the use of a combinatorial approach.

The article examines the efficiency of the electric power industry with respect to the short-run phases of the optimization process in the U.S. It presents information regarding the short-run optimization problems of electric utilities. A distinguishing feature of some regulated industries is the importance of inter-firm co-ordination in achieving technical efficiency. The extent of operating economies that might be realized from a rational ownership pattern depends on the effectiveness of inter-firm co-ordination. The technical unit in electric power generating and transmission is a network of synchronized electrical circuits linking generating stations and distribution points. The breakup of holding companies under the Public Utility Holding Company Act was largely completed by the early 1950's. Subsequent mergers have been few and small, and the existing regulatory framework does not encourage them. At the same time, technological developments in generating, high voltage transmission, and electronics have been continually enlarging the efficient area of system operation.