The extent of competition in the market affects the balance of bargaining power of market participants. When price discrimination is low, it increases consumer welfare - that is, if the price does not correspond to the evaluation of each product by the consumer, then discrimination allows for additional consumers to buy the product at a price,…

This article presents ways to explore mathematical concepts using Catan, a popular board game. After a brief overview of game play, we explore considerations with many potential entry points for mathematical modeling, such as which resource is the best, which resources will be rare or plentiful, where to build, and risk assessment.

Mathematical modeling is a process in which students investigate authentic problems and everyday situations using mathematics. In doing so, they bring their multiple mathematical knowledge bases and cultural funds of knowledge into their solution strategies. During a task called "Abuelo's Birthday", 297 students in grades 3-5 decided how…

Single-period inventory models with uncertain demand are very well known in the business analytics community. Typically, such models are rule-based functions, or sets of functions, of one decision variable (order quantity) and one random variable (demand). In academics, the models are taught selectively and usually not completely. Students are…

The relevance of the problem stated in the article is that in conditions of nonstationary economy the modification of existing approaches and methods is necessary during the formation of the capital. These methods allow taking into account the heterogeneity of factors' change in time and the purpose of the development of a particular company,…

Although it is well known that vaccines against many infectious diseases confer positive economic externalities via indirect protection, analysts have typically ignored possible herd protection effects in policy analyses of vaccination programs. Despite a growing literature on the economic theory of vaccine externalities and several innovative…

Competitive bidding has recently received considerable attention in the literature of economics and operations research. Unfortunately, the classic formulation of the problem developed by Friedman and still expounded (Stark and Mayer) can lead to an incorrect estimate of the expected profit for a bidder when uncertainty about the cost of…

Estimating the probability that a proposed bid will win is obviously a central problem in competitive bidding theory. Unfortunately, a method for doing this, which originated with Friedman and which continues to be expounded in the literature, is logically incorrect. This paper points out the deficiency in that formulation. (Author/MLF)

Two specific approaches of how to evaluate an information retrieval system are explored. The first is a mathematical model for use in studying how to minimize operating costs. The model provides a method for comparative evaluation between systems. The cost model divides the costs of a retrieval system into two components: system costs and user…

A model to calculate the costs of automated cataloging systems based on cataloging copy in a system's data base is developed. The costs derived by the model for two systems, OCLC and BALLOTS, are compared to the costs of an existing manual system. (Author/KP)

Presents a diagrammatic proof for classroom use to demonstrate the quasi-convexity of the indirect utility function. Includes a variation of the price indifference curve. Suggests an exercise in which the student is asked to show that the tangency condition is a restatement of Roy's identity. (DK)

Suggests a framework for estimating the costs associated with shifting from the traditional method of financing and administering U.S. public schools to an educational voucher system. Uses certain framework components to compute "ballpark" estimates in five cost areas: accommodating additional students, record keeping, student…

Describes the design of optimal tree-structured vector quantizers that minimize the expected distortion subject to cost functions related to storage cost, encoding rate, or quantization time. Since the optimal design problem is intractable in most cases, the performance of a general design heuristic based on successive partitioning is analyzed.…

Observes that the envelope theorem, a fundamental tool in duality analysis, is still a puzzle to many people. Argues that the essence of a solution proposed by Paul Samuelson (1947) is also unclear to many people, but can be communicated with a simple cost diagram. Presents and explains the proposed diagram. (DSK)

An efficiency model and a performance function are presented in this technical report. The efficiency model has been tailored to the needs of an information retrieval system while remaining consistent with established economic procedures. The performance function allows for the comparison of several information retrieval systems. A sample…