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Principles of Mathematical Economics

Shapoor Vali
Atlantis Press
Publication Date: 
Number of Pages: 
Mathematics Textbooks for Science and Engineering 3
[Reviewed by
John Curran
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This book covers mathematical topics selected mainly from college algebra and calculus, and gives applications to basic models in economics. The audience is economics students who have either not taken calculus or perhaps never really took to it. In structure, the book alternates between crabbed sections on mathematical topics, and detailed sections on economics. One gets the sense that the author treated the mathematical exposition as something that had to be got on paper, but did not give a lot of thought to the presentation. Strangely, the expository sections for mathematics include examples but hardly ever from economics — indeed, one of the examples is on falling bodies. The sections on economics read like a transcript of the author’s lectures, with running commentary, pandering asides, and lots of board work for elementary examples.

The book has an uneasy relationship with computational tools. The preface makes a pointed argument for the use of “nonlinear” (meaning neither linear nor quadratic) functions in models, a world now open to us due to computers. Such “nonlinear” functions are used sparingly, however, and the book cannot seem to settle on which tool to use, variously Excel, R, Microsoft Mathematics, Google, Maple, and WolframAlpha. The graphics in the book reflect this indecision, and come in a variety of formats, including fuzzy screenshots. There is also no clear policy on when to use technology — on the whole the author misses opportunities to use it constructively.

Although the mathematical treatment is disappointing, the economics sections may be of use for some students. In particular there is extensive discussion of production functions for individual firms and for the economy as a whole. 

John Curran is Associate Professor of Mathematics and the coordinator of the Actuarial Science and Economics Program at Eastern Michigan University.