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Mathematical economics. 2nd ed. (English) Zbl 0568.90001
Cambridge etc.: Cambridge University Press. XXIII, 737 p. hbk: £35.00; $ 54.50; pbk: £17.50; $ 19.95 (1985).
The first edition of this book appeared in 1974 (see Zbl 0313.90008). In the second edition some new material is added to Chapter 1, ”Developments of Nonlinear Programming”, and references to recent work have been included. The rest of the text is taken unchanged from the first edition, apart from a few minor changes in the presentation, and corrections of some typographical errors. The book could have carried the title ”Mathematical Methods of Economic Analysis”. The emphasis is on mathematical optimizing methods, with applications to two topics in economic theory - existence and stability of a competitive equilibrium, and models of economic growth. These topics may not occupy quite the central position they did 15 years ago, and the book is inevitably dated. It does no longer lead the reader ”right to the frontiers of current research” as stated in the Preface to the first edition. To some extent the book may, as the author suggests in the Preface, be superceded by the massive three-volume work ”Handbook of Mathematical Economics” edited by K. J. Arrow and M. D. Intriligator [(1981; Zbl 0456.00035), (1982; Zbl 0522.90001)]. This is however a collective work, which lacks the uniform treatment and the consistent terminology of Takayama’s book. As an integrated presentation of a set of interrelated problems in economic analysis, the new edition of this book may be useful for at least another decade.
Reviewer: K.Borch

MSC:
91B50 General equilibrium theory
91B62 Economic growth models
90-02 Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming