Lectures on the Mathematical Method in Analytical Economics (Dover Books on Mathematics) - Softcover

Schwartz, Jacob

Softcover

ISBN 10: 0486828034 ISBN 13: 9780486828039

Verlag: Dover Publications Inc., 2018

Inhaltsangabe

An early but still useful and frequently cited contribution to the science of mathematical economics, this volume is geared toward graduate students in the field. Prerequisites include familiarity with the basic theory of matrices and linear transformations and with elementary calculus.
Author Jacob T. Schwartz begins his treatment with an exploration of the Leontief input-output model, which forms a general framework for subsequent material. An introductory treatment of price theory in the Leontief model is followed by an examination of the business-cycle theory, following ideas pioneered by Lloyd Metzler and John Maynard Keynes.
In the final section, Schwartz applies the teachings of previous chapters to a critique of the general equilibrium approach devised by Léon Walras as the theory of supply and demand, and he synthesizes the notions of Walras and Keynes. 1961 edition.

Über diesen Titel

Über die Autorin bzw. den Autor

Jacob Theodore Schwartz (1930–2009) taught Mathematics and Computer Science at New York University's Courant Institute, where he founded the Computer Science Department and served as its Chairman from 1969–77. From 1986–89 he was the Director of the Defense Advanced Resource Projects Agency's Information and Science Technology Office. He wrote 18 books and more than 100 mathematical papers and technical reports. Dover also publishes his Introduction to Matrices and Vectors and Relativity in Illustrations.

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Lectures on the Mathematical Method in Analytical Economics

By JACOB T. SCHWARTZ

Dover Publications, Inc.

Copyright © 2018 Dover Publications, Inc.
All rights reserved.

ISBN: 978-0-486-82803-9

Contents

A. The Leontief Model and the Technological Basis of Production, 
1. Introduction and Outline, 3, 
2. Basic Mathematics of the Input-Output Model, 17, 
3. Theory of Prices in the Open Leontief Model. Some Statistics, 29, 
4. Concluding Discussion of the Leontief Model, 45, 
B. Theory of Business Cycles, 
5. Business Cycles — Introductory Considerations, 59, 
6. Mathematical Analysis of a Cycle-Theory Model. Expansive and Depressive Cases, 81, 
7. Consumption in the Cycle-Theory Model. Say's Law, 97, 
8. General Reflections on Keynesian Economics. The Numerical Value of the Multiplier, 111, 
9. A Modified Cycle-Theory Model, 123, 
10. Additional Discussion of Cycle Theory, 139, 
11. A Model of Liquidity Preference, 153, 
12. A Model of Liquidity Preference, Concluded, 169, 
C. Critique of the Neoclassical Equilibrium Theory. Keynesian Equilibria, 
13. Neoclassical or Walrasian Equilibrium. Introduction, 181, 
14. Walrasian Equilibrium in the Case of a Single Labor Sector, 189, 
15. Proof of the Existence of Walrasian Equilibrium, 199, 
16. An Equilibrium Model Combining Neoclassical and Keynesian Features, 215, 
17. Analysis of a Neoclassical Contention, 239, 
18. Additional General Reflections on Keynesian Economics. The Propensity to Consume, 255, 
Index, 279, 

CHAPTER 1

Introduction and Outline

1. What Will and What Will Not Be Treated

Mathematical economics currently includes, and perhaps is even dominated by, a number of branches with which we will have little to do. Thus, in order to define the subject of the present lectures, it is well to say something about these excluded branches. One topic that we shall not discuss to any great length is the subject that might be called efficiency economics in general, and is often called by the several names of its principal techniques — linear programming, operations research, perhaps also theory of games. In these subjects, the aim is to find the optimal adjustment, in one or another sense, to a given situation; they refer with greatest cogency and success to the profit-making possibilities of a single firm. As an omnibus reference to this area of thought let me cite Vajda's Linear Programming and the Theory of Games, and also von Neumann and Morgenstern's sparkling Theory of Games and Economic Behavior. Nor will we deal with econometrics, i.e. applied and theoretical economic statistics, except incidentally. Instead, we shall take economics as the cognitive study of a given object, the economy, and ask in the sense of natural science: what is this object like, how does it behave, and why? For this reason, we find the term analytical prefacing economics in our title. In spirit, our economics will be theoretical or speculative rather than directly empirical, and thus close in its basic approach to what has been called classical economics. In form, however, we will be more systematically mathematical. The branch of mathematics of which we will make greatest use will be the theory of matrices; let me here make reference to D. T. Finkbeiner's Introduction to Matrices and Linear Transformations, to Paul Halmos' Finite Dimensional Vector Spaces, Gantmacher's Theory of Matrices, and note the existence of numerous other introductory works on this subject. From time to time we will use a bit of calculus.

We will begin with a discussion of the theory of equilibrium prices — what has been traditionally called value theory — and go on to a discussion of business cycle theory, beginning with a model like that introduced by Lloyd Metzler, and developing the connection between this cycle theory and the equilibrium analysis that is more commonly called Keynesian. In the economic literature let me cite, in the first place, the famous General Theory of Keynes, which, as a pioneering work of science, is worth studying in spite of its numerous pedagogical and even theoretical mare's nests. A stimulating companion volume for the admirer of Keynes is Henry Hazlitt's The Failure of the New Economics. An Analysis of the Keynesian Fallacies. A superior mathematical exposition of the Keynesian theories is K. Kurihara's Introduction to Keynesian Dynamics; another, particularly fine, work of a similar sort is H. J. Brems's Output, Employment, Investment. Much of what we have to say will make reference to the " input-output " model of W. Leontief, on which there exists a vast literature. A good sample of this literature, full of references, is Activity Analysis of Production and Allocation, T. C. Koopmans, ed. Our attempts to compare speculative results with economic reality will be enormously facilitated by the extensive and painstaking work of the National Bureau of Economic Research, published in the form of a great many separate studies. A very fresh and stimulating empirical account of business cycles is the easily available Business Cycles and their Causes by W. C. Mitchell.

2. A Bouquet of Warnings

Mathematics may perhaps have a valuable role to play in economics — but its application brings several dangers. Mathematics necessarily works with exact models. In the course of investigating such a model, it is easy to forget that the mathematical exactness of one's reasoning has nothing to do with the exactness with which the model reflects economic reality. For this reason, a few dampening admonitions are in order. I quote the first and most severe from Ludwig von Mises' Human Action:

The problems of prices and costs have been treated also with mathematical methods. There have even been economists who held that the only appropriate method of dealing with economic problems is the mathematical method and who derided the logical economists as "literary" economists.

If this antagonism between the logical and the mathematical economists were merely a disagreement concerning the most adequate procedure to be applied in the study of economics, it would be superfluous to pay attention to it. The better method would prove its preeminence by bringing about better results. It may also be that different varieties of procedure are necessary for the solution of different problems and that for some of them one method is more useful than the other.

However, this is not a dispute about heuristic questions, but a controversy concerning the foundations of economics. The mathematical method must be rejected not only on account of its barrenness. It is an entirely vicious method, starting from false assumptions and leading to fallacious inferences. Its syllogisms are not only sterile; they divert the mind from the study of the real problems and distort the relations between the various phenomena.

The deliberations which result in the formulation of an equation are necessarily of a nonmathematical character. The formulation of the equation is the consummation of our knowledge; it does not directly enlarge our knowledge. Yet, in mechanics the equation can render very important practical services. As there exist constant relations between various mechanical elements and as these relations can be ascertained by experiments, it becomes possible to use equations for the solution of definite technological problems. Our modern industrial...

Details zur Ausgabe

• Verlag: Dover Publications Inc.
• Erscheinungsdatum: 2018
• Sprache: Englisch
• ISBN 10: 0486828034
• ISBN 13: 9780486828039
• Einband: Taschenbuch
• Anzahl der Seiten: 304
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Soc. Agr. La Raia Ss; http://www.la-raia.it; ; Strada Monterotondo, 79; Novi Ligure; 15067; Italien