Lectures on the Mathematical Method in Analytical Economics

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.

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.

A. The Leontief Model and the Technological Basis of Production
1. Introduction and Outline
2. Basic Mathematics of the Input-Output Model
3. Theory of Prices in the Open Leontief Model. Some Statistics
4. Concluding Discussion of the Leontief Model

B. Theory of Business Cycles
5. Business Cycles—Introductory Considerations
6. Mathematical Analysis of a Cycle-Theory Model. Expansive and Depressive Cases
7. Consumption in the Cycle-Theory Model. Say's Law
8. General Reflections on Keynesian Economics. The Numerical Value of the Multiplier
9. A Modified Cycle-Theory Model
10. Additional Discussion of Cycle Theory
11. A Model of Liquiidity Preference
12. A Model of Liquidity Preference, Continued 

C. Critique of the Neoclassical Equilibrium Theory. Keynesian Equilibria
13. Neoclassical or Walrasian Equilibrium. Introduction
14. Walrasian Equilibrium in the Case of a Single Labor Sector
15. Proof of the Existence of Walrasian Equilibrium
16. An Equilibrium Model Combining Neoclassical and Keynesian Features
17. Analysis of a Neoclassical Contention
18. Additional General Reflections on Keynesian Economics. The Propensity to Consume

Index