Lectures on the Mathematical Method in Analytical Economics

✍ Scribed by Jacob T. Schwartz

• Publisher: Gordon and Breach
• Year: 1961
• Tongue: English
• Leaves: 296
• Series: Mathematics and Its Applications, Volume 1
• Category: Library

✦ Synopsis

Mathematical economics has made immense technical progress in
the last twenty years. Unfortunately, it has to a too large extent
remained isolated within the larger historical context of economic
debate, somehow ignoring rather than clarifying the great issues
around which this debate has raged; like a delicate precision clock-
work which the economist admires, as in a jeweler's window, before
setting back to serious work with pick and shovel. For this reason
I have tried, in the lectures from which the present volume is taken,
to direct attention particularly to these issues, and have attempted
to put economics in the foreground and mathematics together with
mathematical rigor in the background-although, alas, mathematics
in doing its good services has a way of calling attention to itself.
Where perfect generality has meant relative vagueness of results,
while reasonable assumptions have led to suggestive conclusions,
I have, in consequence, preferred to make rather than to omit these
assumptions.

✦ Table of 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 Walrssian 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