Jan van Daal and Albert Jolink

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CONTENTS
Preface  ix
Acknowledgements  xii
Conventions  xiii
Part I Prologue

1 ON THE USE OF MATHEMATICS IN
ECONOMIC ANALYSIS  3
Mathematics and economic theory  3
Mathematics and economic practice  5
Walras and the objections against the use of mathematics  6
Walras and the mechanical analogies  6
2 FREE COMPETITION AND GENERAL
EQUILIBRIUM  8
Free competition  8
General equilibrium  10
3 ON THE NOTION OF UTILITY AS
DEVELOPED BY WALRAS  13
Social wealth  13
‘Valories’ and value in exchange  14
Utility and demand  17
4 WALRAS’S GRAPHIC ANALYSIS OF THE
EXCHANGE OF TWO GOODS  20
Demand as an aggregate  20
Market equilibrium  22
Some special cases  24
Part II Walras’s equilibrium models
5 WALRAS’S EXCHANGE MODEL  29CONTENTS
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The theorem of maximum utility of commodities  29
The individual demand functions  32
Exchanging two goods  33
Bartering an arbitrary number of goods  34
Exchanging an arbitrary number of goods  36
Discussion  39
6 THE NOTION OF CAPITAL  41
The three categories of capital  41
Capital in the production process  43
7 THE ENTREPRENEUR  44
The entrepreneur  44
Profits and losses  46
8 PRODUCTION  49
Fixed coefficients of production  49
Flexible coefficients of production  51
Marginal productivity  52
9 WALRAS’S PRODUCTION MODEL  55
Individual demand and supply  56
The model  57
Discussion  59
10 THE RATE OF NET INCOME AND THE
FUTURE  61
Prices, depreciation and returns to capital  61
Savings  63
11 WALRAS’S MODEL OF CAPITAL FORMATION  67
The individual demand and supply equations  67
The twentieth-century model of capital formation  69
Optimal allocation of capital  72
Dynamics and uncertainty  73
The role of the entrepreneur in capital formation  74
12 ON THE FUTILITY OF LESSONS 26 AND 27
OF THE ÉLÉMENTS  77
The nineteenth-century model of capital formation  77
The theorem on the optimality of capital formation  78
Discussion  81
13 CIRCULATING CAPITAL  83
The notion of circulating capital  83
The model of capital formation with circulating capital  85CONTENTS
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14 A PRELUDE TO THE MONEY MODELS  89
Developments in monetary thought  89
The nineteenth-century cash balances approach  90
Walras’s macro money model  91
15 WALRAS’S EQUILIBRIUM MODEL WITH
FIAT-MONEY  94
The individuals’ cash balances  94
The supply of money  95
The demand for money  97
Equilibrium in the market for money services  98
The price equations  99
Walras’s quantity theory of money  99
Payments in the fiat-money model  100
16 WALRAS’S EQUILIBRIUM MODEL WITH
COMMODITY-MONEY  102
The model  102
Discussion  105
On the nature of money in Walras’s models  105
Part III  Extension
   
17 REALITY AND REALISTIC UTOPIAS  109
Simplification or generalization?  109
A utopian reality  111
18 FREE COMPETITION REVISITED  113
Laissez-faire and free competition  114
The organization of production  115
The distribution of income  118
19 WALRAS’S ‘GENERAL GENERAL
EQUILIBRIUM MODEL’  120
Synthesis: Walras’s utopian reality  120
Discussion  126
Appendices
   
I    A LIFE SKETCH OF LÉON WALRAS  129
The antecedents  129
Like father, like son  130
The beginning of a career  131
Professor at Lausanne  132
The years of rest  134CONTENTS
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II   ON WALRAS’S WORKS  135
Publishing the complete economic works  135
Léon Walras’s economic autobibliography  137
III  LETTER FROM LÉON WALRAS TO
HERBERT SOMERTON FOXWELL  148
IV THE EQUATIONS OF WALRAS’S COMPLETE
MODELS  151
The model with fiat-money  151
The model with commodity-based money  155
V   ON THE EXISTENCE OF EQUILIBRIUM AND
ON TÂTONNEMENT  159
Counting variables and equations  159
Modern proofs  160
Tâtonnement  163
Notes  167
References  183
Index of names  188
Subject index  190ix