The Pure Theory of Capital

By F. A. Hayek, Lawrence H. White and Bruce Caldwell

The Pure Theory of Capital, F. A. Hayek’s long-overlooked, little-understood volume, was his most detailed work in economic theory. Originally published in 1941 when fashionable economic thought had shifted to John Maynard Keynes, Hayek’s manifesto of capital theory is now available again for today’s students and economists to discover.

With a new introduction by Hayek expert Lawrence H. White, who firmly situates the book not only in historical and theoretical context but within Hayek’s own life and his struggle to complete the manuscript, this edition commemorates the celebrated scholar’s last major work in economics. Offering a detailed account of the equilibrium relationships between inputs and outputs in an economy, Hayek’s stated objective was to make capital theory—which had previously been devoted almost entirely to the explanation of interest rates—“useful for the analysis of the monetary phenomena of the real world.” His ambitious goal was nothing less than to develop a capital theory that could be fully integrated into the business cycle theory.

• Language: English
• Publisher: University of Chicago Press
• Release date: Aug 25, 2011
• ISBN: 9780226321295

Book preview

F. A. HAYEK (1899–1992), recipient of the Presidential Medal of Freedom in 1991 and cowinner of the Nobel Memorial Prize in Economics in 1974, was a pioneer in monetary theory and the principal proponent of libertarianism in the twentieth century.

BRUCE CALDWELL is the Joe Rosenthal Excellence Professor in the Department of Economics at the University of North Carolina, Greensboro. He is the author of Beyond Positivism: Economic Methodology in the Twentieth Century and Hayek’s Challenge: An Intellectual Biography of F.A. Hayek, the latter also published by the University of Chicago Press.

LAWRENCE H. WHITE is the F. A. Hayek Professor of Economic History at the University of Missouri–St. Louis. He is author of several books, most recently The Theory of Monetary Institutions. His work has appeared in the American Economic Review and other leading journals. He is a visiting professor at Queen’s University Belfast, and has recently been a visiting lecturer at the Swiss National Bank.

The University of Chicago Press, Chicago 60637

The University of Chicago Press, Ltd., London

© 2007 by the Estate of F. A. Hayek

All rights reserved. Published 2007

Printed in the United States of America

16 15 14 13 12 11 10 09 08 07            1 2 3 4 5

ISBN-13: 978-0-226-30299-1 (cloth)

ISBN-10: 0-226-32099-5 (cloth)

ISBN-13: 978-0-226-32129-5 (e-book)

Library of Congress Cataloging-in-Publication Data

Hayek, Friedrich A. von (Friedrich August), 1899–1992.

The pure theory of capital / F. A. Hayek; edited by Lawrence H. White; [editorial foreword], Bruce Caldwell.

p. cm. — (The collected works of F. A. Hayek; v. 12)

Originally published: London : Macmillan and Co., 1941.

"Two more appendices that were not in the original have been added. The first is a one-page comment by Hayek on an article by Professor Friedrich Lutz titled ‘Professor Hayek’s Theory of Interest.’ Both the Lutz paper and Hayek’s comment appeared in the November 1943 issue of the journal Economica. Appendix 5 contains a longer piece by Hayek, ‘Time-Preference and Productivity: A Reconsideration,’ that appeared in the February 1945 issue of Economica"—p. .

Includes bibliographical references and index.

ISBN-13: 978-0-226-32099-1 (cloth : alk. paper)

ISBN-10: 0-226-32099-5 (cloth: alk. paper)

1. Capital. 2. Investments. 3. Interest. I. White, Lawrence H. (Lawrence Henry) II. Title.

HB501.H392 2007

332'.041—dc22                                         2006025441

The paper used in this publication meets the minimum requirements of the American National Standard for Information Sciences—Permanence of Paper for Printed Library Materials, ANSI Z39.48-1992.

THE COLLECTED WORKS OF

F. A. Hayek

VOLUME XII

THE PURE THEORY OF CAPITAL

EDITED BY

LAWRENCE H. WHITE

The University of Chicago Press

PLAN OF THE COLLECTED WORKS

Edited by Bruce Caldwell

The plan is provisional. Minor alterations may occur in titles of individual books, and several additional volumes may be added.

THE COLLECTED WORKS OF F. A. HAYEK

Founding Editor: W. W. Bartley III

General Editor: Bruce Caldwell

Published with the support of

The Hoover Institution on War, Revolution and Peace Stanford University

The Earhart Foundation

The Pierre F. and Enid Goodrich Foundation

The Morris Foundation, Little Rock

CONTENTS

Editorial Foreword, by Bruce Caldwell

Editor’s Acknowledgements, by Lawrence H. White

Editor’s Introduction, by Lawrence H. White

THE PURE THEORY OF CAPITAL

Preface

Table of Contents

Analytical Table of Contents

Text to The Pure Theory of Capital

Appendices

Guide to Terms

Bibliography

Notes

Index

EDITORIAL FOREWORD

Bruce Caldwell

The Pure Theory of Capital occupied a great deal of Hayek’s time during the 1930s. As noted in the editor’s introduction by Lawrence H. White, there were some false starts as well as some full stops. Though he was more or less done with it by the end of 1939, the exigencies of the war delayed its publication until 1941.

It is a great pleasure to present here, as volume number 12 in the series, the Collected Works version of the book. As with all the other volumes, this one contains an editor’s introduction as well as numerous explanatory footnotes to help the reader follow Hayek’s argument. More so than is usually the case, both the introduction and the explanatory notes are invaluable aids in this volume, for capital theory is one of the most opaque areas of economics, and Hayek’s book is accordingly one of the most difficult of his technical contributions. We are in Professor White’s debt for the light he sheds on the arguments in the text, as well as for placing the book within an historical and theoretical context.

The text is faithful to the original, and includes Hayek’s preface, both the standard and the analytical table of contents, as well as the three appendices that Hayek had originally included. Two more appendices that were not in the original have been added. The first is a one-page comment by Hayek on an article by Professor Friedrich Lutz titled Professor Hayek’s Theory of Interest. Both the Lutz paper and Hayek’s comment appeared in the November 1943 issue of the journal Economica. Appendix 5 contains a longer piece by Hayek, Time-Preference and Productivity: A Reconsideration, that appeared in the February 1945 issue of Economica. Following the appendices is an index listing pages where terms are defined, as well as Hayek’s bibliography, both of which were included in the original. Though all of Hayek’s citations in the text have been standardized to reflect modern form, the bibliography is not: it is just as it was in the original.

I thank Larry White for doing a superb job of editing this volume, and also for doing the initial creation of a master text from which to work. Kevin Welding produced master copies of the appendices, and Brandon Beck of the index of definitions and the bibliography. Brandon also assisted me in doing a line-by-line check of the text against the original. I finally thank the Earhart Foundation, the Pierre F. and Enid Goodrich Foundation, and the Morris Foundation for their financial support of this volume and of the Collected Works series as a whole.

EDITOR’S ACKNOWLEDGEMENTS

Lawrence H. White

I wish to thank Bruce Caldwell for his judicious guidance as series editor, and additionally for sharing his findings from the Hayek-Machlup correspondence in the Hayek Collection at the Hoover Institution. I thank Jack Birner for incisive comments, and for providing a copy of Hayek’s unpublished notes to The Pure Theory of Capital. Roger Garrison, Israel Kirzner, and George Selgin provided helpful comments on early drafts of the introduction. None of the aforementioned is responsible for the shortcomings that remain in this volume. John L. Chapman provided able research assistance in the early stages of the project.

EDITOR’S INTRODUCTION

Lawrence H. White

[William Bartley]: Wouldn’t you say in retrospect that capital theory in the Austrian sense ended with Pure Theory of Capital?

Hayek: I’d say very largely. No one has done what I hoped would be done by others.¹

[Interviewer]: You had participated in the capital controversies of the 1930s along with Professor Hayek and Professor Knight. How do you evaluate that debate and your rôle in it?

[Fritz] Machlup: I think it’s very valuable and I think we should go back to it. It’s too bad that Hayek’s Pure Theory of Capital is no longer being read and that nobody tries now to work on it, after all, it is not the end. The relation of money capital to pure capital has still to be worked in. It’s terribly important, but there is still not sufficient interest in it.²

In sharp contrast to his vibrant and much-debated lectures published as Prices and Production ten years earlier, F. A. Hayek’s 1941 book The Pure Theory of Capital attracted little attention. Years of painstaking intellectual effort had produced a dry treatise that became, not coincidentally, Hayek’s last book in economic theory. The Pure Theory of Capital offers a detailed account of the equilibrium relationships between inputs and outputs in an economy where production takes time and where some capital goods are not completely versatile. It moves from the relatively simple type of input-output mapping assumed in Prices and Production to increasingly complex types of relationships between dated inputs and outputs. Hayek’s stated objective was to make capital theory—which had previously been devoted almost entirely to explanation of the interest rate—useful for the analysis of the monetary phenomena of the real world.³ His ambitious goal, then, was nothing less than to develop a capital theory that could be fully integrated into business cycle theory. That no subsequent writers have actually applied The Pure Theory of Capital to business cycle analysis suggests that what he ultimately produced was overly elaborate for the purpose.

The Book’s Place in Hayek’s Research Programme

The Pure Theory of Capital began as attempt to re-state the business cycle theory of Prices and Production with a more rigorous capital-theoretic foundation. As Don Bellante and Roger Garrison note, Prices and Production was intended only as an outline.⁴ In the preface to the second edition of Prices and Production, Hayek explained that it was a sketchy outline at best. The invitation to give the lectures that were published as Prices and Production

came at a time when I had arrived at a clear view of the outlines of a theory of industrial fluctuations but before I had elaborated it in full detail or even realised all the difficulties which such an elaboration presented. The exposition, moreover, was limited to what I could say in four lectures, which inevitably led to even greater oversimplification than I would probably have been guilty of in any other case.⁵

Later in the same paragraph Hayek added:

Contact with scientific circles which were less inclined than I was to take for granted the main propositions of the ‘Austrian’ theory of capital on which I have drawn so freely in this book has shown—not that these propositions were wrong or that they were less important than I had thought for the task for which I had used them—but that they would have to be developed in far greater detail and have to be adapted much more closely to the complicated conditions of real life before they could provide a completely satisfactory instrument for the explanation of the particularly complicated phenomena to which I have applied them.⁶

This was the agenda Hayek would pursue in The Pure Theory of Capital.

Among the key simplifications of Prices and Production was Hayek’s well-known graphical device in Lecture II representing an economy’s aggregate ‘structure of production’ as a series of ‘stages’ leading to the output of consumers’goods. At each stage, an application of ‘original means of production’ (labour and land inputs) adds value to goods-in-process. In the case of continuous and even application of inputs over time, the rising value of the goods-in-process describes the hypotenuse of a right triangle (one leg is value, the other is time).

The Hayekian triangle thus drawn corresponded to the simple case of ‘continuous-input point-output’ production that had earlier been analysed by economists William Stanley Jevons and Eugen von Böhm-Bawerk.⁷ Such a case can be illustrated by considering a growing tree, supposing that the tree must be continuously tended. (If no tending is needed between planting and harvesting, the production process would be ‘point-input point-output’.) The tree (a capital good) ‘matures’ into firewood (a consumer good) with the application of land and labour inputs over time. Or consider a grazing steer that matures into steaks. With a perfectly even application of inputs over the production process, an ‘average period of production’ (APP), summarising the duration or time-consumption or ‘roundaboutness’ of the process in ‘technical’ terms (independent of the interest rate), can readily be identified: it is one-half the length of the process from start to finish. For each unit of land or labour that the process ‘bottles up’ for longer than the APP, there is another unit that it bottles up for correspondingly less time.

Under the classical assumption that workers are paid during the duration of the process by drawing down a previously accumulated ‘wages fund’, greater saving (accumulating a larger fund) allows a longer APP and hence the use of more-productive-but-more-roundabout techniques that yield a greater (undiscounted or steady-state) consumption per worker. A reduction in saving does the reverse. The equilibrium interest rate balances the marginal gain from lengthening the APP against savers’ preference for consuming sooner rather than later.⁸

Hayek soon came to recognise that the case of even-continuous-input followed by point-output is a very special case.⁹ An APP is no longer technically definable (independent of the interest rate) in more complicated cases. One complication, made famous decades later by the ‘reswitching’ examples of the ‘Cambridge controversies’ over capital, is an uneven time-distribution of inputs. A second complication is introduced by durable capital goods that help produce streams (rather than single points) of outputs. With durable capital goods like a lumberjack’s axe in mind, Robert Solow remarked that Böhm-Bawerk, who seemed to be thinking mainly about the age at which trees should be cut down, seemed to worry too little about the implement to be used in felling them.¹⁰ Hayek’s aim in The Pure Theory of Capital was to analyse such complications, relaxing the Böhm-Bawerkian simplifying assumptions about production technology (in particular, no durable inputs or outputs) that Hayek had adopted in Prices and Production.

Also for simplicity, Prices and Production had made its equilibrium benchmark a stationary economy. Under stationarity, the ‘time’ axis of the Hayekian triangle can do double duty. The diagram can be interpreted either as (a) showing the growth in value through time of the particular batch of goods-in-process that will reach consumption on a particular date, or (b) showing the values held at a moment in time (today) by all the goods-in-process across the various stages of completion. Stationarity implies that the through-time profile looks the same as the across-stages profile. In The Pure Theory of Capital, Hayek disentangled these two aspects of time by giving each its own axis (in addition to the value axis). Readers of the book have often had a difficult time making intuitive sense of the resulting ‘three-dimensional’ diagrams.¹¹

In tandem with his work in business cycle theory, Hayek by 1941 had done important work on the meaning of economic equilibrium through time. He had addressed the question in a 1928 essay, Intertemporal Price Equilibrium and Movements in the Value of Money.¹² In the 1937 essay Economics and Knowledge he argued that an economic equilibrium through time is best conceived as the ongoing compatibility of various agents’ plans.¹³ The Pure Theory of Capital puts the compatibility-of-plans concept to work. Though the book begins with the simple case of a stationary economy, Hayek notes that to grapple with many important problems of capital theory—such as the use of inherited capital ‘relics’ that it does not pay to reproduce in the same form, or the transition to a more or less capitalistic structure of production—analysis must go beyond examining stationary states.¹⁴ The broader plan-coordination notion of equilibrium then serves as the relevant benchmark.

Hayek’s Long Struggle with the Book

Hayek admitted in the preface to The Pure Theory of Capital that the book had been a struggle to write, and had not reached the complete form he had planned.¹⁵ In unpublished notes to The Pure Theory of Capital he wrote: The period of gestation of this book has been unduly long and protracted. . . . I fear that even in this last form in which I have finally decided to publish it bears far too much the marks of long toil and labour and has not achieved anything like the comprehensive analysis of the whole problem which I should like to give it.¹⁶ As published, it laid out the capital-theoretic foundations, but did not fully complete the originally intended superstructure: a full-dress re-statement of Hayek’s business cycle theory. As Kenneth Boulding wryly suggested in a review, this development was ironic given that Hayek’s own cycle theory emphasised the economy’s inability to complete projects with overly elaborate foundations:

One has the impression that many of Dr. Hayek’s abstractions are foundations without a superstructure. The theory of capital teaches an important lesson—that foundations may be too elaborate. The lesson of Luke 14:28–31—perhaps the first example of capital theory—may also apply to the construction of intellectual structures.¹⁷

The difficult progress of the book is documented by Hayek’s correspondence in the 1930s with his friend and former Viennese classmate, economist Fritz Machlup.¹⁸ Machlup had gone to the United States on a Rockefeller Fellowship in 1933, and accepted a teaching position at the University of Buffalo in New York in 1935. Machlup provided Hayek with encouragement and advice on numerous occasions during the writing of The Pure Theory of Capital, including extensive line-by-line recommendations for wording changes.

In a letter dated February 15, 1934, Machlup told Hayek that he was awaiting a draft copy of the first part of the book with keen anticipation, which indicates that Hayek probably began the book sometime in 1933. The draft copy arrived a few months later, and Machlup provided Hayek with his first set of extensive comments in September. In addition to three pages of recommendations for revision of specific passages, Machlup repeatedly emphasised the need for clarity in Hayek’s presentation. He suggested that Hayek reorganise his presentation so that diagrams would accompany the relevant part of the text, that the diagrams should only be supplemental to his written formulations, and that formulas used in each chapter should stand on their own rather than requiring the reader to go back to earlier chapters to decipher them. Machlup praised Hayek’s efforts with such difficult material, but clearly thought that much more needed to be done. The next month Hayek replied, saying that he was going to set aside the first part of the book to begin work on the second. In the winter he sent a copy of the first chapter of the second part (in their correspondence this is referred to as chapter 7; in the published version Part II begins with chapter 8), and in April 1935 Machlup sent him some more detailed comments.

Hayek apparently put the book on hold in the summer of 1935, reporting that he was enjoying the summer and working very little, but returned to working on it in the fall. In May of 1936, Hayek wrote to Machlup that he had finished a first draft of the book before the Easter vacation and was now bringing it to completion. In his next letter, dated June 21, 1936, Hayek informed Machlup that he had completely rewritten the introductory section of the book: from that which you have already seen nothing remains. By summer’s end Machlup had received eleven chapters. In the fall of 1936 he provided Hayek with eight pages of line-by-line comments.

In December Machlup, who must have believed that the manuscript was nearly complete, asked Hayek when he expected it to be published. Progress on the manuscript was, however, going sideways. Hayek replied that he was still working on it, and had totally redone the second chapter.¹⁹ In 1937 Hayek reported that he had gotten so frustrated that he had to put the book aside. In the unpublished notes Hayek refers to having tried even the experiment of putting the practically finished manuscript aside for a considerable period.²⁰ Their correspondence languished, and the book was not mentioned again until Feb 14, 1938, when Hayek asked Machlup to send him a few pages from one of the chapters, apparently because he had lost his own copies.

Hayek must have resumed serious work on the book in 1938, judging from a letter to Hayek in November from Vera Lutz, a former student then living in Princeton, who was reporting her progress in typing chapters 20 through 26.²¹ In April 1939 Hayek told Machlup that he was working on a chapter on the business cycle (presumably chapter 27), and by August 1939 he could finally report that the book was almost completed. All but the final revision would be done in the next month or so.

The evidence from the correspondence is consistent with the recollections of G. L. S. Shackle, who was a graduate student at the London School of Economics at the time, describing the difficulties Hayek encountered in trying to write the book:

The Pure Theory of Capital emerged in its published form from several manuscript versions which I had the privilege of reading during its composition. The sustained intensity of thought which it cost its author . . . [required] high moral courage and implacable resolve. . . . As this work progressed through several drafts during the middle and later 1930s, he responded to its everfreshly multiplying difficulties with an intense and sustained effort nothing short of heroic.²²

The correspondence also corroborates one of Hayek’s later explanations for why The Pure Theory of Capital never completed its planned re-statement of Hayek’s business cycle theory, but instead concluded with comparatively brief remarks on the relationship between capital theory and the theory of the cycle. As Hayek told one interviewer,

. . . I never really started on the intended monetary or dynamic continuation. Though I tried hard to concentrate further on this subject, my interest began to wander to other topics.²³

Hayek’s August 1939 letter to Machlup specified his new interest: research on the scientific foundations of economics that would trace the conceptual errors of the last one hundred years, from Saint-Simon to Hitler. Hayek would the earlier three-dimensionallater call this line of research the ‘Abuse of Reason’ project. It would occupy him through the war years and generate such essays as Scientism and the Study of Society and The Counter-revolution of Science, as well as his most famous book, The Road to Serfdom.²⁴ Hayek made it plain in the letter that he was eager to begin his new project.

Complementary to these rising opportunity costs, Hayek in another interview cited declining benefits: to continue to work on the planned re-statement of his cycle theory would have meant working for a result which I already knew, but had to prove it, which was very dull.²⁵

In a third interview Hayek offered a third (but less persuasive) rationale, besides distraction by other topics and fatigue with pure theory, for why he didn’t continue with the intended monetary extension:

It may surprise you, but during the war I was fighting on Keynes’s side against his critics, because Keynes was very much afraid of inflation. I actually had published one or two essays, one reviewing his wartime pamphlet and another one on the problem of combating inflation, which he already approved. During the war years, the great danger had become inflation, no longer deflation; so we were up against inflation. And in these circumstances, where I wanted to strengthen his influence against the inflationists, I did not want to continue the book.²⁶

Given the sharp criticism of Keynes that appears in the published book in chapter 27, we are perhaps entitled to discount the importance of this last rationale.

The Relationship of Hayek’s Theory to Its Predecessors

Hayek described his aim in The Pure Theory as in some respects no more than an attempt towards a systematic development and elabouration of the fundamental ideas underlying the theory of interest of W. S. Jevons, E. v. Böhm-Bawerk, and Knut Wicksell, though he noted that parts of their theory might be changed beyond recognition.²⁷ Among these authors, Hayek gave higher marks for originality and fruitfulness to Jevons than to Böhm-Bawerk:

Böhm-Bawerk in many respects simply developed the ideas propounded by Jevons and made them intelligible to wider circles by elaborating them: but at the same time he gave the impetus to a movement away from what seems to me to be the more fruitful approach on Jevonian lines.²⁸

The ideas about capitalistic production that these authors propounded had come to be known as ‘Austrian’ capital theory after Böhm-Bawerk’s nationality, despite the distinct nationalities of Jevons (English) and Wicksell (Swedish), and despite the fact that Böhm-Bawerk’s theory of interest was not endorsed by his fellow native Austrian economists Carl Menger, Friedrich von Wieser, or Joseph Schumpeter.

Austrian capital theory began with a chapter of Menger’s 1871 Principles of Economics.²⁹ Menger emphasised that the market prices of ‘higher-order’ goods (land, labour, and capital goods) derive from their prospective contributions to the production of valued consumer goods (goods of ‘lower order’). Menger thus inverted the classical ‘real cost’ doctrine according to which the prices of consumer goods derive from the amount of labour or land that goes into them.

Böhm-Bawerk elabourated on Menger’s distinction between higher- and lower-order goods with a fairly straightforward model of aggregate production through time.³⁰ In that model semi-finished goods proceed from the highest (raw material) stage downward through successively lower stages, with the application of land and labour services at each stage, until they finally become consumable products. Böhm-Bawerk’s (in)famous summary measure of the time spent in production was the aforementioned ‘average period of production’.

Hayek used the APP concept in Prices and Production to describe cyclical changes in the ‘length’ of the capital structure. By 1936 Hayek would admit that in general it is in fact inadmissible, to reduce the description of the range of periods for which the different factors are invested to an expression of the type of a single time dimension such as the average period of production.³¹ Hayek accordingly acknowledged that while Austrian capital theory was essentially right and even . . . indispensable for a more detailed analysis, I can see that in the simplified form in which I had to use it in my former book it may be more misleading than helpful.³²

The APP could be misleading because it cannot generally be measured purely in technical terms. An ‘investment period’ (IP) can be technically identified for a particular marginal input such as an hour of labour, measuring the time (or array of times) between its application and the maturing of the final product(s) due to its application. In principle, identifying an input’s contributions to dated output(s) merely generalises the standard concept of identifying the physical product of a marginal unit of input in timeless production. Beyond the very simplest cases, many inputs go jointly into producing a given final product, and many final outputs (at many dates) result jointly from inputs that go into producing a durable tool. Finding the average or aggregate IP for the entire series of inputs that produces a given final product, a fortiori for the aggregate of final products produced by an entire economy, would require weighting and summing the IPs associated with all the various inputs. The proper relative weights on inputs at different dates (the relative amounts ‘tied up’ in present value terms) vary with the rate of interest. Only in special cases can an average be formed of various IPs in purely technical terms, independent of the interest rate, as would be required for the APP to serve as a datum in a theory determining the interest rate. The Pure Theory of Capital aimed to show that the analysis of time-consuming production can proceed in a modified fashion, and can still reach the key conclusions associated with Austrian capital theory, without relying on an interest-rate-independent ‘average period of production’.³³

In the place of the APP measure, which is a simple scalar, Hayek (in chapters 8 and 9 below) offered the more complex notion of the time distribution of the output due to a moment’s input, a function that maps from a date-zero marginal input dose to the array of dates at which its physical products will mature. This mapping can be represented either by an ‘input curve’ that shows the share of the total date-zero input to which each later date’s output is due, or by an ‘output curve’ that shows the share of the total all-dates output (attributable to date-zero input) that each date’s output represents. The difference between the two curves reflects compound interest, corresponding in equilibrium to the greater physical productivity of the more time-consuming production processes chosen.

The greater physical productivity of more time-consuming techniques, Hayek explained, is not an empirical generalisation but a necessary feature of the frontier of potentially well-chosen techniques in the face of any positive discount rate.³⁴ If a more time-consuming technique is not physically more productive, it is dominated and never chosen.

In an interview with Jack High in the late 1970s, Hayek identified the book’s aim as the rehabilitation of Böhm-Bawerk’s theory. The book’s notorious complexity was due to replacing the APP with more sophisticated concepts:

[High]: You have written an extraordinarily difficult book on capital theory—in my opinion, it’s difficult. What message did you want to convey in that book?

Hayek: To put it briefly, I think that while Böhm-Bawerk was fundamentally right, his exposition in terms of an average period of production was so over-simplified as to mislead in the application. And that if we want to think the Böhm-Bawerk idea through, we have to introduce much more complex assumptions. Once you do this, the things become so damned complicated it’s almost impossible to follow it.

Q2: Did you have any idea the work was going to be that complicated when you undertook it?

Hayek: No, no. I certainly didn’t. It very gradually dawned upon me that the whole thing seemed to change its aspect once you could not put it in the simple form that you could substitute a simple average period of production for the range of investment periods. The average period of production is the first model showing a principle, but it is almost inapplicable to the real situation.³⁵

Hayek considered Wicksell’s work on capital and interest to have been the most immediate predecessor to The Pure Theory of Capital. In the area of interest theory, Wicksell and his students have systematically developed the productivity approach. It is in the shape into which this type of theory has been fashioned by Wicksell that it provides the most useful basis for the present study.³⁶ Wicksell in turn had seen his own analysis as a re-statement and extension of Böhm-Bawerk’s theory.³⁷

In Wicksell we find versions of four of the key concepts that Hayek emphasises in The Pure Theory of Capital:

1. The essential rôle of capital arises from the time-consuming nature of production.³⁸

2. Two key features distinguish capital goods from other inputs: capital goods (a) are non-permanent (get used up) and (b) can be used up faster or slower. Pure land and labour, by contrast, are permanent and yield an invariable flow of services.³⁹

3. The economy’s capital structure can be sliced cross-sectionally at a moment in time (thus viewing capital goods as factors of production cooperating with land and labour) or sliced lengthwise through time (thus viewing capital goods as semi-finished goods in the process of reaching final consumption with the successive application of land and labour services).⁴⁰

4. Net capital formation requires a diversion of input services that could otherwise go to the immediate production of consumer goods.⁴¹

Hayek departed from Wicksell by offering a consistently forward-looking conception of capital, in contrast to Wicksell’s backward-looking suggestion that capital be regarded as a mass of saved-up labour and saved-up land.⁴² In his essay-review of Hayek’s book, Arthur Smithies argued that this departure leads necessarily to rejection of the average period of production device: For, as [Hayek] correctly points out, when capital is defined as a congeries of heterogeneous resources, the only way to calculate an average is to weight these resources according to their relative values and their relative values ‘will inevitably depend on the rate of interest’.⁴³ But even on Wicksell’s backward-looking view, the same problem arises: a weighting would be necessary to calculate an average from labour and land inputs that had been incorporated into the ‘saved-up’ mass at different dates, and the weights will depend on the rate of interest.

Irving Fisher’s work on capital and interest, early in the twentieth century, had a seminal influence on neoclassical capital and growth theory.⁴⁴ Böhm-Bawerk and Wicksell had already made the analysis of intertemporal production largely subordinate to explaining the phenomenon of interest and the height of interest rates, but Fisher took this tendency to the extreme. Hayek’s approach in The Pure Theory of Capital was the reverse: he made the theory of interest subordinate to explaining the structure of intertemporal production. With regard to determination of the interest rate, Hayek declared that Fisher’s 1930 book had provided the most systematic work on the subject which we possess, a formally unimpugnable exposition of the theory of interest.⁴⁵ Hayek accordingly adopted Fisher’s expository apparatus for understanding the interest rate as an equilibrium exchange rate between the near and distant future.⁴⁶ In that apparatus, the equilibrium interest rate emerges from tangency between an economy-wide intertemporal transformation curve (a production-possibility frontier between near-future and distant-future output) and a representative agent’s intertemporal indifference curves.⁴⁷

Fisher’s apparatus accorded intertemporal transformation and time-preference logically co-equal status as determinants of the interest rate. Intertemporal transformation is sometimes called ‘productivity of capital’, but the ambiguity of the latter phrase has given rise to misunderstandings. Productivity in the sense of intertemporal transformation is measured at the margin by the extra product that results from extending the temporal length of an investment period. It must be carefully distinguished from productivity in the sense of the usefulness of capital goods, which is measured by the marginal product that results—for any given production period—from having more tools. Böhm-Bawerk’s well-known critique of ‘productivity theories’ (attempts to explain interest by capital productivity in the second sense) made the point that the usefulness of capital goods explains why positive prices are paid to rent tools and machines, just as positive wages are paid to hire labour and rent land, but it does not explain interest. Böhm-Bawerk’s critique did not show that an economy’s array of intertemporal transformation opportunities (as isolated by Fisher and Hayek) is irrelevant to explaining its interest rate. Contrary to some commentators, then, Böhm-Bawerk’s positive theory—in which intertemporal transformation plays a key rôle—was not inconsistent with his own demolition of ‘productivity theories’ of interest. Such commentators included Hayek himself, who stated that Böhm-Bawerk’s effective, although I think mistaken critique of the earlier productivity theories of interest had the effect of causing later developments to centre increasingly round the ‘psychological’ or ‘time-preference’ element in his theory rather than the productivity element.⁴⁸

Hayek in The Pure Theory of Capital took the position that intertemporal transformation is in practice more important than time-preference for determining the interest rate, graphically represented by the slope at which the intertemporal transformation and indifference curves are tangent, in the sense that the intertemporal transformation curve is in practice less bowed than the representative agent’s intertemporal indifference curve. Later Hayek published a reconsideration on that point, where he noted that his earlier position assumed a long-run equilibrium, but he now recognised that intertemporal indifference curves are likely to be less bowed than the short-run intertemporal transformation curve for an unexpected drop in the willingness to save.⁴⁹ Whichever was more bowed, Hayek’s analysis of interest determination in terms of the two sets of curves was thoroughly Fisherian.

Fisher’s interest theory, like Hayek’s production theory, is an intertemporal equilibrium theory in which goods and services are dated (that is, distinguished by when they are used).⁵⁰ For Fisher’s purpose—explaining the interest rate as an equilibrium intertemporal exchange rate—it was sufficient to consider the simplest possible intertemporal production choice: one composite commodity and two time periods. In the representative agent version, as noted, the slope of the tangency between the intertemporal production possibility frontier and the representative agent’s intertemporal indifference curves determines the equilibrium interest rate. For Hayek’s purpose in The Pure Theory of Capital—understanding the structure of production in a world where capital goods are more or less specific to particular uses—it was necessary to generalise to many inputs, and to dehomogenise inputs from outputs. Thus Hayek rightly commented that because of . . . his concentration on interest rather than on the methods of production, Professor Fisher’s work hardly touches on a good deal of what is treated as important in the present study.⁵¹ Hayek’s innovation in his 1928 essay, made the central focus of his 1941 book, was the notion of a multi-good intertemporal equilibrium. That notion was needed to analyse the problems of intertemporal production planning connected with specific capital goods.⁵² Hayek’s principal concern in the 1928 article was with the equilibrium path of the price level over time. For that purpose he needed just two goods—a composite consumption commodity and money—at each date. The behaviour of the price level over time is the behaviour of the money price of the composite consumption good. In his later business cycle works, and finally and most fully in The Pure Theory of Capital, Hayek considered the problems of intertemporal planning connected with a variety of capital and consumption goods and a variety of agents.

In contrast to Hayek’s earlier work on business cycles, The Pure Theory of Capital makes little reference to the writings of Ludwig von Mises. Hayek does offer a passing catch-all acknowledgement to Mises’s work on the business cycle.⁵³ The only specific work of Mises that he cites, and that in an appendix, is a 1928 monograph on monetary policy,⁵⁴ although a 1933 Mises essay on Inconvertible Capital⁵⁵ appeared in the bibliography.⁵⁶ He does not refer to Mises’s Nationalökonomie, the German-language predecessor of Mises’s magnum opus Human Action (in which capital theory is prominently discussed), published in 1940, but this is because he only received it in manuscript form in August 1939, when his own manuscript was more or less completed.⁵⁷

In Hayek’s view, the capital-and-interest theories most useful for his analysis of production were those along the lines of Jevons, Böhm-Bawerk, and Wicksell, which stressed the ‘productivity of capital’ and were in consequence based on an analysis of the material structure of production.⁵⁸ Mises, by contrast, favoured a theory of interest (sometimes called the ‘pure time-preference’ theory) that views the material productivity of capital goods in either sense as irrelevant to explaining the interest rate. For Mises, the productivity of having additional tools explains only their rental prices (as Böhm-Bawerk had argued). Intertemporal transformation in value terms is entirely the result of present-value discounting in the pricing of capital goods; the discount rate in turn is explained entirely by time-preference. Mises had little to say about the trade-off between near-future and distant-future physical output. To a Fisherian, this trade-off is crucial for determining the prospective scarcity of near-future relative to distant-future output, and thereby the equilibrium rate of time-preference. When Hayek subsequently reviewed Mises’s Nationalökonomie in the pages of the Economic Journal, he accordingly commented that on a first reading his development of the psychological element in the Böhm-Bawerkian theory, although highly illuminating in some respects, seems to the reviewer as a whole less convincing than most parts of the work.⁵⁹

The 1930s Capital Debates

In a series of journal articles in the 1930s Hayek (with help from Fritz Machlup) debated capital theory at length with Frank Knight, and more briefly with Nicholas Kaldor. ⁶⁰ Perhaps surprisingly, the Hayek-Knight debate does not figure explicitly in The Pure Theory of Capital. All references to Knight, with one exception, are favourable.⁶¹ The exception registers Hayek’s dissent from Knight’s mystical notion that capital must be viewed as a perpetual fund, and refers the reader to Hayek’s 1936 article on The Mythology of Capital.⁶²

Important differences between Hayek and Knight nonetheless remain evident in The Pure Theory of Capital. Hayek sharply criticised the approach (which he attributed to the Cambridge School, but which was in this respect akin to Knight’s) that treats one part of capital as being permanent, and the other part as involving no waiting whatsoever: all the problems of capital are then evaded.⁶³ Pervading the book is Hayek’s rejection of the Knightian propositions that (1) capital may be regarded as a homogeneous fund; (2) the permanent maintenance of capital is to be taken for granted; (3) there is no economically meaningful distinction to be made between ‘original factors’ (land and labour) and capital; (4) input and output are synchronous, so production is essentially instantaneous, and concepts of time-duration in production (the period of production or the investment period) are useless; and (5) production and consumption are simultaneous, so it is pointless to speak of ‘waiting’.⁶⁴

Alan Ebenstein has suggested that conflict between Knightian and Hayekian capital theory remained a live issue at the University of Chicago (where Knight had taught) when Hayek joined the University’s Committee on Social Thought in 1950. He quotes Chicago economist Milton Friedman as saying that the Chicago economics department "didn’t agree with [Hayek’s] economics. Prices and Production, his capital theory—if they had been looking around the world for an economist to add to their staff, their prescription would not have been the author of Prices and Production".⁶⁵

Reception and Subsequent Influence on Mainstream Economics

The Pure Theory of Capital was published just as the ‘Keynesian revolution’ was sweeping the economics profession. From the perspective of the ‘New Economics’ of pervasively unemployed (hence effectively non-scarce) labour and capital, Hayek’s concern with optimally allocating scarce factors of production was hopelessly old-fashioned. Hayek was a well-known critic of Keynes, and the book’s final paragraph was sharply anti-Keynesian. The book’s professional reception was accordingly chilly. In the opening sentence of a lengthy essay-review in the American Economic Review, Arthur Smithies likened Hayek’s message to old-time religious fundamentalism:

Professor Hayek has addressed a weighty appeal to his fellow economists to return from the pursuit of Mammon to the contemplation of economic fundamentals; and since his belief is, and always has been, that the ultimate truth was revealed in varying degrees to Jevons, Böhm-Bawerk, and Wicksell, his present book consists in the main of higher criticism and extension of the work of these authors, rather than of new developments in economic doctrine.⁶⁶

Kenneth Boulding offered a similar analogy, though his appears more sympathetic to Hayek:

Mr. Keynes’s economics of surprise, like Hitler’s, may be admirable in producing spectacular immediate success. But we need Puritan economists like Dr. Hayek to point out the future penalties of spendthrift pleasures and to dangle us over the hell-fire of the long run.⁶⁷

Writing two decades later, during the Keynesian heyday, Carl Uhr commented:

For their time, approximately 1920–35, analyses of the Wicksell-Åkermanvon Hayek type represented outstanding achievements both in capital and business cycle theory. Since then, and particularly with the arrival of the so-called ‘Keynesian revolution’, very little more is heard of capital structure analyses on the one hand and capital shortage explanations of the upper turning point of business cycles on the other.⁶⁸

Keynesian theory depicted current income as proximately determined by current expenditure (Y = C + I + G) rather than by prior production. The ‘circular flow’ supplanted capital theory in macroeconomics. Current-period analysis displaced intertemporal analysis. The interest rate no longer played an equilibrating rôle. Left to its own devices, the economy could readily get stuck at a level of expenditure too small to achieve full employment. Smithies found it remarkable (note his apparently sneering use of quotation marks) that Professor Hayek’s point of view is that a ‘real’ economy, if left to itself, will automatically achieve ‘equilibrium’ and that the disturbances that occur in real life are due to the subversive influence of money.⁶⁹ Keynesian theory, as Uhr put it, ‘demoted’ the interest rate from the rôle of guiding intertemporal allocation to that of rewarding the sacrifice of liquidity.⁷⁰ Though it never became mainstream doctrine, some Keynesians nearly overthrew the idea that capital is scarce, and needs to be carefully allocated, in favour of the ‘secular stagnation’ thesis that remunerative uses of capital are or soon will be hard to come by.

Whatever the full set of reasons for the success of the Keynesian revolution, the popularity of Hayek’s approach undoubtedly suffered in part because of the author’s policy stance.⁷¹ Economists and policy-makers eager to do something about the Great Depression rejected Hayek’s counsel of non-activist monetary policy. Uhr wrote of the Hayekians’ failure to interpret the Great Depression in a sufficiently meaningful manner to suggest criteria for realisable economic policy.⁷² Hayek’s message—that the way to avoid an economic collapse is to prevent monetary policy from creating an unsustainable boom in the first place—was regarded as an irrelevant ‘counsel of perfection’ in the midst of a deep depression. The fact that passages from The Pure Theory of Capital were later reprinted in a compendium of The Critics of Keynesian Economics underscores the point that Hayek’s analysis was alien to the new macroeconomic mainstream.⁷³

Since the late 1950s some of the concerns addressed by Hayek’s capital theory have reclaimed economists’ attention, in the form of the neoclassical growth theory developed by Robert Solow and others. Growth theory is all about intertemporal allocation, particularly the trade-off between current consumption and future consumption (via savings and capital accumulation). And yet Hayek’s work had no apparent impact on the development of neoclassical growth theory. Jack Birner has offered two explanations.⁷⁴ The first is that growth theorists were too focused on immediate modelling and econometric problems to look into old books and journals for guidance. The second is that what they did know about the older literature did not encourage them to look further. Birner relates an interview with Solow in support of the second explanation:

In an interview with the author (20 April 1989), Solow admitted that he knew Hayek’s Prices and Production: "I did read Hayek as a student (. . .) I found it completely incomprehensible. I was assigned to read Prices and Production (. . .) [It was] not that I thought it was wrong so much as I did not understand it (. . .) I thought there’s got to be something wrong with the man who could write that. And I never read [any other work of Hayek’s], I simply found it incomprehensible".⁷⁵

This statement is consistent with Solow’s earlier published remark that I find the earlier discussions [between Böhm-Bawerk and Clark, and between Hayek and Knight] terribly confusing and occasionally incomprehensible to a contemporary economist.⁷⁶

Solow would likely have found little of use in The Pure Theory of Capital, or in the Hayek-Knight debates, had he read them. Although neoclassical growth theory does revolve around the trade-off between consumption (today) and capital accumulation (for the sake of future consumption), it typically treats the capital stock as an undifferentiated aggregate. In ‘one-sector’ growth models the capital good is even identical to the consumption good. Capital en masse (denoted K) combines with labour (L) in production, with the resulting volume of output governed by the level of technology. Elapsing time enters the model in the form of time-paths for capital accumulation, labour force growth, and output growth, not in the form of time-consuming production. ‘Real business cycle’ theorists subsequently adapted the Solow model to help explain business cycles. (Their preferred impulse for generating the business cycle is technology shocks, not monetary shocks, hence the label ‘real’.) More recently ‘endogenous growth’ theorists have focused on explaining the technological improvements that are empirically associated with the lion’s share of growth in per-capita output (the share associated with capital accumulation is much smaller).

Hayek’s capital theory, by contrast, focuses on the time elapsing within a production process between the application of inputs and the final emergence of consumption goods. It matters for the theory that capital takes the form of partly finished goods-in-process, and impermanent tools, intended to produce particular outputs at particular future dates. The structure and composition of the capital stock—not just aggregate quantity of capital—matter crucially both for long-run growth and for business cycles.

Expositors of neoclassical capital theory have similarly overlooked The Pure Theory of Capital even when they have discussed Austrian capital-theoretic concepts. Jack Hirshleifer, in a textbook along Fisherian lines, cited only Böhm-Bawerk and Wicksell in connection with the notions of the period of production and of capital as goods-in-process.⁷⁷ This is understandable given that Hirshleifer did not go beyond the simple stationary Böhm-Bawerkian case of a homogeneous capital good in various stages of completion (the parable of the growing stand of trees of various ages), whereas Hayek’s aim in The Pure Theory was (as noted above) precisely to investigate more complicated cases. Edwin Burmeister in a monograph on Capital Theory and Dynamics mentioned in passing the Austrian tradition associated with such economists as Böhm-Bawerk, Wicksell, and Hayek, but neither cited nor listed in his bibliography any work by any of the three.⁷⁸

Austrian Capital Theory after Hayek

There are at least two branches of Austrian capital theory since 1941. In Europe a ‘neo-Austrian’ capital theory, based more on Böhm-Bawerk than on Hayek of the Pure Theory of Capital, was developed by John Hicks and subsequently by Peter Berhholz, Malte Faber, and their associates.⁷⁹ Hicks’s ‘neo-Austrian’ efforts began with a 1967 essay reconsidering Prices and Production. Hicks proposed that Hayek’s theory was a fore-runner of the growth theory of more recent years, and briefly sketched a theory of secular changes in real factors (rather than the monetary disturbances of Hayek’s cycle theory) that might bring about the capital shortage that is characteristic of the Hayekian crisis.⁸⁰ In the 1973 monograph Capital and Time: A Neo-Austrian Theory, Hicks worked out in some detail the implications of an ‘Austrian’ production technology (time lags between inputs and resulting outputs) for growth theory.⁸¹ Though he mentioned Hayek, Hicks made no reference there to The Pure Theory of Capital.

The subsequent ‘neo-Austrian’ capital theorists have focused on mathematical analysis of time-filled production. In that respect their research has been close in spirit to the central chapters of The Pure Theory of Capital: they analyse intertemporal allocation under various assumptions about the temporal structure of available production techniques. They have rightly emphasised that their work builds directly on Böhm-Bawerk and Wicksell, rather than on Hayek’s extensions and modifications of the earlier work.

In the United States the members of an ‘American Austrian’ school have in various ways combined Hayek’s analysis of the structure of production with Mises’s ‘pure time-preference’ analysis of interest. Into this school we can place Mises himself (who relocated to the U.S. in 1940, taught at New York University from 1945 to 1969, and included chapters on capital and interest in his Human Action of 1949), Ludwig Lachmann (who published Capital and Its Structure in 1956 while teaching in South Africa, but later became a visiting professor at NYU), Murray Rothbard, Israel Kirzner, Peter Lewin, and Roger Garrison.⁸²

Hayek’s efforts in the central chapters of The Pure Theory of Capital were relentlessly abstract and constructive, devoted to forming and illustrating comparative-equilibrium propositions under stringent simplifying assumptions. Lachmann’s work, by contrast, was relentlessly deconstructive, devoted to emphasising what is lost in abstraction from the complexities of the capital structure. Hayek’s efforts were not excluded from Lachmann’s criticism.⁸³ Hayek was aware of what was lost in his abstract model-building for the sake of isolating particular aspects of the capital structure, and inserted appropriate caveats throughout The Pure Theory of Capital. But he would not have written the book as he did had he not felt that something can be gained from such abstractions, namely useful explanations of real-world phenomena. It is thus something of a surprise to read the following statement by Hayek in his interview with Jack High:

I think the most useful conclusions drawn from what I did are really in Lachmann’s book on capital. Like so many things, I am afraid, which I have attempted in economics, this capital-theory work more shows a barrier to how far we can get in efficient explanation than sets forth precise explanations. All these things I’ve stressed—the complexity of the phenomena in general, the unknown character of the data, and so on—really much more point out limits to our possible knowledge than [are] contributions that make specific predictions possible.⁸⁴

Perhaps we can attribute this statement to Hayek’s being in a pessimistic mood at the time. While The Pure Theory of Capital does not enable prediction of specific magnitudes, it does (unlike Lachmann’s work) endeavour to predict patterns of resource allocation.

Israel Kirzner’s insightful Essay on Capital drew on The Pure Theory of Capital extensively, citing it at least two dozen times.⁸⁵ Given Kirzner’s aim of providing a critical discussion of the rôle of capital as a ‘prologue’ to capital theory,⁸⁶ it is not surprising that he mostly drew on the first seven ‘introductory’ chapters of The Pure Theory of Capital, rather than from the technical chapters engaged in equilibrium analysis of various temporal production patterns. More recent works in the ‘American Austrian’ tradition by Garrison and Lewin, like the just-noted works by Mises, Lachmann, and Kirzner, have been largely thematic discussions about capital theory and its implications rather than exercises in constructing capital theory for comparative-equilibrium analysis.⁸⁷

In applying Hayekian capital theory to the analysis of business cycles, Garrison has consciously gone back to the more tractable model of Prices and Production. As Hayek and Machlup noted in the interview statements used as our epigraph, no one has attempted further to elaborate or apply the analytical tools specifically developed in The Pure Theory of Capital.

If time and money are the universals of macroeconomic theorising, as Garrison has put it⁸⁸, then The Pure Theory of Capital in the form Hayek left it falls short of macroeconomics. It focuses on time (in production) to the exclusion of money. Garrison, who has done more than anyone else to keep Austrian business cycle theory a live research project, argues that the three-dimensional diagrams of The Pure Theory are more elaborate than is suitable for macroeconomic analysis, whereas the simple triangle of Prices and Production ‘is just right’.⁸⁹ On this view it is no accident that neither Hayek nor anyone else has used The Pure Theory of Capital (rather than Prices and Production) in work extending or empirically applying Austrian cycle theory.

PREFACE

This highly abstract study of a problem of pure economic theory has grown out of the concern with one of the most practical and pressing questions which economists have to face, the problem of the causes of industrial fluctuations. The attempt to elaborate a chain of reasoning which seems to throw important light on this question had made it painfully clear to me that some of the theoretical tools with which we are at present equipped are quite inadequate for the task. The nature of the contribution to the explanation of industrial fluctuation which I had attempted involved an extensive use of concepts and theorems which fall within the province of the theory of capital and interest. This is, of course, a field which almost above all others has been the centre of theoretical interest since the beginning of our science. The reason why, in spite of this, the results of past work on these problems proved unsatisfactory tools in the analysis of more complicated phenomena seems to be, as I try to explain in the introductory chapters, that in the past these phenomena have been studied for a different purpose and on assumptions which deprive them of most of their significance in a different context.

In this state of affairs it seemed imperative, before going on with a further elaboration of the explanation of industrial fluctuations, to turn back to the revision of the fundamentals and to work out a theory of capitalist production which would prove adequate for the analysis of dynamic changes. It was with great reluctance that I convinced myself of this necessity, and I have much sympathy with the prevailing attitude which shows an increasing impatience with all attempts at further refinement of the abstract groundwork and which is anxious to proceed with the more concrete work on the processes which we observe in the real world. Yet I have become definitely convinced that nothing holds up real progress so much as this very impatience which disregards the necessity of first getting the foundations clearly laid out.

My reluctance to undertake this work would have been even greater if from the beginning I had been aware of the magnitude of the task that awaited me. As at first contemplated, this study was intended as little more than a systematic exposition of what I imagined to be a fairly complete body of doctrine which, in the course of years, had evolved from the foundations laid by Jevons, Böhm-Bawerk, and Wicksell. I had little idea that this task of systematisation would uncover serious gaps in the reasoning which had yet to be bridged, and that some of the simplifications employed by the earlier writers had such far-reaching consequences as to make their conceptual tools almost useless in the analysis of more complicated situations. The most important of these inappropriate simplifications, of the dangers of which I became aware at a comparatively early stage, was the attempt to introduce the time factor into the theory of capital in the form of one single relevant time interval—the ‘average period of production’. But it gradually became clear that this supposed simplification evaded so many essential problems that the attempt to replace it by a more adequate treatment of the time factor raised a host of new questions which had never been really considered and to which answers had to be found.

It was inevitable that in a first approach to an analysis of the dynamic problems in this field I should have used whatever tools were available, and I must not complain of the manifold misunderstandings which the use of these imperfect instruments caused and of the objections to which it has given rise. And it would be idle to pretend that I was myself always aware of all the limitations and dangers of what I then still regarded as legitimate simplifications. But while I still believe