Linear Theory of Fixed Capital and China’s Economy: Marx, Sraffa and Okishio

132 Pages·2017·2.797 MB·English

by  Bangxi Li (auth.)

Bangxi Li
Linear Theory of
Fixed Capital and
China’s Economy
Marx, Sraffa and Okishio
’
Linear Theory of Fixed Capital and China s
Economy
Bangxi Li
Linear Theory of Fixed
’
Capital and China s
Economy
Marx, Sraffa and Okishio
123
BangxiLi
Schoolof Social Sciences
TsinghuaUniversity
Beijing
China
ISBN978-981-10-4064-1 ISBN978-981-10-4065-8 (eBook)
DOI 10.1007/978-981-10-4065-8
LibraryofCongressControlNumber:2017932783
©SpringerNatureSingaporePteLtd.2017
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Preface
This book is a collection of papers that comprises the doctorate dissertation of the
author defended at Waseda University, June 2012. In addition, some papers pub-
lishedafterthedefenceareincluded.ThosearelistedintheBibliographypartatthe
end of this book.
The author tried to do his best in arranging the contents of the papers in a
readable way. As a result, the book consists of 10 chapters. Most of chapters were
published as independent articles, so that they contained a lot of duplicated
descriptions. The author tried to minimise duplications throughout the book, but
some still remain for the convenience of readers.
A brief and overall introduction of the volume will be given in what follows.
The following chapters are all related to fixed capital theory and China’s
economy.
The first part ofthebookdeals with thetheory offixedcapitalalong theline of
Marx,Sraffa,OkishioandMorishima.Thesecondhalfisdedicatedtoestimationof
fixed capital coefficients of China’s economy and some computation results on
China based on the estimated coefficients. Details will be given in Chap. 1,
Introduction.
Mostoftheoriesoffixedcapitalsofardiscussedaremoreorlessnon-operational
ones because there was no available data offixed capital coefficients. Applications
ofMarx’slabourtheoryofvaluehavebeenmade with no-joint-productionmodels
that ignore fixed capital. Models dealt with in this book are all linear multi-sector
models,withafocusonfixedcapital.Somedetailsoffixedcapitalaremadeclearin
a systematic approach, and this leads us to carry out several computations and
simulations with explicit consideration offixed capital.
Theappendixisincludedinthisbook,becauseitrevealsthemotivationandthe
starting point of author’s research in this field.
This book is supported by The Social Science Foundation of Beijing
(No.15JGB125)andProjectofIndependentResearchPlanSupportedbyTsinghua
University (No. 2014z21044).
The author is indebted to many professors, colleagues and friends. Thanks are
due to Profs. T. Nakatani (Professor Emeritus of Kobe University, Rector of
v
vi Preface
Onomichi City University, Japan), M. Kasamatsu (Waseda University, Japan), T.
Asada (Chuo University, Japan), Y. Sato (Hosei University, Japan), Y. Niisato
(UniversityofToyama,Japan),MENGJie(RenminUniversityofChina),ZHANG
Yu (Renmin University of China), RONG Zhaozi (Anhui University), MA Yan
(Shanghai University of Finance and Economics), ZHANG Zhongren (University
of Shimane), QI Shuchang (National Bureau of Statistics of China), ZHAO Feng
(Renmin University of China), L. Pasinetti (Milano, Italy), B. Schefold (Göthe
Universität, Germany), H.D. Kurz (University of Graz, Austria), N. Salvadori
(Universitá diz Pisa, Italy), C. Bidard (Université Paris Ouest, France), Yagi
Takashi (Meiji University, Japan) and Tsuduki Eiji (Nanzan University, Japan).
Last but not least, the author would like to express the deepest and the most
profound thanks and gratitude to his teacher, Professor Emeritus of Waseda
University, Yoriaki Fujimori. Under his tutelage and encouragement, the author
could start acquiring the knowledge of mathematical Marxian political economy
streaming from Okishio.
Theauthorwouldliketoexpresshisthankstoeditors ofSpringer, Beijing, Mz.
ZHAO Wei and QIU Han, for their kind helps and patience.
Researches presented in this book have been made by applying various
open-sourceandfreesoftware,suchasTEX,Scilab,Maximaandothers.Hence,the
author would like to thank to developers of these open-source software.
Beijing, China Bangxi Li
Contents
1 Introduction... .... .... ..... .... .... .... .... .... ..... .... 1
1.1 Brief History of Mathematical Marx’s Political Economy
in Japan .. .... .... ..... .... .... .... .... .... ..... .... 1
1.2 Plan of Chapters.... ..... .... .... .... .... .... ..... .... 3
1.3 Basic Framework of the Marx-Sraffa Model.... .... ..... .... 5
2 Sraffa-Okishio-Nakatani’s Fixed Capital Theory .. .... ..... .... 7
2.1 Introduction ... .... ..... .... .... .... .... .... ..... .... 7
2.2 Reduction à la Sraffa-Okishio-Nakatani ... .... .... ..... .... 7
2.2.1 Okishio-Nakatani Reduction .. .... .... .... ..... .... 8
3 Renewal Dynamics of Fixed Capital .... .... .... .... ..... .... 13
3.1 Introduction ... .... ..... .... .... .... .... .... ..... .... 13
3.2 Normal Depreciation. ..... .... .... .... .... .... ..... .... 14
3.2.1 Yamada-Yamada and Markov Process .. .... ..... .... 14
3.2.2 Stationary State.... .... .... .... .... .... ..... .... 17
3.3 Accelerated Depreciation .. .... .... .... .... .... ..... .... 17
3.4 Concluding Remarks ..... .... .... .... .... .... ..... .... 19
4 Profit and Growth in the SON Economy. .... .... .... ..... .... 21
4.1 Introduction ... .... ..... .... .... .... .... .... ..... .... 21
4.2 Framework of Analysis.... .... .... .... .... .... ..... .... 21
4.2.1 The Reproduction Model with Only 1 Type
of Fixed Capital ... .... .... .... .... .... ..... .... 21
4.2.2 The Model of 4 Commodities from 2 Sectors. ..... .... 22
4.2.3 The Equilibrium of Production Prices and the Level
of Activities . ..... .... .... .... .... .... ..... .... 23
4.2.4 The Reduced Price System ... .... .... .... ..... .... 24
4.2.5 Reduced Quantity System.... .... .... .... ..... .... 26
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4.3 The Cambridge Equation in SON.... .... .... .... ..... .... 27
4.3.1 Some Preparations.. .... .... .... .... .... ..... .... 27
4.3.2 The Cambridge Equation of the SON Economy.... .... 28
4.4 Concluding Remarks ..... .... .... .... .... .... ..... .... 30
5 Economic Durability and Hardening Effects of Fixed Capital. .... 33
5.1 Introduction ... .... ..... .... .... .... .... .... ..... .... 33
5.2 The Model .... .... ..... .... .... .... .... .... ..... .... 33
5.3 Simulation of the Determination of Economic Durability... .... 35
5.3.1 The Numerical Value Settings. .... .... .... ..... .... 35
5.3.2 The Standard Maximum Problem and Production
Price Ratios.. ..... .... .... .... .... .... ..... .... 35
5.3.3 The Activity Level of Production Processes .. ..... .... 36
5.4 Simulation of the Hardening Effect of Fixed Capital . ..... .... 37
5.4.1 Numerical Settings . .... .... .... .... .... ..... .... 37
5.4.2 Production Prices and Activity Levels
of the Production Process .... .... .... .... ..... .... 38
5.5 Simulation with Physical Durability.. .... .... .... ..... .... 40
5.6 Concluding Remarks ..... .... .... .... .... .... ..... .... 42
5.6.1 On the Endogenous Determination of Economic
Durability ... ..... .... .... .... .... .... ..... .... 42
5.6.2 On the Hardening Effect of Fixed Capital.... ..... .... 43
5.6.3 Comparison with Physical Durability ... .... ..... .... 44
5.6.4 Theoretical Implication .. .... .... .... .... ..... .... 46
6 Marx-Sraffa Equilibria as Eigensystems . .... .... .... ..... .... 47
6.1 Mathematical Preliminaries. .... .... .... .... .... ..... .... 47
6.1.1 Marx-Sraffa Equilibria... .... .... .... .... ..... .... 49
6.2 Possibility of Unstable Marx-Sraffa Equilibrium. .... ..... .... 53
6.2.1 A Basis of Numerical Computation. .... .... ..... .... 53
6.2.2 Marx-Sraffa Price Equilibrium. .... .... .... ..... .... 54
6.2.3 Marx-Sraffa Activity Equilibrium .. .... .... ..... .... 55
6.2.4 The Equilibrium Quantity of the Marx-Sraffa Model .... 56
6.2.5 The Dynamics of the Production Price System..... .... 56
6.2.6 The Dynamics of the Activity and the Quantity
Systems. .... ..... .... .... .... .... .... ..... .... 57
6.3 Concluding Remarks ..... .... .... .... .... .... ..... .... 58
7 Fixed Capital and China’s Economy 1995–2000... .... ..... .... 59
7.1 Introduction ... .... ..... .... .... .... .... .... ..... .... 59
7.2 Estimation of Marginal Fixed Capital Coefficients ... ..... .... 60
7.2.1 Basic Framework .. .... .... .... .... .... ..... .... 60
7.2.2 Sraffa-Fujimori Method.. .... .... .... .... ..... .... 61
7.2.3 Notes on Data..... .... .... .... .... .... ..... .... 64
Contents ix
7.3 Wage-Profit Curves à la von Neumann-Leontief .... ..... .... 65
7.3.1 Basic Concept..... .... .... .... .... .... ..... .... 65
7.3.2 Computation Procedure with Respect to Input-Output
Data ... .... ..... .... .... .... .... .... ..... .... 67
7.3.3 Computation Results.... .... .... .... .... ..... .... 69
7.4 Concluding Remarks ..... .... .... .... .... .... ..... .... 74
8 Marx’s Labour Values in China’s Economy.. .... .... ..... .... 75
8.1 Introduction ... .... ..... .... .... .... .... .... ..... .... 75
8.2 Value System and Production Price System.... .... ..... .... 76
8.2.1 Notations and Preliminary Notes... .... .... ..... .... 76
8.2.2 Values.. .... ..... .... .... .... .... .... ..... .... 76
8.2.3 Production Prices .. .... .... .... .... .... ..... .... 77
8.2.4 Rate of Surplus Value... .... .... .... .... ..... .... 77
8.3 Organic Composition of Capital, Fixed Capital-Labour
Ratio and Rate of Surplus Value .... .... .... .... ..... .... 79
8.3.1 Organic Composition of Capital ... .... .... ..... .... 79
8.3.2 Fixed Capital-Labour Ratios.. .... .... .... ..... .... 79
8.4 Spearman’s Rank Correlation Coefficients . .... .... ..... .... 80
8.5 Concluding Remarks ..... .... .... .... .... .... ..... .... 80
9 Turnpike Paths for China’s Economy 1995–2000.. .... ..... .... 83
9.1 Introduction ... .... ..... .... .... .... .... .... ..... .... 83
9.2 Kantorovich’s Long-Term Planning Model. .... .... ..... .... 83
9.2.1 DOSSO’s Model... .... .... .... .... .... ..... .... 85
9.2.2 Similarity and Difference Between DOSSO
and Kantorovich Model.. .... .... .... .... ..... .... 85
9.3 Long-Term Planning Theory and China’s Economy.. ..... .... 87
9.3.1 Kantorovich’s Output Path ... .... .... .... ..... .... 87
9.3.2 The Additional Restrictions on Fixed Capital . ..... .... 89
9.3.3 The Long-Term Plan with a Labour Resource
Constraint ... ..... .... .... .... .... .... ..... .... 90
9.4 Concluding Remarks ..... .... .... .... .... .... ..... .... 93
10 Concluding Remarks.... ..... .... .... .... .... .... ..... .... 95
Appendix A: Input-Output Tables and Marx’s 2-Sector Model ... .... 97
References.... .... .... .... ..... .... .... .... .... .... ..... .... 117
Index .... .... .... .... .... ..... .... .... .... .... .... ..... .... 121
List of Figures
Figure 5.1 The economic determination of the durability
offixed capital: s¼sða;rÞ .... .... .... .... .... ..... .. 38
Figure 5.2 The economic determination of durability
offixed capital: s¼sðb;rÞ .... .... .... .... .... ..... .. 41
Figure 5.3 The relationship between the profit rate and economic
durability (a¼0:90) ..... .... .... .... .... .... ..... .. 43
Figure 5.4 The relationship between the efficiency and economic
durability (r ¼0:20) ..... .... .... .... .... .... ..... .. 44
Figure 5.5 The wage-profit curve in an economic durability
and a physical durability.. .... .... .... .... .... ..... .. 45
Figure 5.6 The aged fixed capital prices based on economic durability,
physical durability, and hardening effect.. .... .... ..... .. 45
Figure 7.1 The convergence of the iteration.... .... .... .... ..... .. 63
Figure 7.2 The wage-profit curve à la von Neumann-Leontief (1987) . .. 71
Figure 7.3 W-P curve (1990) .. ..... .... .... .... .... .... ..... .. 71
Figure 7.4 W-P curve of 1992 . ..... .... .... .... .... .... ..... .. 72
Figure 7.5 W-P curve of 1995 . ..... .... .... .... .... .... ..... .. 72
Figure 7.6 W-P curve of 1997 . ..... .... .... .... .... .... ..... .. 73
Figure 7.7 W-P curve of 2000 . ..... .... .... .... .... .... ..... .. 73
Figure 9.1 The optimal solution of Kantorovich’s long-term planning
and actual values (1997, fixed capital).... .... .... ..... .. 92
Figure 9.2 The optimal solution of Kantorovich’s long-term
planning and actual values (1997, current goods) ... ..... .. 92
Figure 9.3 The optimal solution of Kantorovich’s long-term planning
and actual values (1997, consumption goods).. .... ..... .. 93
Figure A.1 Consumption-growth curve of 1981 . .... .... .... ..... .. 100
Figure A.2 C-G curve of 1987 . ..... .... .... .... .... .... ..... .. 101
Figure A.3 C-G curve of 1990 . ..... .... .... .... .... .... ..... .. 101
Figure A.4 C-G curve of 1992 . ..... .... .... .... .... .... ..... .. 102
Figure A.5 C-G curve of 1995 . ..... .... .... .... .... .... ..... .. 102
Figure A.6 C-G curve of 1997 . ..... .... .... .... .... .... ..... .. 103
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