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

This book discusses both linear economic theory and its application to China's recent economy from, 1987-2000, with an emphasis on fixed capital. It starts with the development of Marx-Sraffa linear economic models with fixed capital. The author then addresses various topics, including formal explanations of Sraffa-Okishio-Nakatani’s (SON) reduction of the whole economy to its subsystem of brand-new commodities, the renewal dynamics of fixed capital and the Marx-Engles-Ruchti-Lohmann effect as well as its extension to the accelerated depreciation case; and simulations of the economic durability of fixed capital. Further, in a general joint-production system, equilibria are computed as the spectra of the matrix pencil defining the equilibrium of the systems and the so-called Cambridge equation are extended to the case of SON's economy. By simulating the case of all final products being invested for capital goods, it estimates the fixed capital coefficients from investment data on China's economy 1995-2000. Based on this, the book describes the wage-profit curves of the open China economy. By applying the estimated fixed capital coefficients, the book presents the computation of the labour values of major commodities in China, and the turnpike of the stage 1995-2000, with fixed capital. It compares the value system with the production price system, and thus points out some structural issues of China's economy that are worth discussing. Preface 5 Contents 7 List of Figures 10 List of Tables 12 1 Introduction 14 1.1 Brief History of Mathematical Marx's Political Economy in Japan 14 1.2 Plan of Chapters 16 1.3 Basic Framework of the Marx-Sraffa Model 18 2 Sraffa-Okishio-Nakatani's Fixed Capital Theory 20 2.1 Introduction 20 2.2 Reduction à la Sraffa-Okishio-Nakatani 20 2.2.1 Okishio-Nakatani Reduction 21 3 Renewal Dynamics of Fixed Capital 26 3.1 Introduction 26 3.2 Normal Depreciation 27 3.2.1 Yamada-Yamada and Markov Process 27 3.2.2 Stationary State 30 3.3 Accelerated Depreciation 30 3.4 Concluding Remarks 32 4 Profit and Growth in the SON Economy 33 4.1 Introduction 33 4.2 Framework of Analysis 33 4.2.1 The Reproduction Model with Only 1 Type of Fixed Capital 33 4.2.2 The Model of 4 Commodities from 2 Sectors 34 4.2.3 The Equilibrium of Production Prices and the Level of Activities 35 4.2.4 The Reduced Price System 36 4.2.5 Reduced Quantity System 38 4.3 The Cambridge Equation in SON 39 4.3.1 Some Preparations 39 4.3.2 The Cambridge Equation of the SON Economy 40 4.4 Concluding Remarks 42 5 Economic Durability and Hardening Effects of Fixed Capital 44 5.1 Introduction 44 5.2 The Model 44 5.3 Simulation of the Determination of Economic Durability 46 5.3.1 The Numerical Value Settings 46 5.3.2 The Standard Maximum Problem and Production Price Ratios 46 5.3.3 The Activity Level of Production Processes 47 5.4 Simulation of the Hardening Effect of Fixed Capital 48 5.4.1 Numerical Settings 48 5.4.2 Production Prices and Activity Levels of the Production Process 49 5.5 Simulation with Physical Durability 51 5.6 Concluding Remarks 53 5.6.1 On the Endogenous Determination of Economic Durability 53 5.6.2 On the Hardening Effect of Fixed Capital 54 5.6.3 Comparison with Physical Durability 55 5.6.4 Theoretical Implication 57 6 Marx-Sraffa Equilibria as Eigensystems 58 6.1 Mathematical Preliminaries 58 6.1.1 Marx-Sraffa Equilibria 60 6.2 Possibility of Unstable Marx-Sraffa Equilibrium 64 6.2.1 A Basis of Numerical Computation 64 6.2.2 Marx-Sraffa Price Equilibrium 65 6.2.3 Marx-Sraffa Activity Equilibrium 66 6.2.4 The Equilibrium Quantity of the Marx-Sraffa Model 67 6.2.5 The Dynamics of the Production Price System 67 6.2.6 The Dynamics of the Activity and the Quantity Systems 68 6.3 Concluding Remarks 69 7 Fixed Capital and China's Economy 1995--2000 70 7.1 Introduction 70 7.2 Estimation of Marginal Fixed Capital Coefficients 71 7.2.1 Basic Framework 71 7.2.2 Sraffa-Fujimori Method 72 7.2.3 Notes on Data 75 7.3 Wage-Profit Curves à la von Neumann-Leontief 76 7.3.1 Basic Concept 76 7.3.2 Computation Procedure with Respect to Input-Output Data 78 7.3.3 Computation Results 80 7.4 Concluding Remarks 85 8 Marx's Labour Values in China's Economy 86 8.1 Introduction 86 8.2 Value System and Production Price System 87 8.2.1 Notations and Preliminary Notes 87 8.2.2 Values 87 8.2.3 Production Prices 88 8.2.4 Rate of Surplus Value 88 8.3 Organic Composition of Capital, Fixed Capital-Labour Ratio and Rate of Surplus Value 90 8.3.1 Organic Composition of Capital 90 8.3.2 Fixed Capital-Labour Ratios 90 8.4 Spearman's Rank Correlation Coefficients 91 8.5 Concluding Remarks 91 9 Turnpike Paths for China's Economy 1995--2000 94 9.1 Introduction 94 9.2 Kantorovich's Long-Term Planning Model 94 9.2.1 DOSSO's Model 96 9.2.2 Similarity and Difference Between DOSSO and Kantorovich Model 96 9.3 Long-Term Planning Theory and China's Economy 98 9.3.1 Kantorovich's Output Path 98 9.3.2 The Additional Restrictions on Fixed Capital 100 9.3.3 The Long-Term Plan with a Labour Resource Constraint 101 9.4 Concluding Remarks 104 10 Concluding Remarks 106 Appendix A Input-Output Tables and Marx's 2-Sector Model 108 A.1 Introduction 108 A.2 Preprocessing Input-Output Tables 109 A.2.1 Computing the Coefficients for Input-Output Systems 109 A.3 Marx's 2-Sector Model 116 A.3.1 The Ratio λi of Capital Goods to Demand in a Closed Economy 116 A.3.2 Difference in Data: Major Renewal 117 A.3.3 The 2-Sector Model in an Open Economy 119 A.3.4 China's 2-Sector Input-Output Tables 120 A.4 The Turnpike for China's Economy 122 A.4.1 Linear Programming Problem 123 A.4.2 Preprocessing Data 124 A.5 Concluding Remarks 125 References 127 Index 131 Front Matter....Pages i-xiv Introduction....Pages 1-6 Sraffa-Okishio-Nakatani’s Fixed Capital Theory....Pages 7-12 Renewal Dynamics of Fixed Capital....Pages 13-19 Profit and Growth in the SON Economy....Pages 21-31 Economic Durability and Hardening Effects of Fixed Capital....Pages 33-46 Marx-Sraffa Equilibria as Eigensystems....Pages 47-58 Fixed Capital and China’s Economy 1995–2000....Pages 59-74 Marx’s Labour Values in China’s Economy....Pages 75-82 Turnpike Paths for China’s Economy 1995–2000....Pages 83-94 Concluding Remarks....Pages 95-96 Back Matter....Pages 97-122