In the 'sixties, the reproduction model was often the subject of analysis and discussion in economic literat ure. Discussion was by criticism of the neo-classical concept of capital as well as by a renewed interest in the labour theory of value. Criticism of the use of a homogeneous concept of capital resulted in the re switching debate as it is called, where the positing of problems is limited, and the results are ultimately meagre. The renewed interest in the labour theory of value opened interesting perspectives, at least if one rejects the rather fruitless debate on Marx's transform ation problem, as it is called. The main question then is: are the prices determined objectively or do factors of demand also play an essential role? This book by Dr. van Schaik deals with this famous theme. The various models with single and joint reproduction are classified and analysed with great surveyability. The consistent distinction between quantity and price systems, the appropriate use of the matrix notation and the careful definition of concepts, guarantee the accessibility to a difficult matter. Models of Leontief, the Austrian School, Burmeister-Dobell and others appear as special cases of the more general Von Neumann-Sraffa structure. In view of the often fragmentary handling of jOint production in economic literature and of the concept of fixed capital which is linked to it, Dr. van Schaik's book fulfils a long-felt want.
Table of Contents1. Single Production.- 1.1. Pure reproduction.- 1.2. Surpluses.- 1.2.1. Balanced growth.- 1.2.2. Non-basics.- 1.3. The distribution of surpluses.- 1.3.1. Labour.- 1.3.2. The solution of the quantity system.- 1.3.3. The solution of the price system.- Appendix 1.a. Lemmas.- 2. Joint Production.- 2.1. Processes and commodities.- 2.1.1. Introduction.- 2.1.2. Non-basics.- 2.2. Weak joint production.- 2.2.1. Identification and process-dependency.- 2.2.2. Cost functions.- 2.3. Strong joint production.- 2.3.1. Negative embodied labour coefficients.- 2.3.2. The numéraire-question.- 2.3.3. Corner-point solutions.- Appendix 2.a. Model 2.1.- Appendix 2.b. Equal input proportions.- Appendix 2.c. Non-basics and equilibrium.- 3. Fixed Capital.- 3.1. Profiles of vintages.- 3.2. The Simple Sraffa model.- 3.2.1. The point-input-flow-output profile.- 3.2.2. Book-values and depreciations.- 3.2.3. The core system.- 3.2.4. The rest-value problem.- 3.2.5. Scrappage and replacement.- 3.2.6. A corner-point solution.- 3.2.7. The equilibrium between savings and investments.- 3.3. The Austrian reproduction model.- 3.3.1. Introduction.- 3.3.2. The flow-input-point-output profile.- 3.3.3. The solution.- 3.3.4. The flow-input-flow-output profile.- 3.4. Unequal life-spans.- 3.4.1. Several machines with a life-span of T years.- 3.4.2. Machines with an unequal life-span.- 3.4.3. Variable coefficients.- 3.5. The Leontief model with fixed capital.- 3.5.1. Misconceptions.- 3.5.2. Morishima’s opinion.- 3.5.3. Comparison with the Sraffa model.- 3.5.4. The opinion of Domar and Lange.- 3.5.5. Bródy’s opinion.- 3.5.6. Generalization.- Appendix 3.a. Generalization of the Simple Sraffa model.- Appendix 3.b. Superimposed joint production.- Appendix 3.c. Unequal life-spans.- 4. Unequal Efficiency.- 4.1. Forms of unequal efficiency.- 4.2. A model with three industries.- 4.3. Loss of productivity.- 4.3.1. Introduction.- 4.3.2. Uniform loss of productivity determined by conditions on the demand side.- 4.3.3. Differentiated loss of productivity determined by conditions on the demand side.- 4.3.4. A corner-point solution.- 4.3.5. Loss of productivity determined by conditions on the supply side.- 4.4. Higher operating costs.- 4.4.1. Introduction.- 4.4.2. Economic life-span.- 4.4.3. Uniform higher operating costs.- 4.4.4. Inefficiency and reswitching of techniques.- 4.5. Conclusion.- Appendix 4.a. The opinions of Burmeister and Dobell.- Appendix A. Outline of the Transformation Problem.- A.1. The surpluses.- A.2. The disposal of surpluses.- A.3. The distribution of surpluses.- Appendix B. International Trade.- B.1. Introduction.- B.2. Assumptions.- B.3. Autarchy.- B.4. Free trade.- B.5. Consequences of free trade.- B.6. Trade without specialization.- Appendix C. The traditional vintage model.- C.1. Introduction.- C.2. The quantity system.- C.3. The price system.- Appendix D. The traverse.- D.1. The Simple Sraffa model.- D.2. Planned traverse.- D.3. Non-planned traverse.- D.4. The neo-Austrian model.