Price Effects in Input-Output Relations: A Theoretical and Empirical Study for the Netherlands 1949–1967: (201 Lecture Notes in Economics and Mathematical Systems)

1.1. Pre Ziminary remarks Input-output analysis is one of the most extensively used tools of economic science. It has been introduced by Leontief (1941) who assumed that inputs into a production process of a particular sector of economic activity is a constant fraction of the output of that process in physicaZ terms. National account statisticians, however, record the inputs and outputs of sectors of economic activity in money flows. If those flows were voZumes (evalu­ ated at constant prices, pertaining to a certain base year) they could represent the physical amounts Leontief dealt with. Then, the Leontief assumption turns into constancy of ratios of volumes of inputs to volumes of output. For an over­ view of (traditional) input-output analysis we refer to section 4.1.1. In practice, however, input-output tables in volumes are seldom available; since as a rule they are expressed in monetary vaZues (i.e. evaluated at current prices). In that case one generally assumes that the ratios between inputs (in value terms) and outputs (in value terms) are constant. In appendix B to chapter 4 we prove that the two variants described above can be couched in terms of the (neo-classical) theory of costs subject to a production function.

Table of Contents:
1. Introduction.- 1.1 Preliminary remarks.- 1.2 Outline of the study.- 2. Theory of production and costs.- 2.1 Introduction.- 2.2. Assumptions underlying neo-classical theory of production and costs.- 2.3. Elasticities of substitution.- 2.4. On the existence of a unique cost minimum.- 2.5. Neo-classical theory of costs.- Appendix 2.A. Proof of theorem 1.- Appendix 2.B. Proof of corrolary 1.- Appendix 2.C. A generalization of lemma 2 of Barten, Kloek and Lempers.- Appendix 2.D. A modified version of proposition 7 of Shephard.- 3. Constant elasticities of substitution class of production functions.- 3.1. Introduction.- 3.2. Neo-classical properties of the CES production function.- 3.3. Application of the theory of costs to the h-homogeneous CES production function.- 3.4. The two-level CES production function.- Appendix 3.A. Theoretical restrictions on the parameters of the two-level CES production function.- Appendix 3.B. Derivation of input demand relations, the cost function, the Allen partial elasticities of substitution for the two-level CES production function and a reformulation for time series analysis.- 4. Theory of price effects in input-output relations: some models.- 4.1. Introduction.- 4.2. Generalization of input-output analysis based on one-level CES production functions.- 4.3. Introduction of technical change into the generalized input-output model.- 4.4. The two-level CES production function in input-output analysis.- 4.5. Aggregation of the demand relations for a firm to a demand relation.- of an industry.- 4.6. Two other studies dealing with substitutability in input-output analysis.- Appendix 4.A. The CBS classification of sectors.- Appendix 4.B. Constancy of input-output ratios.- 5. Methods of estimating price effects in input-output relations.- 5.1. Introduction.- 5.2. Conceptualization.- 5.3. Estimation of the model.- 5.4. Applying methods of estimation to generalized input-output models.- Appendix 5. A. Maximum likelihood estimation in case of autocorrelation within an input group.- 6. Estimated price effects in input-output relations: the Netherlands, 1949-1967.- 6.1. Introduction.- 6.2. Assembling the data.- 6.3. Performance of one-level CES models, 1949-1958, compared with traditional models.- 6.4. Application of one-level CES models to 1949-1966.- 6.5. Comparison of the estimates between the two periods of observation.- 6.6. Application of the two-level CES model.- 6.7. Summary of the conclusions.- Appendix 6.A. Tables relating to the one-level CES models.- Appendix 6.B. The statistics of Spearman, Theil and Somermeyer.- Appendix 6.C. Tables relating to the two-level CES model.- 7. Summary and conclusions.- Notes.- References.- Author’s index.