Average and Best-Practice Production Functions in German Industry

Abstract

THERE is a long tradition of theoretical analyses of production in management sciences and in business administration. While the classical production function long played a dominant role in production theory of the firm, it became less and less acceptable after Leontief introduced his production function with limitational factors of production and constant coefficients and after Gutenberg advanced the hypothesis that production within the firm should be analyzed on the basis of individual pieces of machinery rather than on the basis of aggregate production functions for the legal entity as a whole. The so-called Gutenberg production function is a production function with limitational factors of production and coefficients of production that vary according to the intensity of production. There are very few empirical tests of theoretical production functions at the firm level in Germany. Engineering production functions were developed and estimated by Hall [i], and empirical tests of production functions of the Gutenberg type were carried out by Presmar [2] for individual pieces of equipment. To my knowledge there are no empirical tests of firm production functions using financial data. The present paper reports on work in progress. Work on empirical production functions forms part of a larger research project on empirical models of firm growth carried out in Bonn with financial assistance of the Deutsche Forschungsgemeinschaft. The paper reviews results derived by Werhahn [3], von Maltzan [4], Fischer [5] and Fuhrmann [6]. In this study we elaborate the production possibilities on the micro level (firms) in two ways using a vintage model to describe the production possibilities of individual firms. Firstly, we want to study long-run behavior. A putty-putty technology is assumed. We for this purpose derive a production function which has been estimated for each firm of the chemical industry. Under the additional assumption that all firms have the same production function except for efficiency differences we have tried to estimate an average as well as a best-practice production function for the whole chemical industry. Secondly, we want to analyze short-run behavior of the productive system. A putty-clay technology seems an appropriate assumption in this context. In such a model we get expressions for capacity and labor demand connected