An applied trancendental logarithmic cost function : economies of scale and elasticities of substitution in selected South African manufacturing sectors (1972-1990).
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Moll (1991) has criticised the proposal that demand restructuring should act as the impetus for economic growth in a post-apartheid South Africa on the grounds of, a lack of empirical support. The demand restructuring thesis is premised on two empirically testable assertions: firstly that realisable economies of scale are greater in labour-intensive wage goods sectors than in luxury goods and secondly that in manufacturing as a whole labour can easily substitute for capital. While a number of studies employing either the Cobb-Douglas (Cobb & Douglas, 1948) or Constant Elasticity of Substitution (CES) ( Arrow, Chenery, Minhas & Solow, 1961) functions have attempted to quantify these features of technology, their conclusions are potentially invalid. Both functions impose the maintained hypotheses of homotheticity, homogeneity and seperability a priori. As primary hypothesis tests regarding the magnitude of parameters depend on the validity of both the hypothesis being tested and the underlying maintained hypotheses, the plausibility of maintained hypotheses is an important consideration when choosing a functional form for econometric analysis. Homotheticity and homogeneity constrain the theoretical determinants of economies of scale and seperability. The theoretical determinants of substitution thus limit the contexts in which functions which embody these hypotheses are likely to be appropriate. The mathematical concept of duality has permitted the development of flexible, general functions, such as the Transcendental Logarithmic Cost Function (Christensen, Jorgensen and Lau, 1971, 1973), which rather than imposing, permits the testing of the most commonly imposed maintained hypotheses. By applying this function to three sub-sectors of South African manufacturing both the validity of the commonly imposed maintained hypotheses and the empirical premises of the demand restructuring position are assessed in this dissertation. This application indicates that not only are the hypotheses of homotheticity, homogeneity and seperability invalid but that the inappropriate imposition of homotheticity, homogeneity and seperability invalid but that the inappropriate imposition of homotheticity biases estimates of scale downwards. Evidence also emerges to challenge Moll's (1991) assertions regarding the empirical validity of demand restructuring.