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Production Economics: A Dual Approach to Theory and Applications (Volume 1) (v. 1): Melvyn A. Fuss, Daniel McFadden

These two volumes of studies grew out of a series of seminars held in x969 and have as their theme the view that it is better to work in terms of cost or profit functions than to deal with production functions directly. The first volume contains the basic theoretical analysis and the second volume reports on some empirical work.

Part I opens with a chapter by McFadden, who provides a most welcome summary of the proofs and principal results of Shephard's approach to cost and production functions. It sets the tone for the chapters which follow. Part I is completed by chapters by Hanoch, who prefers to work with polar functions, and by Fuss, who introduced multiple outputs and normalised (in terms of output price) profit functions.

Part II opens with another valuable summary: Fuss, McFadden, and Mundlak survey the various functional forms used in production analysis. Of the econometrically popular Taylor series expansions they warn in vain that: 'If a parsimonious flexible form is fitted to the observations over an extensive domain, as is normally the case in econometric production analysis, then the fitted form will not in general be a second order approximation to the true function at any point.'

There follows a chapter by McFadden on the Generalised Linear Profits Function and one by Hanoch which extends his polar functions to include a wider range of definitions of elasticity of substitution. Part II ends with an exploration by Fuss and McFadden of how production efficiency may be traded for production flexibility in the face of uncertain future factor price ratios. Some interesting new ground is opened up.

Volume I closes with a set of technical appendices aimed at making the volume complete. Throughout both volumes, proofs are given in terms of set theory which, though very general, seem to express premises in ways which lack any ready translation into assessable economic language, and this reader at any rate is left with an uncomfortable suspicion that by agreeing with their premises one accepts more than one realises.

Volume II opens with a chapter by Bruno on the important but usually ignored problems of intermediate goods. Working with value added has implications for separability, aggregation, and productivity measurement. This theme is continued by Diewert, who in the chapter which follows, argues that using value added, rather than gross output, is tantamount to assuming constant relative factor prices. Part III ends with a paper by Denny on value added and homotheticity.

Part IV considers some microecbnomic applications of these ideas. McFadden examines the assumptions underlying the usual estimates of the elasticity of substitution and carries out his own estimation using electricity generating plant data. Diamond, McFadden, and Rodriguez set out (and partially solve) the problem of identifying technological change and the dangers of mis- representing biased technological change as some (spurious) elasticity of substitution. Belifante uses data on steam generating plant to emphasise the importance of the embodied-disembodied distinction and examines the rate of embodiment in estimating an average practice techniques 'frontier'. Fuss reports on his previous work on discriminating between putty-putty, putty-clay, and clay-clay technologies. He concludes thai for electricity generating plant, putty-clay is appropriate but sidesteps the problems which arise when the choice of capital has to be made when future prices are uncertain. Part IV closes with a paper by Cowing showing how restricted profits and restricted cost functions are necessary if the data apply to a regulated industry.

Part V claims to be about macroeconomics, but in fact both its papers are to do with disaggregated models. Denny and Pinto use a model with many inputs and many outputs to estimate demand and substitution elasticities for Canada, and in the final chapter Frenger uses Norwegian data to explore the responsive- ness of input-output coefficients to changes in price ratios. It is a valuable contribution to the work, the all too .little work, being done in this area. Overall these volumes constitute a useful collection of proofs and an invaluable summary of results of the work deriving from Shephard's duality approach to production. If there is an omission it is that the case for using this approach is nowhere strongly and clearly stated. Claims are made for it by the occasional aside but it is not clear that the very strong assumptions about factor markets, firm behaviour, and the structure of the error terms yield.a reduced form more suited to empirical work than the direct approach.

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