On the Shape and Location of the Production Possibility Curve (original) (raw)

Economica, 1973

Abstract

In a recent issue of this Journal, James R. Melvin developed a useful diagrammatic technique for deriving the production possibility curve in the Lerner-Pearce diagram that is analogous to the Savosnick construction in the Edgeworth-Bowley contract box.' Among other things, Melvin produces the proposition that concavity to the origin of the production possibility curve increases around fixed endpoints when in the two-sector model of general equilibrium (i) the elasticity of technical substitution (ETS) between labour and capital falls, and (ii) the difference between optimal factor utilization ratios between the two goods increases. His demonstration is, however, irrelevant to the question of the influence of the ETS and/or the degree of difference between factor utilization ratios of the two goods on the location and shape of the production possibility curve, because, in order to get his fixed endpoints, Melvin has to introduce an appropriate (and arbitrary) change in the factor endowment of the economy, exactly sufficient to permit the economy to produce the same maximum amount of each good. Hence his result in the one case depends both on the reduction in the ETS and on the associated required change in the factor endowment, while in the other it depends both on increasing the difference between factor utilization ratios and on changing the factor endowment.2 In response to Melvin's analysis, Messrs. Scarth and Warne correctly have demonstrated the relationship between changes in the ETS and the production possibility curve.3 In the present paper we present what we believe to be a correct analysis of the second problem. Melvin's analysis of an increase in the difference between factor utilization ratios of the two goods and its effect on the shape and location of the transformation curve around fixed endpoints suffers from the same defect displayed by his analysis of changing the ETS, namely, that his result depends both on the change he postulates and an implicit (but necessary) increase in the factor endowment. However, the investigation of the production possibility effect of increasing the difference between factor utilization ratios alone is simpler than the investigation of a change in the ETS, for unlike the latter there is no need for a reference factor utilization ratio, independent of factor ' J. R. Melvin, "On the Derivation of the Production Possibility Curve", Economica, vol. 38 (1971), pp. 287-94; K. M. Savosnick, "The Box Diagram and the Production Possibility Curve", Ekonomnisk Tidskrift, vol. 60 (1958), pp. 183-97. 2. 3 Footnotes on next page. 305

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