The Characteristics of Optimum Inventions: An Isotech Approach
Technical has become a controversial social issue, but the nature of technical progress is badly understood. Economists may best contribute to the discussion by analyzing technical change as an instance of choice subject to a constraint of limited technological opportunity. The innovation possibility frontier (Charles Kennedy) is one hypothetical constraint on technological opportunity. Models based on the innovation possibility frontier customarily assume steady growth (E. M. Drandrakis and Edmund S. Phelps, William Fellner and McCain) and are rather well understood. They have been incisively criticized by Nordhaus, who proposed, as a general alternative, the hypothesis of an isotech map. An exploration of the characteristics of optimum inventions, in terms of the isotech hypothesis seems of some interest. A single isotech, the C-isotech, is the set of all techniques attainable at a given cost, C. Thus in the standard neoclassical model, the production function is the zero-isotech. The isotech map will depend on the history of technical development as a whole and so cannot be stable over time.' The generality of the isotech hypothesis makes it possible to raise some questions of considerable interest, which are beyond the range of the innovation possibility frontier hypothesis. Because scale is a major determinant of the social impact of technology, (E. Schumaker) we shall as an example explore John K. Galbraith's imperatives of large scale.2 We first explore some characteristics of optimum inventions. We suppose that an invention is characterized by capital intensity, k, and labor intensity, n, as usual; and also by the minimum capital scale [, and the durability of the capital good, m. The capital good is supposed to be a one-hoss shay. The isotech map is represented by a cost function
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