Journal Article Further Comment on “Smoothing” by Output Variation Get access Roger A. McCain Roger A. McCain Western Washington State College Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Economics, Volume 88, Issue 3, August 1974, Pages 496–498, https://doi.org/10.2307/1881948 Published: 01 August 1974

Abba Lerner's formulation of the optimum division of remains interesting although in some ways ambiguous. The comment by William Breit and William Culbertson in this Review is evidence of both points. There is still no formal proof of the theorem for an arbitrary number of persons, even if its outlines are clear enough. The equal assumption remains unclear. This note contains a proof of the weak' theorem for N persons. It uses a concept of ignorance derived from information theory.2 Throughout this paper the term income is used in a somewhat special sense, following Lerner et al.; a sense somewhat akin to Gary Becker's full (p. 497).3 It is evaluated on the assumption that the individual works the maximum feasible hours at maximum effort; purchases of (quantitative or qualitative) leisure are treated like any other purchases.4 Moreover, it is assumed that we may discuss redistribution without considering the effect of resulting price changes on the utility-of-income schedules, (see Lerner (1944) pp. 23-24). Suppose that the distribution of by individual shares is given, that is, when Yi is the of individual i, and Y is total Yi/ Y = yi is a given constant for i = 1, ... ,N. The yi may be regarded as the probabilities that an incremental dollar of purchasing power goes to individual i. Now, suppose it is known that each individual's utility function is drawn from a finite family fj(Yi), for j = 1, . . . , J; i = 1, N. The probability that individual i's utility function is function j is pij. The expected utility of a dollar of purchasing power allocated to individual i is

In the process of cultivation of taste, tastes are changed by the experience of consumption. To model this we might assume that cultivation of taste for a particular good involves a change in only one parameter of the utility function, and that the other parameters, that is, the underlying utility function, remains unchanged. For example, assume that there are just two goods, x and z, of which x is subject to cultivation of taste, and z is not. Then

Two approaches are used to explore the implications for environmental policy of a possible endogenous bias of technical progress for environmental degradation. Using a frontier approach of innovation-possibility and the alternative approach that is critical of innovation-possibility, the author finds that both models indicate a bias for pollution when there is no charge for environmental amenities. The result is that pollution increases faster than production. He concludes that if pollution is to be stabilized in a growing economy, the price must be positive and flexible so that it can rise in response to labor productivity and wage increases. 17 references.

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

In a recent article in this Review, William Fellner explored the implications of the neoclassical theory of economic growth for the measurement of technological change. His model assumed two inputs, capital and labor, and constant returns to scale. Fellner speculated that capital and land are readily substitutable, and hence no separate rent category of income, or land category of inputs, need be provided. It is the purpose of this note to demonstrate that when land is introduced explicitly as a factor of production in a model with factor-augmenting technological change, it can be dealt with in a way that validates Fellner's model as regards the capital and labor interactions; but moreover the introduction of land as a separate factor of production contributes to the predictivity of the model by resolving, at least in part, a criticism of neoclassical growth theory made by B. Frey. A Constant Elasticity of Substitution (CES) production function for three factors of production adequate to the purpose of this paper may be written