Knowledge that Transforms

This paper is concerned with the use of spectral analysis to analyze data generated by computer simulation experiments with models of economic systems. An example model serves to illustrate two different applications of spectral analysis. First, spectral analysis is used to construct confidence bands and to test hypotheses for the purpose of comparing the results of the use of two or more alternative economic policies. Second, spectral analysis is employed as a technique for validating an econometric model.

In this paper the question of induced factor augmenting technical change in the context of the profit maximizing firm is addressed. The Kennedy innovation possibility frontier is employed to describe the opportunities available to the firm for factor augmentation and from it the direction of factor augmentation can be chosen. In addition, this opportunity curve can be shifted inwards or outwards according to the expenditure on research and development. The selection of the direction and extent of technical change is first determined via a myopic decision rule and then by maximization of the present value of the stream of net revenue from production and sale of output less the cost of technical advance. In the latter problem the maximum principle of Pontryagin is employed. Questions regarding the existence of stationary states and stability are resolved, and the optimal solutions are compared with the myopic decision rules. IN THIS PAPER further results relating Hicks' theory of induced technical change to the traditional theory of the profit maximizing firm are presented. The mechanism for technical change is disembodied factor augmentation instead of, as presumed in our earlier work, alteration of the parameters of the production function. It turns out, however, that many of the conclusions regarding the effects of technical progress are invariant to the way in which that progress is represented. The assumption of factor augmentation pursued here also yields results not obtained under the alternative model of parametric change studied earlier. Moreover, by using factor augmentation as the vehicle for representing technical change, our results are closely related to and can be compared with those of others working in the area of induced innovation, although those models are macroeconomic in focus [2, 3, 4, 5, 6, 7]. In our analysis we envisage a single firm to whom the state of technology is an endogenous variable, alterable at a positive cost; the firm strives to maximize a discounted profits stream over the indefinite but certain future. This problem differs from the one faced by the firm in the more traditional analysis insofar as the firm selects not only the optimal levels of the factors of production, and thereby the level of production, but the optimal technology as well. The desired optimal policies are derived from the appropriate maximization problem. These policies are then compared with those the firm would pursue if it were following a myopic policy of maximizing the instantaneous rate of profit growth under the same opportunities. In addition to discussion of the optimal rate and direction of technical change, the effects of technical change on the firm are also investigated. In particular, the impact upon the rate of production, cost of production, and factor shares are described.

ZELLNER, KMENTA, AND DRfEZE in a recent article [3] specified for the firm a Cobb-Douglas production model in which the traditional profit maximization assumption was modified to explicitly recognize the stochastic nature of profits. Assuming that firms maximize the mathematical expectation of profits, the authors found that under conditions of pure competition least squares estimation of the production function from cross section data on firms' output and inputs provides consistent estimates of the production function parameters if certain reasonable specifying assumptions are satisfied. Since considerable attention has recently turned to the more general CES production function, the purpose of this note is to point out that use of the Zellner, Kmenta, and Dreze framework with a CES production function will also result in a model which permits consistent estimation of the production function parameters from single equation estimation of the production function relation itself. Section 1 below is devoted to demonstration of this conclusion. In addition, in Section 2 attention is turned to specification and estimation of a related model for a firm operating as a pure monopolist.