I. Introduction, 253. — II. Allocation of output among plants, neglecting transmission losses, 254. — III. Practical solution of this problem, 258. — IV. Allocation of output, making allowances for transmission losses, 261. — V. Practical solution, making allowances for transmission losses, 265. — VI. Conclusion, 268.

IN their audit of the sources of economic growth a number of writers have, in recent years, focussed on technical and improvements in the quality of capital and labor rather than increases in the quantity of factors of production. Implicitly, if not explicitly, this work has generated new theoretical propositions about aggregative production functions and has led to the revival of efforts to estimate them. This research has been pursued on a number of fronts, but much of it is centered in its applications on the United States economy. This paper reports the results of some experiments with a model that postulates technical progress together with possible nonconstant returns to scale using data relating to the United States economy. Though the assumption of embodiment of technical in factors of production is one of the latest fashions in growth models, the conventional trim is constant returns to scale. Models allowing for scale economies or diseconomies may even seem somewhat old-fashioned, although a number of studies have, in fact, emphasized the combination of improvements in factor qualities and increasing returns in explaining United States growth.' R. M. Solow, observed by A. Smithies 2 to be the Pied Piper of research on technical change, though consistently assuming constant returns for the United States economy whether he is leading us in the direction of disembodied or embodied change, has recently reported some statistical calculations for the German economy without the constant returns restriction.3 The relationship of economic to the size of the economy has been the subject of speculation for as long as there have been economists.4 Contemporary attempts at measurement, however, may not only have failed to give sufficient emphasis to the role of scale economies or diseconomies, but may have made, as a consequence, faulty assessments of the role played by other influences on the growyth process. A model that postulates constant returns to scale, one suspects, would overstate the growth resulting from technical when confronted with data generated by a generally growing economic system subject to increasing returns and, vice versa. The model would understate the growth due to technical change when the data are generated by a growing economy subject to decreasing returns. A. A. Walters [13], for example, obtains sharply increasing returns to scale for the Cobb-Douglas model of disembodied technical change applied to 1909-1949 data for the United States economy and finds a much lower rate of shift (i.e., technical progress) of the production function than Solow [9] with the same model applied to the same time period but with the restriction of constant returns.5 One should also recognize that for some models which assume constant returns, identification of both growth and scale parameters may not even be possible.

One of the principal quantitative techniques used in the studv of costs and benefits of regulation involves the evaluation of consumer's and producer's surplus. Examples are [2], [3], [4], [6]. The method can be caricatured as follows: Obtain data on quantity and price for the output produced by the regulated industry. Obtain estimates of the slopes of the demand and marginal cost from cross-section or timeseries estimates of elasticities. Calculate where demand and marginal cost would intersect. Complete a triangle whose vertexes are (1) the predicted intersection of marginal cost and demand, (2) the current demand price, and (3) the current estimated marginal cost. Add to the area of this dollar triangle the direct total cost of the entire regulatory machinery-the budget of the regulatory agency and the budget for lawyers, accountants, engineers, public relations men, and for all the other costs incurred by those being regulatedand you have an estimate of the social cost of regulation. Waiving their validity and accuracy for the moment, the calculations assume that a feasible social alternative to the regulated status quo is, in fact, described by the intersection of the measured marginal cost and demand curves, and that this alternative situation can be reached without new direct regulation costs offsetting the savings. If the social optimum were to require a price-output configuration for the regulated industry described by the pricemarginal cost equality, and this equality could be brought into being by a costless restructuring of the regtulated industry into one behaving like a competitive industry, then the social choice is trivial. The complex statistical calculations are unnecessary. However, if pure competition or its simulation are not viable alternatives to the regulated status quo because of decreasing unit costs often considered characteristic of public utilities, then the calculations are beside the point. Dismantling the regulatory machinery will save the resources used by the regulatory process, but the laissez-faire outcome will probably be oligopoly with its absence of price competition, excessive product differentiation, wasteful sales promotion and advertising, excess capacity, and expensive legal talent to forestall and defend antitrust prosecutions. The measured demand and marginal cost curves and the triangle provide no information about a new deregulated equilibrium. And it is not a valid proposition that entry of firms, threats of entry, and oligopolistic rivalry will be an improvement over regulated monopoly. So far I have not challenged the proposition that the intersection of demand and * Research support of the National Science Foundation is gratefully acknowledged.