TECHNICAL CHANGE AND PRODUCTION FUNCTION 3I7 mation as old-fashioned capital goods are re- The Aggregate Production Function placed by the latest models, so that the capital- Returning now to the aggregate production labor ratio need not change systematical lunction, we have earned the right to write it But this raises problems of definition and meas- in the form (ra). By use of the(practically urement even more formidable than the ones already blithely ignored. This whole area of scale. this can be further simplified to the form interest has been stressed by fellner For comparison, Solomon Fabricant has q=A(1)f(k,), estimated that over the period I87I-I95I which formed the basis of Chart I. It was there about go per cent of th e increase in output per noted that a simple plot of q against h would capita is attributable to technical progress. give a distorted picture because of the shift Presumably this figure is based on the stand- factor A(t). Each point would lie on a different ard sort of output-per-unit-of-input calcula- member of the family of production curves But we have now provided ourselves with an It might seem at first glance that calculations estimate of the successive values of the shift of output per unit of resource input provide factor. (Note that this estimate is quite inde- pendent of any hypothesis about the exact a relatively assumption-free way of measuring shape of the production function. )It follows productivity changes. Actually I think the im- from (3)that by plotting q(t)/A(t) against plicit load of assumptin ats to a if anything the method proposed above is con- single member of the family of curves in Chart I, and we can then proceed to discuss the shape Not only does the usual choice of weights for of f(k, I)and reconstruct the aggregate pro computing an aggregate resource-input involve tion function. a scatter of /A againy duc- something analogous to my assumption of com- shown in Chart 4 petitive factor markets, but in addition the cr terion output a weighted sum of inputs CHART 4 would seem tacitly to assume (a) that technical I change is neutral and (b) that the aggregate production function is strictly linear. This ex- plains why numerical results are so closely parallel for the two methods. We have already verified the neutrality and as will be seen sub gives an excellent fit, though clearly inferior to some alternatives …°“· rS. Fabricant, " Economic Progress and Economic Change, "34th Annual Report of the National Bureau of Economic Research(New York, I954) For an excellent discussion of some of the problems, see M Abramovitz"Resources and Output Trends in the U.S. a2 since I87o, American Economic Review, Papers and Pro ceedings, XLVI (May I956),5-23. Some of the qu here raised could in principle be answered by the method sed here. For example, the contribution of improved Considering the amount of a priori doctoring as levels of skilled labor as separate inputs. I owe to which the raw figures have undergone, the fit is W. Schultz a heightened awareness that a lot of remarkably tight. Except, that is, for the layer appears as shifts in the production function must of points which are obviously too high. These represent improvement in the quality of the labor input, maverick observations relate to the seven last portant kind. Nor ought it be forgotten thar on of an im- and therefore a result of real capital format even straight years of the period, I943-49. From the way technical progress has a cost side. they lie almost exactly par rallel to the main