Knowledge that Transforms

THE following production functions have been derived from business records of 609 Iowa farms for 1942, kept at Iowa State College.2 These records give a complete picture of all the business transactions and holdings of each farm and are carefully checked. They are, however, far from typical for the average Iowa farm. Their relationship to actual production conditions at the farm is perhaps comparable to the relationship between yields from careful experiments at an agricultural experiment station to the actual yields of an average field. We have included altogether 609 farm records in our analysis. They have been divided into four main types of farming (dairy, hogs, beef feeders, crops). We use as a regression equation a function which is linear in the logarithms. This is none other than the production function which Paul H. Douglas used in his many empirical studies.3 We do not, however, make the assumption of homogeneity, i.e., the sum of the regression coefficients is not necessarily equal to one. In fact, we shall later present a test of significance designed especially to test, in a fashion, the assumption of a linear homogeneous production function. The reasons which prompt us to use this particular form of the production function are the following: (1) It gives immediately elasticities of the product with respect to the factors of production (Paul H. Douglas called them flexibilities). That is, we get answers to the question: By how many per cent will the product increase on the average if the given factor increases by 1 per cent. Elasticities are dimensionless numbers and independent of the units of measurement. (2) Our form of the production function permits the phenomenon of decreasing marginal returns to come into evidence without using too many degrees of freedom. This would not be possible if we should fit a linear function