Knowledge that Transforms

IN A PREVIOUS article1 I made a brief and incomplete survey of the theory of depreciation. In the present paper I discuss its practice. One obstacle to practical progress in this field is that mathematically trained minds are seldom well informed on what accountants actually do. The latter are therefore more often criticized for methods which they are not using than for those which they are. Even otherwise valuable contributions thus elicit opposition quite unnecessarily. The inappropriate antithesis tends to discredit the rest of the argument and prompts general retorts, for instance that is a of . . . determined by the practices of men.-Where accounting treatment diverges from economic theory, a similar divergence is likely to be found between economic theory and practice.2 Such an attitude, in turn, is not very helpful or progressive, even if the dangerous phrase tool of business is interpreted only in its best possible sense. In the article cited, I probably added to the already existing confusion by calling sample methods by certain names without proper qualification, although the same names are commonly applied to substantially different methods. The truth is that the familiar singlemachine formulae permit of different interpretations. To clarify the situation, the present paper identifies a greater number of methods unequivocally by developing their basic many-machine equations and comparing the results. References to practice and to individual writers' ideas are made wherever possible, before choosing a method which appears best suited to the practical needs of large enterprises and the investing public.

In the work done to obtain demand functions from market data, the influence of income changes on demand has been usually eliminated (by Professor Schultz and others) by regarding the national income per head, R, as a linear component of the demand function; sometimes a parameter supposed to characterize the distribution (such as Pareto's a or some index of concentration)' was used as another such component, e.g.:

PARETO deserves a place of honor among those economists who have aimed at a unification of theoretical-quantitative and empirical-quantitative approach to economic problems. His, sometimes misplaced,' exaltation of method led him to affirm that the progress of economic science in future will depend to a large extent upon investigation of empirical laws, derived from statistics, which will then be compared with known theoretical laws, or will lead to discovery of new laws. The new empirical laws will be essentially result of application to statistical data of methods of interpolation.2 Pareto's empirical formula which describes distribution of personal incomes seemed to open a wide and promising perspective of fruitful research. Professor Benini-who, following Pareto's suggestion, conceived in 1907 bold plan of a new science of inductive quantitative economics-contended that Pareto, by stating his law of incomes, had written first chapter of that new science.3 So far Pareto's and Benini's hopes have not been fulfilled. Though statistics and verification have played in last few decades a role of increasing importance, progress of economic theory has been mainly achieved by a process of scientific investigation, which is by no means that suggested by Pareto in passage quoted above. Interpolation has continued to be a useful statistical tool for practical purposes; but empirical and quite arbitrary formulae, on which it is based, generally are lacking in scientific interest. Pareto's Law forms an exception. The fact that incomes, in different places and epochs, are approximately distributed in accordance with this law, gives it a special significance. Though more than forty years have now elapsed since Pareto enunciated it, it is still attracting attention of economists and statisticians.3 I only need recall de-

BEFORE COMMENTING on Dr. Graves' note, I wish here to put on record a recent change in my own terminology. Dr. Graves quotes me correctly as having formerly said that capital increase is properly But since my efforts thus to restrict the use of the term to have met with little success, I have decided to capitulate on that point. In a book which I am preparing on What should be taxable income? I am suggesting that, paradoxically, we may avoid ambiguity by giving two meanings to income. One is or or simply yield. The other is servicesplus-capital-income or or simply enrichment (sometimes called accretion-sometimes earnings). This concession is made in deference to the fact that usage vacillates between the two concepts, and that both are useful. They are well exemplified in the stock market in the yield of a stock as contrasted with its earnings. I am also prompted to make this change by the hope of helping to lift the discussion of income from the level of words to the level of ideas. Apart from terminology, however, I have seen no reason since 1897 to change my attitude. Nor do I find anything in Dr. Graves' discussion which would incline me to change it. In summarizing my conclusions, Dr. Graves is likely to mislead many readers: (a) They may not understand that in what he calls my assumption (2) negative psychic services were omitted explicitly in order to create a simplified case-just as he himself makes various assumptions to create his five special cases. In my ECONOMETRICA article, negative psychical services were far from overlooked or disregarded. But I was leading up to the problem of taxation in which negative psychical services have to be either neglected or treated by rule of thumb.' (b) The same is true of his reference to my assumption (5) to the effect that services are worth their cost. In my article, much attention was given to the discrepancies between the worth of services or uses and money cost. But, with his eye on only my most simplified case, Dr. Graves remarks: