Also published in: ‘Jan Tinbergen Selected Papers’, edited by L.H. Klaassen, L.M. Koyck and H.J. Witteveen, Nort- Holland Publishing Company, Amsterdam, 1959, pp. 165-181
ON READING Professor Hotelling's interesting paper General Welfare . . . which appeared in the July, 1938 issue of ECONOMETRICA, it occurred to me that a word of comment may be useful in order to prevent that more be read into the fundamental theorem of the paper and its conclusions than they really contain. The generalized Dupuit theorem proved by Professor Hotelling does not state that satisfaction is necessarily reduced if we increase the portion of the total tax levy which is represented by excise taxes and correspondingly reduce the portion represented by an incomie tax, and that satisfaction is increased by a change in the opposite direction. In other words the theorem does not state that total satisfaction is necessarily reduced if the total tax burden (supposed given) is shifted in the direction away from income taxes and increased if the burden is shifted towards income taxes. Professor Hotelling's statement, change from income to excise taxes has resulted in a net loss of satisfactions. Conversely, . . . (page 251) may suggest such an interpretation, although of course Professor Hotelling did not intend to convey this idea. The fact that the direction of change is immaterial is seen simply by noticing that Professor Hotelling's proof of the reduction in satisfaction is entirely independent of whether his magnitude bm (the change in the income tax) is positive or negative. The only relevant question is whether the excise taxes are proportional or nonproportional to the prices that existed before the imposition of the excise taxes. It is the nonproportionality of the excise taxes, and only this, that produces a reduction in satisfaction. This reduction has nothing to do with the fact that excise taxes exist, nor even with the fact that they are high (positive or negative). Professor Hotelling's statement about inefficiency of an economic system in which there are excise taxes or bounties (page 253) is certainly apt to be misunderstood. Also in regard to the assumptions back of the analysis there are one or two points that ought to be brought out a little more explicitly. They necessitate rather important qualifications in the practical conclusions. I therefore believe it is worth while to go over the ground in another way which will bring out these points more clearly.
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-