The Dupuit Taxation Theorem - Frisch, Ragnar (Econometrica, 1939)
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.