Economic essays

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Monograph

Identifikator:: 1753623200

URN:: urn:nbn:de:zbw-retromon-136107

Document type:: Monograph

Title:: Economic essays

Place of publication:: New York

Publisher:: Macmillan

Year of publication:: 1927

Scope:: viii, 368 S.; Ill., graph. Darst.

Digitisation:: 2021

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: A statistical method for measuring "marginal utility" and testing the justice of a progressive income tax / Irving Fisher

Collection:: Economics Books

A STATISTICAL METHOD FOR MEASURING ‘MARGINAL UTILITY” 187 whether progressive or regressive taxation is indicated but the exact degree of progressiveness or regressiveness. The most satisfactory way to picture this mathematically is to plot the two points S;, W; and S3;, W3 on “doubly logarithmic” paper, join these two points by a straight line, and measure the slope of that line. If the slope is 45°, then S; W,=8; W3 and the tax should be at a uniform rate; if it slopes downward more steeply than 45°, the tax should be progressive; if less steeply, regressive. The slope itself tells us at what percentage rate the want for a dollar decreases for each 1 per cent increase in income. This figure for the slope can, of course, be attained arith- metically without plotting." This slope is what Marshall, in a different application, called “elasticity.” Extension of the Theory All the essentials of the method have now been stated. But it may be well to point out that, by successive applications, its range can be extended indefinitely or as far as the budgetary statistics are available. That is, we may continue to choose identical families con- formably to the same prescription that for every family in Odd- land there will exist in Evenland another family provided with an income such as will lead it to choose the same, and equally desirable, food ration; whereas for every such family chosen in Evenland there must be another in Oddland that will have an income such as will lead it to choose the same, and equally desir- able, housing accommodation. We have hitherto supposed only Cases 1, 2,3. We now add Cases 4, 5, 6, 7, etc., all the odd figures referring to Cases in Oddland and all the even figures to Cases in Evenland, as shown in Chart II which is merely a schedule of Cases 1, 2, 3, 4, 5, etc., with a chasm or ocean between Oddland and Evenland. Our calculations evidently constitute a sort of triangulation by which we pass back and forth from Case 1 via Case 2 to Case 3, thence, via Case 4 to Case 5 and so on. The Chart shows schematically what I mean by “triangulation.” * We need merely equate the logarithms of the two sides of equation (3) and likewise of equation (4) and then divide one of these new equations by the other and calculate out the right hand side on the basis of the statistical figures it contains.

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