The Personal Distribution of Income

Steindl, Josef

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Document type:: Works

Collection:: Josef Steindl Collection

Title:: The Personal Distribution of Income

Author:: Steindl, Josef

Scope:: Typoskript, 24 Seiten (23 Seiten auf Durchschlagpapier), mit zahlreichen handschriftlichen Anmerkungen und Anstreichungen

Year of publication:: 1972

Source material date:: August-September 1972

Language:: English

Note:: Unveröffentlichtes Typoskript.

Topic:: Stochastic processes and size distribution

Shelfmark:: S/M.52.8

DOI:: https://doi.org/10.48671/nls.js.AC14446372

extent an inversion of the other; in addition, each will be influenced by the dispersion f the values r^und the other recession line. Thus ltfiT. each-.*# each of the regression lines will represent a compromise between the two underlying relations the weight of them being different in the one and the ither regression line. No regression line therefore will be a true reflection of an underlying causal (or rather stochastic ) relation. We shall have a better chance of understanding the meaning of joint size distributions of this type if we regard them as residues of a growth process. Cet us therefore return to the allometric law. As far as its relation to the joint distribution wealth-income is concerned we have to make two observations: 1) If the regression line income on wealth could be regarded as an expression of the allometric law then, as it will he remembered, the regression coefficient is the rati ■ of the tw P&ret ja efficients if the inc me and the wealth distributi n 2) Foil wing up the idea that wealth can be explained fr m saving ver a certain time and saving can be explained fr m inc me taking saving r pensity as given, we can deirive the distributi n f wealth fr m that of income in much the same way as the ther way r undi V/e explain the saving distributi n as a c nvnluti n ofjthe income distribution and >f thesistribution f the propensity to save ( savings ratio ): q«(s) - q(y) * g ( Vy - s ), (9) and the wealth distribution a s a convalution of this and the time the saving has accumulated ( which will be finite in the case of earned income but not necessarily for unearned income )s q«»( w ) « ^ q'(s) * h ( s - w ) (10) From this wealth distribution we should by means f the original transformati n (6) c me back to the income distribution

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