Eichhorn, Wolfgang; Gleißner, Winfried On a functional differential equation arising in the theory of the distribution of wealth. (English) Zbl 0567.35013 Aequationes Math. 28, 190-198 (1985). The paper under review deals with the functional differential equation \((i)\quad p_ t(x,t)+(\beta +n\gamma)p(x,t)+\beta xp_ x(x,t)=\gamma n^ 2p(nx,t),\) \(x,t\in (0,+\infty)\), arising in the theory of the distribution of wealth. The author studies properties of solutions of (i) of the type \(p(x,t)=p(t)x^{-c},\) where \(c>1\), and multiplicative solutions \(\psi (x,t)=u(x)v(t)\). The proof uses an explicit expression of solutions of an initial problem for (i). Reviewer: Z.Kamont Cited in 6 Documents MSC: 35F10 Initial value problems for linear first-order PDEs 35R10 Partial functional-differential equations 91B62 Economic growth models 35C05 Solutions to PDEs in closed form 35A05 General existence and uniqueness theorems (PDE) (MSC2000) Keywords:functional differential equation; distribution of wealth; multiplicative solutions PDFBibTeX XMLCite \textit{W. Eichhorn} and \textit{W. Gleißner}, Aequationes Math. 28, 190--198 (1985; Zbl 0567.35013) Full Text: DOI EuDML References: [1] Champernowne, D. G.,The distribution of income between persons. Cambridge University Press, Cambridge, 1973. [2] Hale, J.,Theory of functional differential equations. Springer, New York-Heidelberg-Berlin, 1977. · Zbl 0352.34001 [3] Ijiri, Y. andSimon, H. A.,Skew distribution and the size of business firms. North Holland, Amsterdam, 1977. [4] Sargan, J. D.,The distribution of wealth. Econometrica25 (1957), 568–590. · Zbl 0078.34002 [5] Shorrocks, A. F.,On stochastic models of size distributions. Rev. Econom. Stud.42 (1975), 631–641. · Zbl 0318.60060 [6] Steindl, J.,The distribution of wealth after a model of Wold and Whittle. Rev. Econom. Stud.39 (1972), 263–279. [7] Walter, W.,Über ein Modell zur Pareto-Verteilung. Applicable Anal.11 (1980/81), 233–239. · Zbl 0459.35084 [8] Wold, H. O. A. andWhittle, P.,A model explaining the Pareto distribution of wealth. Econometrica25 (1957), 591–595. · Zbl 0077.33806 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.