February 2015
Intermediate to advanced
392 pages
17h 52m
German
Content preview from Mathematik für Wirtschaftswissenschaftler, 2nd Edition
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10.3. Partielle Ableitungen
295
Die Funktion f heißt homogen und die Zahl r heißt Homogenitätsgrad von f,
wenn für alle Punkte x = (xi,···, xn) des Definitionsbereiches gilt:
f(Xx) = /(λχι,...,λχη) = X
r
f(x) für alle λ > 0. (10.11)
In Worten: Eine Vervielfachung aller unabhängigen Variablen mit ein und demselben
positiven Faktor λ führt zu einer Vervielfachung der abhängigen Variablen mit dem
Faktor λ
Γ
.
• Lineare Funktionen - ohne absolutes Glied - sind homogen vom Grad 1.
Die Summe zweier homogener Funktionen vom gleichen Homogenitätsgrad r hat
ebenfalls den Homogenitätsgrad r. Das Produkt zweier beliebiger homogener Funk-
tionen hat die Summe ...
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