1.5 Individuelle Nachfrage 1.5.1 V eranderungen des Einkommens
Werbung
1-30 Prof. Dr. K. Schmidt dem Einkommen zu, @ x1 (p1 ; p2 ; m) @m > 0: Normales Gut: Nachfrage nach diesem Gut nimmt mit Halten wir zunachst die Preise beider Guter konstant und betrachten nur Veranderungen des Einkommens. 1.5.1 Veranderungen des Einkommens: Normale und inferiore Guter das Einkommen verandert? der Preis dieses Gutes ver andert? der Preis des anderen Gutes ver andert? Nachfrage nach Gut i, wenn sich Komparativ statische Analyse: Wie verandert sich die ge jeden Gutes in Abhangigkeit von Preisen und Einkommen. x1 = x1(p1; p2; m) x2 = x2(p1; p2; m) Nachfragefunktion des Konsumenten: Optimale Men- 1.5 Individuelle Nachfrage AVWL I (WS 96/97) x2 1-31 Prof. Dr. K. Schmidt x1 rrrr rrr rr rr r r rr r r r r r r r r r r r r r r r r r rrrrrrr r r rrrr r r r rrrrr r rrrr r r rrrr r r rrrrr r r rrrrr r r rrrr r rrrr r r rrr r r rrrrr rr r rrrr r rrrrrrr rrr r r r rrrrr r rrrrr r rrr r r rrr r rrrr r rrrr r rrrr rrrrr r rrrrr r r r r rrrrr rrrrr r r rrrr rrrr r r rrrr rrrr r r rrr rrr r r rrrrr rrrrr r r rrrr rrrr r r r rrr rrrrr r r rrrr rrrrr r rrr rrrr r r r r rrr r rrrr r rrrrr r r r r rrrrr rrrrr r r rrrrr rrrrr r r rrrr rrrrr r r rrrrr r rrr r rrr rrr r r rrr rrrrr r r rrrrr r r rrrrr rrrrr r r rrrrr rrrrr r r rrrrr rrrr r r rrr rrr r rrrr r rrrr r rrrrr r rrrrr r r r r rrrrr rrrrr r r rrrrr rrrrr r rrrrr rrrr r r r r rrr r rrr r rrrr r rrrr r rrrrr r rrrrr r rrrrr r r rrrrr r rrrrr rrr r rrrr r rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr rrrrrrrrr rrrrrrr Figur 1.8: Normale und Inferiore Guter x1 x2 rrrr rrr rr rr r r rr r r r r r r r r r r r r r r r r r rrrrrrr r r rrrr r r r rrrrr r rrrr r r rrrrr r r rrrrr r r rrrr r r rrr r r rrrr r r rrrr r rr rrrr r r rrrrr r rrrrrr rrr r r r rrr r rrrrr r rrrr r rrrr r rrrr r rrrr r rrrrr rrrrr r r rrrrr r r r rrrr rrrr r r rrr r rrr rrr r rrrr r r r r rrrr rrrr r r rrrr rrrr r r rrrrr rrrrr r r rrr rrr r r rrr rrr r rrrr r rrr r r rrrrr r rrrr r r rrrrr rrrrr r rrrrr rrr r r r rrrrr r rrrr r rrr r r r rrrr rrrr r r rrrr rrrr r r rrrr rrrrr r r rrrrr r rrrr r rrrr rrr r r rrrr rrr r r rrr r r r rrrr rrrr r r rrrr rrrr r r rrrrr rrrrr r r rrrr rrrr r r rrr rrr r rrrr r rrrr r r r rrrr rrrr r r rrrrr rrrrr r rrrrr rrrrr r r r rrrrr r r rrrr r rrr r r rrrr r rrr rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr rrr rrrrrrr dem Einkommen ab, @ x1 (p1 ; p2 ; m) < 0 : @m Guter des einfachen Bedarfs oder niedriger Qualitat sind oft inferiore Guter, weil sie bei steigendem Einkommen durch hoherwertige Guter ersetzt werden. Inferiores Gut: Nachfrage nach diesem Gut nimmt mit AVWL I (WS 96/97) 1-32 Prof. Dr. K. Schmidt Einkommens-Konsumkurve x1 m r rrr rrr rrr rr r r r r r r r r r r r r r r r r r r r rrrrrrr r r r rrrrrr r rrrr r r rrrrr r r rrrr r r rrrr r r rrr r rrr r r rrrrr r r rrrrr r r rrrr r rrrrr rrrr r r r rrr r rrrr r rrrr r r r r rrrrr rrrr r r rrrrr r r rrrrr r rrrrr r rrrr r rrrr r rrr r rrr r r rrr r rrr r rrrr r rrrrr r rrrr r rrrrr r r r rrrrr r rrrr r r r r rrrr rrr r r rrr r r r rrrr rrrr r r rrrr rrr r r rrrrr rrrrr r r r r rrrr rrrr r rrrr r rrr r r rrr rrrr r r r r rrr rrrr r r rrrrr r r r rrrrr rrrr r r r rrrrr r r r rrr r rrrr r rrr r rrrr r rrrr r rrr r r rrrr r rrr r r r r rrrrr rrrrr r r rrrr r r r r rrr r rrr r r r rrrr r rrr r rrr r rrrr r rrrr r rrrrr r rrrr r r rrrrr r rrrrr r rrrr r rrrr r rrr r rr rrr r rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr r rrrrrrr Engelkurve x1 r rrr rrr rrr rr r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r rrrrrr r rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr rrrrrr rrrrrrr Figur 1.9: Einkommens-Konsumkurve und Engelkurve x2 Gutermengen im (x1; x2)-Diagramm fur verschiedene Einkommen an. Wird auch Einkommens-Expansionspfad genannt. Engelkurve: gibt die Nachfrage nach einem Gut im (x1; m)Diagramm in Abgangigkeit vom Einkommen an. Einkommens-Konsumkurve: gibt beide nachgefragten AVWL I (WS 96/97) 1-33 m < Einkommens-Konsumkurve x1 x1 = pm1 , x2 = 0. Engelkurve x1 r rrr rrr rrr rrr r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r rrrrrr r rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr rrrrrr rrrrrrr ) Prof. Dr. K. Schmidt x2 Einkommens-Konsumkurve x1 rr rrr rrr r rrr rr r r r r r r r r r r r r r r r r r rrrrrr r r r rrrrrr r r r rrrrrrr r r rrrrr r r rrr r r rrrr r rrrr r r rrrrr r r rrrrr r r rrrr r r rrr rrrrr r rrr r rrrr r rrrrr r r r rrrrr rrrrr r r r r rrr rrrr r rrrrr r r r r rrr rrr r r rrrr rrrr r r rrrr rrrr r r r rrrr rrrrr r rrrrr rrrrr r r rrrr rrrr r r rrr r r rrrr r rrr r r r rrrr rrrrr r rrrr r r r r rrrrr rrrrr r r rrrr rrrr r r rrr rrrr r r r rrr rrr r r rrrr rrrrr r rrrrr r rrrrr r r r rrrr r rrrrr r rrrrr r rrrr r rrr rrr r r r rrrr r rrr r rrrr r rrrrr r rrrrr r rrrrr rrrrr r r r rrrr rrrr r r rrrr rrrr r rrr r rrr r r r rrrr rrrrr r rrrr r r r r rrrrr rrrrr r r rrrr rrrr r rrrr r rrrr r r r rrr rrrr r rrrr r rrr r rrrrr r rrrr rrrrrr r r r r rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr rrrrrrr rrrrrrr m + Engelkurve x1 rr rrr rrr r rrr rr r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r rrrrrr r rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr rrrrrr rrrrrrr + b) Perfekte Komplemente: x1 = p1mp2 , x2 = p1mp2 . x2 r rrr rrr rrr rrr r r r r r r r r r r r r r r r r r r rrrrrr r r rrrr r r r rrrrr r rrrr r r rrrr r r rrrr r r rrrr r rrrr r r rrr r r rrr r r rrrrr r r r rrrr r rrrrrr rrr r r r r rrrr r rrr r rrr r r r rrrr r rrrr r r rrrr r r rrrrr r rrrrr r rrrr r rrrr r rrrr r rrrr r r rrr r rrr r rrr r rrr r rrrr r rrrrr r r r rrrr r rrrr r r r r rrr rrr r rrrr r r r r rrr rrr r r rrrr rrrr r r rrrr rrrr r r r rrrr rrrrr r r rrrr rrr r rrrr r rrr r r rrrr r rrrr r r rrrr r r rrrrr rrrrr r r r rrrr r rrrrr r rrrrr r r r r rrr rrr r r rrr rrrr r r rrrr rrrr r r r r rrrr rrrrr r rrrrr r r r r rrr r rrrr r r r rrr r rrr r rrrr r rrrr r rrrr r rrrr r rrrrr r r r rrrr r rrrr r rrrrr r rrrrr r rrr r rr r rr r r rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr rrrr rrrrrr Beispiele: a) Perfekte Substitute: p1 p2 AVWL I (WS 96/97) 1-34 x2 Engelkurve r rrr rrr rrr rr r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r rrrrrr r rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr rrrrrr rrrrrrr Figur 1.12: Cobb-Douglas Praferenzen x1 m x1 Prof. Dr. K. Schmidt (1,a)m x1 = am p1 , x2 = p2 . Einkommens-Konsumkurve ) r rrr rrr rrr rr r r r r r r r r r r r r r r r r r r r rrrrrrrr r r r rrrrrr r rrr r r rrrr r r rrrrr r r rrrrr r rrrrr r r rrrr r r rrrr r r rrrr r r rrrr r rrrrr rrrrr r rrr r rrrr r rrrr rrrr r r r r rrrr rrrr r r r r rrrr rrrr r rrrrr r rrrrr r rrrrr r rrrrr r rrrrr r r r rrrr r rrrr r rrr r rrrr r rrr r rrrr r r r rrrr r rrrr r rrrrr r rrrrr r rrrr rrrr r r r r rrr rrrr r r rrrr rrr r r rrrr rrrrr r r r rrrrr rrrr r r rrr rrrrr r r rrrr rrrrr r r r r rrr rrrr r rrrr r r r r rrrr rrrr r r r rrrrr r r rrrrr r rrrrr r rrrr r rrrr r rrrrr r rrrr r rrr r rrr r rrrr r rrrrr rrr r r rrrr r r r rrrr r rrr r r r rrrrr r r rrr r rrr r rrrr r rrrr r rrrr r rrrr r r rrrrr r rrrrr r rrrr r rrrrr r rrrr r rr rrrr r rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr r rrrrrrr u(x1; x2) = xa1x12,a c) Cobb-Douglas Praferenzen: AVWL I (WS 96/97) 1-35 Prof. Dr. K. Schmidt Wenn die Engelkurve konkav ist, spricht man von einem Luxusgut: die Nachfrage steigt uberproportional mit dem Einkommen. Wenn die Engelkurve konvex ist, spricht man von einem notwendigen Gut: die Nachfrage steigt unterproportional mit dem Einkommen. Naturlich konnen Praferenzen auch nicht homothetisch sein: Ein Konsument hat homothetische Praferenzen wenn fur alle k > 0 gilt: (x1 ; x2 ) (y1 ; y2 ) () (kx1 ; kx2 ) (ky1 ; ky2 ) Alle diese Beispiele fuhrten zu linearen Engelkurven. Das liegt daran, da alle diese Beispiele zur Klasse der homothetischen Praferenzen gehoren. AVWL I (WS 96/97) 1-36 Engelkurve x1 rrrr rrr rrrr rr r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r rrrrrr r rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr rrrrrr rrrrrrr x1 Figur 1.13: Quasilineare Praferenzen Einkommens-Konsumkurve m x1 ist unabhangig von m. rrrr rrr rrrr rr r r r r r r r r r r r r r r r r r rrr r r rrrrrr r r r rrrrrr r rrrrr r r rrrrr r r rrrr r r rrr r rrrr r r rrrr r r rrrr r r rrrrr r rrrr r rrrrr rrr r rrr r rrrr r rrrr r rrrr r rrrrrrr rrrrr r r r rrrrr rrrrr r r rrr rrrr r rrr rrr r r r rrr rrrr r rrrr r rrrr r rrrr rrrr r r rrrrr rrrrr r rrrr rrrr r r rrr rrr r r rrrr rrrr r rrrr rrrr r r r rrrrr rrrr r r rrrrr rrrr r rrr rrrrr r r rrr rrr r rrrr r rrr r rrrr rrrr r r rrrr rrrrr r r rrrrr rrrrr r rrrr rrrr r r rrrr rrr r rrr rrrr r r rrr rrrr r rrr r rrrr r rrrrr rrrr r r rrrr rrrrr r rrr r rrr r rrrr r r rrr rrr r r r r rrrrr rrrr r r r rrrr r r r r rrrrr r rrrrr r r r r rrrr rrrr r r rr rrr r rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr r rrrrrrr ) Prof. Dr. K. Schmidt Bei quasilinearen Praferenzen gibt es also keine \Einkommenseekte". Solche Praferenzen sind oft realistisch, wenn die Ausgaben fur das betreende Gut nur einen sehr kleinen Teil des Einkommens ausmachen. x2 u(x1; x2) = v(x1) + x2 d) Quasilineare Praferenzen: AVWL I (WS 96/97) 1-37 Prof. Dr. K. Schmidt mit dem Preis ab, Gewohnliches Gut: Nachfrage nach diesem Gut nimmt @ x1(p1; p2; m) < 0 : @ p1 Gien-Gut: Nachfrage nach diesem Gut nimmt mit dem Preis zu, @ x1 (p1 ; p2 ; m) > 0 : @ p1 Gien Guter tauchen sehr selten auf, aber es gibt sie. Beispiel: Nachfrage nach Kartoeln im fruhen 19. Jahrhundert. Wir werden spater sehen, da Gien-Guter inferiore Guter sein mussen, aber nicht umgekehrt. Halten wir jetzt das Einkommen und den Preis des anderen Gutes fest und betrachten Veranderungen des eigenen Preises. 1.5.2 Veranderungen des Preises des Gutes: Gewohnliche Guter und Gien-Guter AVWL I (WS 96/97) AVWL I (WS 96/97) x1 rrrr rrr rrrr rr r r r r r r r r r r r r r r r r r rrr r r rrrrrrrrrrrr r r r rrrrrrrrrrrrrr r r r rrrrrrrrrrrrr r r rrr rrrrrrr r r rr rrrrrr r rrr rrrrr r r rr rrrrrr r r rrr rrrrr r r rrr rrrrrr r r rrrrr rr r rrrrr rrr r r rrrrr rrr r r rrrrr r rrr rrrrr r r rr rrrrr r r rrrrr r rr r rrrrr rrr r r rrrrr rr r rrrrr r rrr r rrrrr r rrr r rrrrr r rrrr rrrrr r r rrrrr r r r rrr r rrrrr r rrrrr r r rrrr r rrrrr r r rrrrr r rr r rrrrr rrr r r rrrrr rrr r rrrrr r r rrr rrrrr r r rrrrr rrr r rrrrr r rrr r rrrrr r rrr r rrrrr r r rrrrr r rrr r rrrrr r rr r rrrrr rrr r rrrrr r r r rrrrr rrr r rrrrr r r r rrr rrrrr r r rrrrr r r rrr rrrrr r r rrr rrrrr r r rrrrr rrr r rrrrr r rrr r rrrrr r r r rrrrr rrr r rrrrr r r r rrrr rrrrr r rrrrr r rr r rrrrr rrr r r rrrrr rrr rrrr r r rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr rrrrrrrrr rrrrrrr x2 Figur 1.14b: Gien-Gut x1 rrrr rrr rr r rr r rr r r r r r r r r r r r r r r r r r rrrrr r r r rrrrrrrrrrrrr r r r rrrrrrrrrrrrrr r r rrrrrrrrrr r r rrr rrrrrrr r r rrr rrrrrr r r rrr rrrrrr r r rr rrrrrr r r rrr rrrrr r rrrr r rrr r r rrr rrrrrrrrr r r rrrrr rrr r rrrrr r rrr r rrrrr r rrrrr r r rrr r rrrrr r rrr r rrrrr r rrrrr rrr r r rrrrr r rrr r rrrrr r r rrrrr r rrr r rrrrr r r rrr r rrrrr r rrrrr r r rrr r rrrrr r r r rrrrr rrr r rrrrr r r r rrrrr rrr r rrrrr r r r r rrrrr rrr r r rrrrr r r rrrrr rrr r r rrrrr r r rrr r rrrrr r r rrrrr r rrr r rrrrr r r r rrrrr r r rrr rrrrr r r r rrrrr rrr r rrrrr r r r r rrrrr rrr r r rrrrr r r r rrrrr r rrrr r rrrrr r r rrrr r rrrrr r rrrrr r r rrr r rrrrr r r r rrrrr rrr r rrrrr r rr r rrrrr r rrr rrrrr r r r rrrrr rrr r r rrrrr r r rrr rrrrr r r r rr rrrrr rr r rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr rrrrrr rrrrrrr Figur 1.14a: Gewohnliches Gut x2 1-38 Prof. Dr. K. Schmidt 1-39 Prof. Dr. K. Schmidt x2 x1 Nachfragekurve x1 rrrr rrr rrrr rr r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r rrrrrr rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr rrrrrr rrrrrrr Figur 1.15: Preis-Konsumkurve und Nachfragekurve Preis-Konsumkurve p1 rrrr rrr rrrr rr r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r rrrr rrrrrrrr r r r rrrrr rrrrrrrrrrr r r r rrrrrrrrrrrrrrrrrrrrrrrr r r rr rrrrrrrrrrrrr r rrr rrr rrrrrr r r rrr rrr rrrrrrr r r rr rrrr rrrrrr r r rrr rrrr rrrrrr r r rrr rrrr rrrrrr r r rrr rrrrrr rrrrrrr r r rr rrrr rrrrrrr r r rrr r r r r rr rrrrr rrrrrrrrrrr r r rr rrrr r r rrr rrrrr rrrrrrrrrr r r rrrrrr rrrrr rrr r r rrrrrr rrrr rrr r r rrrrrr rrr r r rrr r rrrrrr rrrr r r rrrrrr r rrrr rrr r rrrrrr r r r r r r rrr rrrrrr rrrrr r r rrrrrr r r r r r r rrrr r rr rrrrrr r r r rrrrrr r r rrrr r rr rrrrrr r r r r r r rrr rrrrrr rrr r r r rrrrrr r r r r r rrrr rrr r rrrrrr r r r r r r rrrrrr rrr rrr r r rrrrrr r r r r r rrr rrrrrr r rrr r r rrrrrr r r r rr rrrrr r rrrrrr r rr r r r r rrrrrr r rrr rrrr r r rrrrrr r r r r r r rrr rrrrr r rrr r r r r r rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr r rrrrrrr gen im (x1; x2)-Diagramm fur verschiedene Preise von Gut 1 an. Nachfragekurve: gibt die Nachfrage nach einem Gut im (x1 ; p1 )-Diagramm in Abg angigkeit vom eigenen Preis an. Preis-Konsumkurve: gibt beide nachgefragten Gutermen- AVWL I (WS 96/97) 1-40 < p1 x1 Nachfragekurve x1 rr rrr rrr r rrr rr r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r rrrrrr r rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr rrrrrr rrrrrrr x1 = pm1 , x2 Preis-Konsumkurve p1 x1 r rrr rrr rrr rr r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r rrrrrrrr r r rr r rrrrrr r rrrrrrrrrrr r r rrrrrrrrrrrrrrrrrrrrr r r r rrrrrrrrrrrrrrrrrrr r rrr rrr rrrrrr r r rr rrrrr rrrrrrr r r rrr rrrr rrrrr r r rr rrrrr rrrrrrr r r rr rrrr rrrrr r rr rrrr rrrrrr r r rr r r rr rrrrr rrrrrrrrrrr r rrr r r r r rrr rrrrrrrr rrrrrrrrrrr r r rr rrrr rr r r rrrr rrrrrrrrrr rrr r r rrrrrr rrr rrr r rrrr r rrrrrr r r rr rrrrrr r rrrr rr r rrrrrr rrrrr r rr r rrrrrr rrrrr r rr r rrrrrr rrrrr rr r r rrrrrr r r r r r rrr rr r rrrrrr r rrr rrr rrrrrr r r rrrrr rrr rrrrrr r r rrrrr rrrrrr rrr r r r rrrrrr r r r r rrrr rrr r rrrrrr r r r r r rrrrrr r rrr rrr r rrrrrr r rrrrr rr r rrrrrr r rr rrrrr r rrrrrr r r r rrrr rr r rrrrrr r r r r r r rrrrrr rrr rrr r rrrr rrrrrr r rrr r rrrrrr r rrrr rrr r rr r r rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr r rrrrrrr + Nachfragekurve x1 r rrr rrr rrr rr r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r rrrrrr r rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr rrrrrr rrrrrrr + b) Perfekte Komplemente: x1 = p1mp2 , x2 = p1mp2 . Preis-Konsumkurve rr rrr rrr r rrr rr r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r rrr r r rrrrrrrrrrrrrr rrr r r r r rrrrrrrrrrrrrrrrrrrr r r r rrrrrrrrrrrrrrrrrrrrrr r rr rrrrrrrrr r r rrr rrrr rrrrrr r r rr rrrr rrrrrr r r rrr rrrrr rrrrrr r r rr rrrrr rrrrrrr r rrr rrrr rrrrr r r r rrr rrrr rrrrrrr r r rr rrrrr rrrrrrr r rrr r r r r rrr rrrrrrr rrrrrrrrrrr r r r rrrr rrr r r rrr rrrrrrrrrrr rr r r rrr rrrrrr rrr r rrrr r rrrrrr rr r rrrrrr r rrrr rrr r rrrrrr rrrrr r rrr r rrrrrr rrrr r rr r rrrrrr rrrrr rr r r rrrrrr rrr rrr r r rrrrrr r r r r rrr rrr rrrrrr r r r r r rrrrrr r r r rrr rrrr r rrrrrr r rrrrr rrr r rrrrrr r rrrr rrr r rrrrrr r r rr rrrr r rrrrrr r rrr r rrrrrr r rrrrr r rr rrrrrr r r r r r rrrrr rrrrrr rrr r r r r rrrrrr r r r rrrr rrr r rrrrrr r r r r r rrrrrr rrr rrr r rrrrrr r rrrr r r r rrrrrr rr rrrrr r rrrrrr r rr r r r rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr rrrrrrr rrrrrrr x2 = 0. x2 ) Prof. Dr. K. Schmidt Beispiele: a) Perfekte Substitute: p1 p2 AVWL I (WS 96/97) 1-41 Prof. Dr. K. Schmidt Substitute: Nachfrage nach dem betrachteten Gut nimmt zu, wenn der Preis des anderen Gutes steigt: @ x1 (p1 ; p2 ; m) > 0 : @ p2 Wenn Gut 2 teurer wird, \substituiert" der Konsument es durch Gut 1. Extremfall: perfekte Substitute; der Konsument fragt nur das relativ billigere Gut nach. Komplemente: Nachfrage nach dem betrachteten Gut nimmt mit ab, wenn der Preis des anderen Gutes zunimmt: @ x1 (p1 ; p2 ; m) < 0 : @ p2 Der Nutzen aus dem Konsum von Gut 1 steigt mit dem Konsum von Gut 2. Gut 2 wird teurer ) Konsument fragt weniger von Gut 2 nach; ) der Nutzen aus Gut 1 sinkt; ) Konsument fragt auch wenige von Gut 1 nach. Schlielich halten wir das Einkommen und den eigenen Preis fest und betrachten Veranderungen des Preises eines anderen Gutes. 1.5.3 Veranderungen des Preises des anderen Gutes: Substitute und Komplemente AVWL I (WS 96/97) 1-42 Prof. Dr. K. Schmidt Konsument mehr fur Gut 1 ausgibt, mu er bei konstantem Einkommen zwangslaug weniger fur Gut 2 ausgeben. Darum besser im N-Guter Fall betrachten. Vorsicht: Der 2-Guterfall ist hier sehr speziell: Wenn der Extremfall: Perfekte Komplemente; der Konsument will die Guter nur in einem konstanten Verhaltnis konsumieren. AVWL I (WS 96/97) 1-43 Prof. Dr. K. Schmidt p1(x1) x1 rr rrr rrr r rrr rr r r r r r r r r r rr r r rr r r rr r r rr r rr r r rr r r rr r rr r r rr r r rr r rr r r rr r r rr r rrr r r r rrr r r rrr r r rrr r r rrr r r r rrr r r rrr r r rrr r r rrr r r rrr r r rrr r r rrr r r rrr r r rrr r r rrr r r rrr r r rrr r rrrr r r rrrr r r rrr r r rrrr r r rrrr r r rrr r r rrrrr r rrrrr r r rrrr r r rrrr r r rrrr r r rrrrr r r rrrrr r r rrrrr r rrrrrr r r rrrrrrr r r rrrrrr r rrrrrrr r r rrrrrrr r r rrrrrrr r rrrrrrrr r r rrrrrrrr r r rrrrrrrrr r r rrrrrrrrr r rrrrrrrr r r rrrrrr r r rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr rrrrrr rrrrrrr Die inverse Nachfragekurve gibt fur jede Menge x1 an, wieviel das Gut kosten mute, damit der Konsument exakt diese Menge nachfragt. Figur 1.16: Inverse Nachfragekurve p1 Es wird oft nutzlich sein, die Nachfragefunktion x1 = x1(p1; ) nach p1 aufzulosen und die inverse Nachfragefunktion p1(x1) zu betrachten (Vorsicht: geht nur, wenn die Nachfragefunktion monoton ist). 1.5.4 Die inverse Nachfragekurve AVWL I (WS 96/97) 1-44 Prof. Dr. K. Schmidt = p1 p2 Wenn die inverse Nachfragekurve fallt, bedeutet das, da die marginale Zahlungsbereitschaft des Konsumenten mit zunehmendem Konsum abnimmt. p1 = p2 jGRSj ; d.h., im Optimum ist der Preis des Gutes 1 proportional zur GRS. Normiere p2 auf 1. Die GRS mit, wieviel der Konsument von Gut 2 bereit ist aufzugeben, um eine zusatzliche Einheit von Gut 1 zu bekommen. Die inverse Nachfragekurve gibt fur jede Menge x1 den Preis p1 an, bei dem es fur den Konsumenten optimal ist, diese Menge nachzufragen. Also druckt die inverse Nachfragekurve auch die Zahlungsbereitschaft des Konsumenten (in Einheiten von Gut 2) fur jede weitere Einheit von Gut 1 aus. Also gilt: j GRSj Im Optimum mu gelten: tion: Die inverse Nachfrage hat eine interessante Interpreta- AVWL I (WS 96/97)
