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Quasilineare Nutzenfunktion Beispiel Essay

Präferenzen Definition

Präferenzen im Sinne der Haushaltstheorie sind die Vorlieben bzw. die einer Konsumentscheidung zugrunde liegenden Kriterien eines Konsumenten / Haushalts.

Dabei betrachtet man i.d.R. modellhaft Güterbündel mit Mengen von nur einem oder zwei Gütern.

Beispiel

Z.B. könnte das Güterbündel A aus einer Flasche Rotwein, das Güterbündel B aus einer Flasche Weißwein und das Güterbündel C aus einer Flasche Sekt bestehen.

Die Präferenzen können geordnet bzw. gewertet werden und für diese sog. Präferenzrelation bzw. Präferenzordnung geht man von 3 Annahmen aus:

  • Vollständigkeit: alle Güterbündel können miteinander verglichen werden, d.h., für alle Güterbündel A und B ist entweder A besser/gleich B oder umgekehrt B besser/gleich A (im Beispiel: eine Flasche Rotwein ist besser als oder gleich gut wie eine Flasche Weißwein oder umgekehrt);
  • Reflexivität: identische Güterbündel werden mindestens gleich gut eingeschätzt (eine Selbstverständlichkeit);
  • Transitivität: wenn A besser/gleich B und B besser/gleich C ist, dann muss auch gelten, dass A besser/gleich C ist, d.h., wenn der Konsument Rotwein dem Weißwein gegenüber bevorzugt und Weißwein besser als Sekt einschätzt, wird er auch den Rotwein dem Sekt vorziehen.

Präferenzen können durch Nutzenfunktionen abgebildet werden.

Quasilineare Präferenzen liegen vor, wenn die Indifferenzkurven für verschiedene Nutzenniveaus vertikal versetzt sind: die Indifferenzkurven haben eine Form (z.B. eine Kurve oder Gerade) und die verschiedenen Nutzenniveaus werden dadurch dargestellt, dass diese Form nach oben oder unten verschoben wird.

Beispiel: Quasilineare Präferenzen

Quasilineare Präferenzen haben eine Nutzenfunktion der Form:

u(x1,x2) = v(x1) + x2

Dabei steht v(x1) dafür, dass es sich um eine Funktion von x1 handelt, z.B. das Quadrat.

Unsere Nutzenfunktion sei:

u(x1,x2) = x12 + x2

Jetzt kann man sich ein paar Güterbündel überlegen, die ein Nutzenniveau von z.B. 2 haben:

u(0, 2) = 02 + 2 = 0 + 2 = 2.

u(0,5, 1,75) = 0,52 + 1,75 = 0,25 + 1,75 = 2.

u(1, 1) = 12 + 1 = 1 + 1 = 2.

Daraus ergibt sich die in der Grafik unten eingezeichnete rote Indifferenzkurve.

Dies kann man für ein Nutzenniveau von 3 analog machen, daraus ergeben sich z.B. die 3 Güterbündel: u(0, 3), u(0,5, 2,75) und u(1, 2).

Daraus ergibt sich die in der Grafik unten eingezeichnete blaue Indifferenzkurve.

Die beiden Indifferenzkurven sind lediglich vertikal versetzt.

The plan was to start working on my final essay once i got home from band but i decided that now would be a good time instead

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