Produzentenrente Integralrechnung ★ Übung 2 mit Lösung

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Situation: Die Konsumenten wollen möglichst niedrige Preise zahlen und die QuickTel GmbH sowie alle anderen Wettbewerber wollen möglichst hohe Preise realisieren, um die Erlöse zu steigern. • Chef: Marc, letzte Woche habe ich ihre Kollegin Tina mit einem ähnlichen Thema genervt. Heute sind Sie dran. Schauen Sie sich mal folgende Grafik zu unserem Produkt „SchreibPad XC“ an. • Der Marktpreis für dieses Pad hat sich in den letzten Monaten zunehmend erhöht, was auf den stärkeren US Dollar zurückzuführen sei. Klar, das kann schon sein, da alle Anbieter die Dinger aus den USA importieren. Das Verrückte ist, dass unsere Kosten sogar zurückgehen. • Marc: Das ist doch super. Dann würden wir die SchreibPads ja auch für weniger Geld verkaufen, als wir es tatsächlich gemäß des Marktpreises tun. Ich mache mir nur Sorgen um mehr Mitbewerber. • Kannst du noch…? • Flächeninhalte zwischen Graphen sowie zwischen Graph und x-Achse • Übung 1: Marktsituation des Produkts „SchreibPad XC“ • Beschreiben Sie die allgemeine Marktsituation. Weshalb kann es problematisch sein, dass sich der Gleichgewichtspreis zunehmend „zu Gunsten der Anbieter“ verschiebt? • Geben Sie die Koordinaten des Marktgleichgewichts G an. • Berechnen Sie die Fläche PR der Produzentenrente und zeichnen Sie diese zusammen mit G in die Grafik ein. • Was könnte die QuickTel GmbH tun, um die Produzentenrente zu erhöhen? • Übung 2: • Auch der Markt für ein anderes Produkt der QuickTel GmbH lässt sich passend mit einer Nachfrage- und Angebotsfunktion modellieren. Dabei gelten folgende Zusammenhänge zwischen Preisen in €/Stück und x in Stücken: p_N (x)=-0,25x²+32 und p_A (x)=0,5x²+3. • Zeichnen Sie die Nachfragefunktion pN(x) und die Angebotsfunktion pA(x) in das obige Koordinatensystem ein. Beschriften Sie alles entsprechend. • Ermitteln Sie das Marktgleichgewicht mit dem GTR. • Geben Sie sowohl den Höchstpreis pH, als auch die Sättigungsmenge xS an. • Geben Sie den ökonomisch sinnvollen Definitionsbereich Dök für die Nachfragefunktion an. • Berechnen Sie algebraisch den Umsatz, der mit dem Verkauf dieses Produkts realisiert wird. • Welchen Betrag nehmen die Produzenten insgesamt zusätzlich dadurch ein, dass sie das Produkt zum Gleichgewichtspreis pG verkaufen können (Produzentenrente)? • Was du jetzt kannst! • Ich kann die Nachfrage- und Angebotssituation bezüglich eines wirtschaftlichen Gutes beschreiben und interpretieren. • Ich weiß, wie man eine Nachfrage- und Angebotsfunktion in ein Koordinatensystem einträgt. • Ich kenne die Bedeutung des Marktgleichgewichts und weiß, wie man es berechnet. • Ich verstehe, weshalb sich der Höchstpreis und die Sättigungsmenge aus der Nachfragefunktion ergeben und kenne die grafische Lage dieser Punkte. • Ich weiß, dass sich das Intervall des ökonomischen Definitionsbereichs aus 0 und der Sättigungsmenge xS ergibt. • Ich kann den Umsatz eines Produkts im Marktgleichgewicht berechnen. • Ich kenne die Formel zur Berechnung der Produzentenrente und verstehe, wie sich diese Formel zusammensetzt. • Ich kann die Maßzahl der Produzentenrente wirtschaftlich sinnvoll 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