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{"sheet":"Start","index":0,"n_rows":18,"n_cols":10,"rows_kept":18,"cut":false,"hidden":false,"merged":[[13,4,15,9],[1,1,1,9],[3,1,5,2],[17,1,24,6]]}
[]
[null,"Preisbildung im Monopol"]
[]
[null,"Darstellung  der Funktionen",null,null,null,"aX3","bX2","cx","d","d/x"]
[null,null,null,"Kostenfunktion",null,2,-20,250,200]
[null,null,null,"Preis-Absatz-Funktion",null,null,null,-100,800]
[]
[null,"Funktionen werden tabellarisch dargestellt. In die Zellen werden nur die Faktoren eingetragen. Die Spaltenüberschrift "]
[null,"definiert jeweils den Exponenten. "]
[null,"Die oben dargestellte Kostenfunktion lautet also: K = 2x3 - 20x2 + 250x + 200; Die PAF lautet: p = -100x + 800"]
[null,"(Excel bietet die umständliche Möglichkeit zur Eingabe der Funktionen mit Hochzahlen. Bei der gewählten Darstellungsweise müssen nur die"]
[null,"jeweiligen Faktoren geändert werden, um mit den Funktionen rechnen zu können.)"]
[]
[null,null,null,null,"Eingabe der Funktionen und Ergebnisauswertung"]
[]
[]
[]
[null,"In allen Fällen wird die Cournotsche Menge graphisch/tabellarisch (100 x-Werte) und analytisch ermittel und die Abweichung von beiden Lösungen berechnet. Die Preis-Absatz-Funktion hat in allen Fällen die Form p = - cx + d. (Die allgemein übliche Form p=a-bx wird dabei an die hier verwendete Darstellungsweise angepasst. Erlösfunktion: E = - cx2 + dx) Die Cournotsche Menge kann jeweils als ganze Zahl (Stückproduktion) oder als Dezimalzahl (Produktionsmenge in Kilogramm, Metern oder Litern) angezeigt werden. "]

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[]
[null,"Preisbildung im Monopol"]
[]
[null,"Funktionen",null,null,null,null,null,null,"Erlös",null,{"$f":"IF(AND(D6=\"\",E6=\"\"),BerechnungLin!J10,IF(Kontrolle!D6=\"\",BerechnungQua!J10,BerechnungKub!J10))","v":1582.4851717608699}]
[null,null,null,"aX3","bX2","cx","d","d/x","Gesamtkosten",null,{"$f":"IF(AND(D6=\"\",E6=\"\"),BerechnungLin!K10,IF(Kontrolle!D6=\"\",BerechnungQua!K10,BerechnungKub!K10))","v":672.56237168232587}]
[null,"Gesamtkosten",null,2,-20,150,300,null,"variable Gesamtkosten",null,{"$f":"Kontrolle!K5-Kontrolle!G6","v":372.56237168232587}]
[null,"Preis-Absatz-Funktion ",null,null,null,-100,800,null,"fixe Gesamtkosten",null,{"$f":"G6","v":300}]
[null,"variable Gesamtkosten",null,{"$f":"D6","v":2},{"$f":"E6","v":-20},{"$f":"F6","v":150},null,null,"Stückkosten",null,{"$f":"IF(AND(D6=\"\",E6=\"\"),BerechnungLin!G12,IF(Kontrolle!D6=\"\",BerechnungQua!G12,BerechnungKub!G12))","v":187.78828007552414}]
[null,"Stückkosten",null,null,{"$f":"D6","v":2},{"$f":"E6","v":-20},{"$f":"F6","v":150},{"$f":"G6","v":300},"variable Stückkosten",null,{"$f":"IF(AND(D6=\"\",E6=\"\"),BerechnungLin!H12,IF(Kontrolle!D6=\"\",BerechnungQua!H12,BerechnungKub!H12))","v":104.02432539316663}]
[null,"variable Stückkosten",null,null,{"$f":"D6","v":2},{"$f":"F9","v":-20},{"$f":"F6","v":150},null,"fixe Stückkosten",null,{"$f":"BerechnungKub!I12","v":300}]
[null,"Grenzkosten",null,null,{"$f":"3*D6","v":6},{"$f":"2*E6","v":-40},{"$f":"F6","v":150},null,"Grenzkosten",null,{"$f":"IF(AND(D6=\"\",E6=\"\"),BerechnungLin!K12,IF(Kontrolle!D6=\"\",BerechnungQua!K12,BerechnungKub!K12))","v":83.702832037579739}]
[null,"Erlös ",null,null,{"$f":"F7","v":-100},{"$f":"G7","v":800},null,null,"Absatzgrenze (Xmax)",null,{"$f":"(G7/F7)*-1","v":8}]
[null,"Grenzerlös ",null,null,null,{"$f":"2*E12","v":-200},{"$f":"F12","v":800}]
[]
[null,"Geben Sie nach Klick auf \"Eingabe\" die Kostenfunktion und die Preis-Absatz-Funktion ein. Oder kopieren Sie Beispielfunktionen in die entsprechenden Felder."]
[]
[]
[]
[null,"Extrempunkte",null,"€"]
[null,"Gewinnmaximum",null,{"$f":"IF(AND(D6=\"\",E6=\"\"),BerechnungLin!I10,IF(Kontrolle!D6=\"\",BerechnungQua!I10,BerechnungKub!I10))","v":909.92280007854401},"größter Gesamtgewinn; größte Differenz zwischen Erlös und Kosten"]
[null,"Courtnotscher Punkt",null,null,"Die Cournotsche Menge ergibt sich aus dem Schnittpunkt zwischen Grenzkosten und Grenzerlös. Eingesetzt in die entsprechende Preis-Absatz-Funktion wird der gewinnmaximale Preis ermittelt."]
[null,"   Preis",null,{"$f":"IF(AND(D6=\"\",E6=\"\"),BerechnungLin!H10,IF(Kontrolle!D6=\"\",BerechnungQua!H10,BerechnungKub!H10))","v":441.85072070960081}]
[null,"   Menge",null,{"$f":"IF(AND(D6=\"\",E6=\"\"),BerechnungLin!G10,IF(D6=\"\",BerechnungQua!G10,BerechnungKub!$G$10))","v":3.5814927929039917}]
[]
[null,"Plausibilitätskontrolle",null,null,"Im betriebswirtschaftlichen Unterricht ist es eine Herausforderung, harmonisierende Kosten- und Preis-Absatz-Funktionen zu finden. Wenn diese Funktionen nicht harmonieren, erhalten Sie für die wichtigsten Abweichungsgründe einen Hinweis. Gründe könnten z.B. negative variable Stück- oder Grenzkosten, oder nicht eindeutig definierte Cournotpunkte sein. (Es sind nicht alle Abweichungsgründe erfasst.) Bei kubischen Kostenfunktionen der Form ax3-bx2+cx+d müssen Sie auf der Seite 'kubische Kostenfunktion' de Berechnung der Cournotmenge durch Klick auf den Button 'Cornotsche Menge' aktivieren. Andernfalls wird die Cournotmenge nicht korrekt angezeigt, und die Plausibilitätskontrolle arbeitet nicht korrekt."]
[null,{"$f":"IF(OR(BerechnungKub!F116<=0,Kontrolle!G11>Kontrolle!G13,BerechnungKub!H116<=0),\"keine Funktionsharmonie!\",\"Funktionen harmonieren\")","v":"Funktionen harmonieren"}]
[null,{"$f":"IF(BerechnungKub!F116<=0,\"negative variable Stückkosten\",IF(G11>G13,\"Cournotpunkt nich eindeutig definiert'\",IF(BerechnungKub!H116<=0,\"negative Grenzkosten\",\"\")))","v":""}]
[]
[null,"Berechnungen"]
[]
[]
[null,null,null,"K = cx + d",null,null,"K = bx2 + cx + d",null,null,"K = ax3 - bx2 + cx + d"]
[null,"Die anlaytischen Berechnungen unterscheiden sich bei linearen, quadratischen und kubischen Funktionen und werden daher in getrennten Tabellen durchgeführt.",null,null,null,null,"Die Kostenfunktion besteht aus steigenden variablen Stückkosten und konstanten gesamten Fixkosten (d). Die Grenzkosten steigen linear.",null,null,"Die Kostenfunktion besteht aus parabelförmig verlaufenden variablen Stückkosten und konstanten gesamten Fixkosten (d). Die Grenzkosten verlaufen parabelförmig. Die Cournotsche Menge kann durch eine Näherungslösung (Variation der Menge um ganze Zahlen) oder mit der Zielwertsuche von Excel ermittelt werden."]
[null,null,null,"Die Kostenfunktion besteht aus konstanten variablen Stückkosten und Fixkosten (d). Die Grenzkosten entsprechen den konstanten variablen Stückkosten."]

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[null,"aX3","bX2","cx","d","d/x","Ausgabewerte ",null,null,null,null,null,null,"Berechnung der Cournotschen Menge (lineare Kostenfunktion)"]
["K=",{"$f":"Kontrolle!D6","v":2},{"$f":"Kontrolle!E6","v":-20},{"$f":"Kontrolle!F6","v":150},{"$f":"Kontrolle!G6","v":300},null,"Gewinnmaximum tabellarisch",null,null,"Gmax",{"$f":"MAX(I15:I115)","v":909.88799999999992}]
["Kv=",{"$f":"Kontrolle!D8","v":2},{"$f":"Kontrolle!E8","v":-20},{"$f":"Kontrolle!F8","v":150},null,null,null,null,null,"XGmax",{"$f":"VLOOKUP(K2,I15:N115,5,FALSE)","v":3.6000000000000019},null,null,"K = cx + d"]
["Kf=",null,null,{"$f":"D2","v":150},null,null,null,null,null,"PGmax",{"$f":"VLOOKUP(K2,I15:N115,4,FALSE)","v":439.99999999999983},null,null,{"$f":"IF(AND(B9=0,C9=0),(E10-E9)/(D10*-1),\"\")","v":""},null,true]
["E1=",null,{"$f":"Kontrolle!E12","v":-100},{"$f":"Kontrolle!F12","v":800},null,null,"Abweichungen der tabellarischen von der analystischen",null,null,null,{"$f":"(100%*(K2-I10))/100","v":{"$error":"#VALUE!"}}]
["k=",null,{"$f":"Kontrolle!E9","v":2},{"$f":"Kontrolle!F9","v":-20},{"$f":"D2","v":150},{"$f":"Kontrolle!H9","v":300},"Gewinnermittlung. (analytischer Gewinn = 100%)"]
["kv=",null,{"$f":"Kontrolle!E10","v":2},{"$f":"Kontrolle!F10","v":-20},{"$f":"Kontrolle!G10","v":150},null,"Gewinnmaximum analytisch / Cournotscher Punkt"]
["kf=",null,null,null,null,{"$f":"E2","v":300}]
["K'",null,{"$f":"Kontrolle!E11","v":6},{"$f":"Kontrolle!F11","v":-40},{"$f":"Kontrolle!G11","v":150},null,"XGmax","PGmax","Gmax","E","K",null,null,"Aktivieren Sie das Kontrollkästchen, wenn die Cournotsche Menge in ganzen Zahlen angegeben werden soll. (G10)"]
["E'",null,null,{"$f":"Kontrolle!F13","v":-200},{"$f":"Kontrolle!G13","v":800},null,{"$f":"IF(P4=TRUE,ROUND(N4,0),N4)","v":{"$error":"#VALUE!"}},{"$f":"(G10*D11)+E11","v":{"$error":"#VALUE!"}},{"$f":"J10-K10","v":{"$error":"#VALUE!"}},{"$f":"G10*H10","v":{"$error":"#VALUE!"}},{"$f":"(B2*(G10*G10*G10))+(C2*(G10*G10))+(D2*G10)+E2","v":{"$error":"#VALUE!"}}]
["PAF",null,null,{"$f":"Kontrolle!F7","v":-100},{"$f":"Kontrolle!G7","v":800},null,"k","kv","kf","E'","K'"]
["Xmax",{"$f":"Kontrolle!K12","v":8},null,null,null,null,{"$f":"(C6*(G10*G10))+(D6*(G10))+(E6)+(F6/G10)","v":{"$error":"#VALUE!"}},{"$f":"(C7*(G10*G10))+(D7*G10)+E7","v":{"$error":"#VALUE!"}},{"$f":"F8","v":300},{"$f":"(D10*G10)+E10","v":{"$error":"#VALUE!"}},{"$f":"(C9*(G10*G10))+(D9*G10)+E9","v":{"$error":"#VALUE!"}}]
[null,null,null,null,null,null,{"$f":"N4","v":""},{"$f":"(G13*D11)+E11","v":{"$error":"#VALUE!"}},{"$f":"J13-K13","v":{"$error":"#VALUE!"}},{"$f":"G13*H13","v":{"$error":"#VALUE!"}},{"$f":"(D2*G13)+E2","v":{"$error":"#VALUE!"}}]
["X","K","K+Gmax","Kf","k","kv","kf","K'","E-K","E","E'","PAF1","X","Berechnung bei linearer Kostenfunktion (K=ax+b)"]
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[{"$f":"A16+$A$16","v":0.16},{"$f":"($B$2*(A17*A17*A17))+($C$2*(A17*A17))+($D$2*A17)+($E$2)","v":323.49619200000001},{"$f":"BerechnungLin!B17+BerechnungLin!$I$10","v":{"$error":"#VALUE!"}},300,2021.8512000000001,{"$f":"$E$7","v":150},1875,{"$f":"($C$9*(A17*A17))+($D$9*(A17))+$E$9","v":143.75360000000001},-198.05619200000001,125.44,768,784,0.16]
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[{"$f":"A18+$A$16","v":0.32},346.01753600000001,{"$f":"BerechnungLin!B19+BerechnungLin!$I$10","v":{"$error":"#VALUE!"}},300,1081.3047999999999,150,937.5,137.81440000000001,-100.25753600000002,245.76,736,768,0.32]
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[0.64,388.33228800000001,{"$f":"BerechnungLin!B23+BerechnungLin!$I$10","v":{"$error":"#VALUE!"}},300,606.76919999999996,150,468.75,126.85759999999999,82.707712000000015,471.04,672,736,0.64]
[0.72,398.37849599999998,{"$f":"BerechnungLin!B24+BerechnungLin!$I$10","v":{"$error":"#VALUE!"}},300,553.30346666666662,150,416.66666666666669,124.3104,125.78150399999998,524.16,656,728,0.72]
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[0.87999999999999989,417.87494399999997,{"$f":"BerechnungLin!B26+BerechnungLin!$I$10","v":{"$error":"#VALUE!"}},300,474.85789090909094,150,340.90909090909093,119.44640000000001,208.68505599999997,626.55999999999995,624,712,0.87999999999999989]
[0.95999999999999985,427.33747199999999,{"$f":"BerechnungLin!B27+BerechnungLin!$I$10","v":{"$error":"#VALUE!"}},300,445.14320000000004,150,312.50000000000006,117.12960000000001,248.50252799999993,675.83999999999992,608,704,0.95999999999999985,null,null,null,null,{"$f":"(($D$10*$R$25)+($D$9*-1*$R$25)+$E$10-$E$9)/$C$9","v":-25},{"$f":"(($D$10*$S$25)+($D$9*-1*$S$25)+$E$10-$E$9)/$C$9","v":-211.66666666666666}]
[1.0399999999999998,436.61772799999994,{"$f":"BerechnungLin!B28+BerechnungLin!$I$10","v":{"$error":"#VALUE!"}},300,419.82473846153846,150,288.46153846153851,114.8896,287.22227199999998,723.83999999999992,592,696,1.0399999999999998,{"$f":"IF(AND(Kontrolle!D6=\"\",Kontrolle!E6=\"\"),\"\",IF(Kontrolle!D6=\"\",\"Sie haben eine quadratische Kostenfunktion angegeben. Wechseln Sie zur Kontrollseite und dann zur 'quadratischen Kostenfunktion'.'\",\"Sie haben eine kubische Kostenfunktion angegeben. Wechseln Sie zur Kontrollseite und dann zur 'kubischen Kostenfunktion'.\"))","v":"Sie haben eine kubische Kostenfunktion angegeben. Wechseln Sie zur Kontrollseite und dann zur 'kubischen Kostenfunktion'."},null,null,null,{"$f":"SQRT($R$27)","v":{"$error":"#NUM!"}},{"$f":"SQRT($S$27)","v":{"$error":"#NUM!"}}]
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[1.2,454.65600000000001,{"$f":"BerechnungLin!B30+BerechnungLin!$I$10","v":{"$error":"#VALUE!"}},300,378.88,150,250,110.64,361.34399999999999,816,560,680,1.2]
[1.28,463.42630400000002,{"$f":"BerechnungLin!B31+BerechnungLin!$I$10","v":{"$error":"#VALUE!"}},300,362.05180000000001,150,234.375,108.63039999999999,396.73369599999995,860.16,544,672,1.28,null,null,null,null,{"$f":"1-R29","v":{"$error":"#NUM!"}}]
[1.36,472.03891200000004,{"$f":"BerechnungLin!B32+BerechnungLin!$I$10","v":{"$error":"#VALUE!"}},300,347.08743529411765,150,220.58823529411762,106.69759999999999,431.00108799999992,903.04,528,664,1.36]
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[{"$f":"IF(AND(Kontrolle!D6=\"\",Kontrolle!E6=\"\"),\"\",IF(Kontrolle!D6=\"\",\"Sie haben eine quadratische Kostenfunktion angegeben. Wechseln Sie zur Kontrollseite und dann zur 'quadratischen Kostenfunktion'.'\",\"Sie haben eine kubische Kostenfunktion angegeben. Wechseln Sie zur Kontrollseite und dann zur 'kubischen Kostenfunktion'.\"))","v":"Sie haben eine kubische Kostenfunktion angegeben. Wechseln Sie zur Kontrollseite und dann zur 'kubischen Kostenfunktion'."}]

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[{"$f":"IF(AND(Kontrolle!D6=\"\",Kontrolle!E6=\"\"),\"\",IF(Kontrolle!D6=\"\",\"Sie haben eine quadratische Kostenfunktion angegeben. Wechseln Sie zur Kontrollseite und dann zur 'quadratischen Kostenfunktion'.'\",\"Sie haben eine kubische Kostenfunktion angegeben. Wechseln Sie zur Kontrollseite und dann zur 'kubischen Kostenfunktion'.\"))","v":"Sie haben eine kubische Kostenfunktion angegeben. Wechseln Sie zur Kontrollseite und dann zur 'kubischen Kostenfunktion'."}]

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["kf=",null,null,null,null,{"$f":"E2","v":300}]
["K'",null,{"$f":"Kontrolle!E11","v":6},{"$f":"Kontrolle!F11","v":-40},{"$f":"Kontrolle!G11","v":150},null,"XGmax","PGmax","Gmax","E","K",null,null,null,{"$f":"(($D$10*$N$7)+($D$9*-1*$N$7)+$E$10-$E$9)/$C$9","v":12.826858855893553}]
["E'",null,null,{"$f":"Kontrolle!F13","v":-200},{"$f":"Kontrolle!G13","v":800},null,{"$f":"IF(P7=TRUE,ROUND(N7,0),N7)","v":3.5814927929039917},{"$f":"(G10*D11)+E11","v":441.85072070960081},{"$f":"J10-K10","v":909.92280007854401},{"$f":"G10*H10","v":1582.4851717608699},{"$f":"(B2*(G10*G10*G10))+(C2*(G10*G10))+(D2*G10)+E2","v":672.56237168232587},null,null,null,{"$f":"SQRT($O$9)","v":3.5814604361759397}]
["PAF",null,null,{"$f":"Kontrolle!F7","v":-100},{"$f":"Kontrolle!G7","v":800},null,"k","kv","kf","E'","K'",null,null,null,{"$f":"$O$10/$N$7","v":0.99999096557499256}]
["Xmax",{"$f":"Kontrolle!K12","v":8},null,null,null,null,{"$f":"(C6*(G10*G10))+(D6*(G10))+(E6)+(F6/G10)","v":187.78828007552414},{"$f":"(C7*(G10*G10))+(D7*G10)+E7","v":104.02432539316663},{"$f":"F8","v":300},{"$f":"(D10*G10)+E10","v":83.701441419201615},{"$f":"(C9*(G10*G10))+(D9*G10)+E9","v":83.702832037579739}]
[null,null,null,null,null,null,{"$f":"N7","v":3.5814927929039917},{"$f":"($N$7*$D$11)+$E$11","v":441.85072070960081},{"$f":"J13-K13","v":909.92280007854401},{"$f":"$N$7*$H$13","v":1582.4851717608699},{"$f":"(B2*(N7*N7*N7))+C2*(N7*N7)+(D2*N7)+E2","v":672.56237168232587}]
["X","K","K+Gmax","Kf","k","kv","kf","K'","E-K","E","E'","PAF1","X"]
[0,{"$f":"($B$2*(A15*A15*A15))+($C$2*(A15*A15))+($D$2*A15)+($E$2)","v":300},{"$f":"B15+$I$10","v":1209.922800078544},{"$f":"$E$2","v":300},null,null,null,null,{"$f":"J15-B15","v":-300},{"$f":"($C$5*(A15*A15))+($D$5*A15)","v":0},{"$f":"($D$10*A15)+$E$10","v":800},{"$f":"($D$11*A15)+$E$11","v":800},0,null,null,null,{"$f":"IF(AND(Kontrolle!D6=\"\",Kontrolle!E6=\"\"),\"Sie haben eine lineare Kostenfunktion angegeben. Wechseln Sie zur Kontrollseite und dann zur 'linearen Kostenfunktion'.\",IF(Kontrolle!D6=\"\",\"Sie haben eine quadratische Kostenfunktion angegeben. Wechseln Sie zur Kontrollseite und dann zur 'quadratischen Kostenfunktion'.\",\"\"))","v":""}]
[{"$f":"$B$12/100","v":0.08},{"$f":"($B$2*(A16*A16*A16))+($C$2*(A16*A16))+($D$2*A16)+($E$2)","v":311.87302399999999},{"$f":"B16+$I$10","v":1221.795824078544},{"$f":"$E$2","v":300},{"$f":"B16/A16","v":3898.4127999999996},{"$f":"C16/A16","v":15272.447800981799},{"$f":"$F$6/A16","v":3750},{"$f":"($C$9*(A16*A16))+($D$9*(A16))+$E$9","v":146.83840000000001},-248.51302399999997,{"$f":"($C$5*(A16*A16))+($D$5*A16)","v":63.36},{"$f":"($D$10*A16)+$E$10","v":784},{"$f":"($D$11*A16)+$E$11","v":792},{"$f":"B12/100","v":0.08}]
[{"$f":"A16+$A$16","v":0.16},{"$f":"($B$2*(A17*A17*A17))+($C$2*(A17*A17))+($D$2*A17)+($E$2)","v":323.49619200000001},1233.4189920785441,300,2021.8512000000001,7708.8687004909007,1875,{"$f":"($C$9*(A17*A17))+($D$9*(A17))+$E$9","v":143.75360000000001},-198.05619200000001,125.44,768,784,{"$f":"M16+$M$16","v":0.16},"Aktivieren Sie das Kontrollkästchen, wenn die Cournotsche Menge in ganzen Zahlen angegeben werden soll. (G10)"]
[{"$f":"A17+$A$16","v":0.24},334.87564800000001,1244.798448078544,300,1395.3152,5186.6602003272665,1250,140.7456,-148.635648,186.24,752,776,0.24]
[{"$f":"A18+$A$16","v":0.32},346.01753600000001,1255.9403360785441,300,1081.3047999999999,3924.8135502454502,937.5,137.81440000000001,-100.25753600000002,245.76,736,768,0.32]
[0.4,356.928,1266.8508000785441,300,892.31999999999994,3167.1270001963603,750,134.96,-52.927999999999997,304,720,760,0.4]
[0.48000000000000004,367.61318399999999,1277.5359840785441,300,765.86079999999993,2661.5333001636332,625,132.1824,-6.6531839999999534,360.96000000000004,704,752,0.48000000000000004,null,{"$f":"IF(D9>0,(E10-E9)/(D9+(D10*-1)),\"\")","v":""}]
[0.56000000000000005,378.07923200000005,1288.0020320785441,300,675.14148571428575,2300.0036287116855,535.71428571428567,129.48159999999999,38.560767999999996,416.64000000000004,688,744,0.56000000000000005,"Berechnung der Cournotschen Menge durch Näherungswerte"]
[0.64,388.33228800000001,1298.2550880785441,300,606.76919999999996,2028.5235751227251,468.75,126.85759999999999,82.707712000000015,471.04,672,736,0.64]
[0.72,398.37849599999998,1308.3012960785441,300,553.30346666666662,1817.0851334424224,416.66666666666669,124.3104,125.78150399999998,524.16,656,728,0.72,"Wählen Sie eine Menge in Zelle N31. Verändern Sie diese mit dem Drehfeld jeweils um 1, bis der Wert in Zelle N33 möglichst nahe am Wert 0,0 ist. Orientierung z.B. an der tabellarisch/graphischen Ermittlung."]
[0.79999999999999993,408.22399999999999,1318.1468000785439,300,510.28000000000003,1647.68350009818,375.00000000000006,121.84,167.77600000000001,576,640,720,0.79999999999999993,null,null,null,"Übliche Berechung mit p/q-Formel (führt zu etwas unübersichtlichen Zelladressierungen) J"]
[0.87999999999999989,417.87494399999997,1327.7977440785439,300,474.85789090909094,1508.8610728165274,340.90909090909093,119.44640000000001,208.68505599999997,626.55999999999995,624,712,0.87999999999999989]
[0.95999999999999985,427.33747199999999,1337.2602720785439,300,445.14320000000004,1392.9794500818168,312.50000000000006,117.12960000000001,248.50252799999993,675.83999999999992,608,704,0.95999999999999985]
[1.0399999999999998,436.61772799999994,1346.540528078544,300,419.82473846153846,1294.7505077678309,288.46153846153851,114.8896,287.22227199999998,723.83999999999992,592,696,1.0399999999999998]
[1.1199999999999999,445.721856,1355.6446560785439,300,397.96594285714292,1210.3970143558429,267.85714285714289,112.7264,324.83814399999994,770.56,576,688,1.1199999999999999]
[1.2,454.65600000000001,1364.578800078544,300,378.88,1137.1490000654533,250,110.64,361.34399999999999,816,560,680,1.2,null,null,null,"p/2",{"$f":"($D$10+($D$9*-1))/$C$9/2","v":-13.333333333333334}]
[1.28,463.42630400000002,1373.3491040785441,300,362.05180000000001,1072.9289875613626,234.375,108.63039999999999,396.73369599999995,860.16,544,672,1.28,4,null,{"$f":"(($D$10*$N$31)+($D$9*-1*$N$31)+$E$10-$E$9)/$C$9","v":1.6666666666666667},"x1",{"$f":"$R$30+SQRT((($D$10+($D$9*-1))/$C$9/2)*(($D$10+($D$9*-1))/$C$9/2)+(($E$10-$E$9)/$C$9))","v":3.5814859418203664},{"$f":"IF(R31>R32,\"d\",\"nd\")","v":"d"}]
[1.36,472.03891200000004,1381.961712078544,300,347.08743529411765,1016.1483177048117,220.58823529411762,106.69759999999999,431.00108799999992,903.04,528,664,1.36,null,null,{"$f":"SQRT($P$31)","v":1.2909944487358056},"x2",{"$f":"$R$30-SQRT((($D$10+($D$9*-1))/$C$9/2)*(($D$10+($D$9*-1))/$C$9/2)+(($E$10-$E$9)/$C$9))","v":-30.248152608487032},{"$f":"IF(R32<R31,\"nd\",\"d\")","v":"nd"}]
[1.4400000000000002,480.49996800000002,1390.4227680785441,300,333.6805333333333,965.57136672121112,208.33333333333331,104.8416,464.14003200000019,944.64000000000021,511.99999999999994,656,1.4400000000000002,{"$f":"1-P33","v":0.67725138781604866},null,{"$f":"$P$32/$N$31","v":0.3227486121839514},"Xc",{"$f":"IF(S31=\"d\",R31,R32)","v":3.5814859418203664}]
[1.5200000000000002,488.81561599999998,1398.7384160785441,300,321.5892210526315,920.22264215693679,197.36842105263156,103.0624,496.14438400000017,984.96000000000015,495.99999999999994,648,1.5200000000000002]
[1.6000000000000003,496.99200000000008,1406.914800078544,300,310.62,879.32175004908981,187.49999999999997,101.35999999999999,527.00799999999992,1024,479.99999999999994,640,1.6000000000000003]
[1.6800000000000004,505.03526400000004,1414.9580640785441,300,300.61622857142851,842.23694290389517,178.57142857142853,99.734399999999994,556.72473600000012,1061.7600000000002,463.99999999999994,632,1.6800000000000004]
[1.7600000000000005,512.95155199999999,1422.874352078544,300,291.44974545454539,808.45133640826339,170.45454545454541,98.185599999999994,585.28844800000024,1098.2400000000002,447.99999999999989,624,1.7600000000000005]
[1.8400000000000005,520.74700800000005,1430.6698080785441,300,283.01467826086952,777.53793917312157,163.04347826086951,96.713599999999985,612.69299200000023,1133.4400000000003,431.99999999999989,616,1.8400000000000005]
[1.9200000000000006,528.42777600000011,1438.3505760785442,300,275.22279999999995,749.1409250409082,156.24999999999994,95.318399999999983,638.93222400000002,1167.3600000000001,415.99999999999989,608,1.9200000000000006]
[2.0000000000000004,536,1445.922800078544,300,267.99999999999994,722.96140003927189,149.99999999999997,94,664.00000000000023,1200.0000000000002,399.99999999999989,600,2.0000000000000004]
[2.0800000000000005,543.46982400000002,1453.392624078544,300,261.28356923076916,698.74645388391525,144.2307692307692,92.758399999999995,687.89017600000011,1231.3600000000001,383.99999999999989,592,2.0800000000000005]
[2.1600000000000006,550.84339200000011,1460.766192078544,300,255.02008888888886,676.28064448080727,138.88888888888886,91.593599999999995,710.59660800000017,1261.4400000000003,367.99999999999989,584,2.1600000000000006]
[2.2400000000000007,558.12684800000011,1468.0496480785441,300,249.16377142857141,655.37930717792131,133.92857142857139,90.505599999999987,732.11315200000013,1290.2400000000002,351.99999999999989,576,2.2400000000000007]
[2.3200000000000007,565.32633600000008,1475.2491360785441,300,243.67514482758617,635.88324830971703,129.31034482758616,89.494399999999985,752.43366400000014,1317.7600000000002,335.99999999999983,567.99999999999989,2.3200000000000007]
[2.4000000000000008,572.44800000000009,1482.3708000785441,300,238.51999999999995,617.65450003272656,124.99999999999996,88.56,771.55200000000013,1344.0000000000002,319.99999999999983,559.99999999999989,2.4000000000000008]
[2.4800000000000009,579.49798400000009,1489.4207840785441,300,233.66854193548383,600.57289680586439,120.96774193548383,87.702399999999997,789.46201600000018,1368.9600000000003,303.99999999999983,551.99999999999989,2.4800000000000009]
[2.5600000000000009,586.48243200000002,1496.405232078544,300,229.09469999999993,584.53329378068099,117.18749999999996,86.921599999999998,{"$f":"J47-B47","v":806.15756800000031},1392.6400000000003,287.99999999999977,543.99999999999989,2.5600000000000009]
[2.640000000000001,593.40748800000006,1503.3302880785441,300,{"$f":"B48/A48","v":224.77556363636359},{"$f":"C48/A48","v":569.44329093884221},113.6363636363636,86.21759999999999,821.63251200000036,1415.0400000000004,271.99999999999977,535.99999999999989,2.640000000000001]
[2.7200000000000011,600.27929600000016,1510.2020960785442,300,220.6909176470588,555.22135885240573,110.29411764705878,85.590399999999988,835.88070400000015,1436.1600000000003,255.99999999999977,527.99999999999989,{"$f":"M48+$M$16","v":2.7200000000000011}]
[2.8000000000000012,607.10400000000004,1517.0268000785441,300,216.82285714285706,541.79528574233689,107.1428571428571,85.039999999999992,848.89600000000041,1456.0000000000005,239.99999999999977,519.99999999999989,2.8000000000000012]
[2.8800000000000012,613.88774400000011,1523.8105440785441,300,213.15546666666663,529.10088336060539,104.16666666666663,84.566399999999987,860.67225600000029,1474.5600000000004,223.99999999999977,511.99999999999989,2.8800000000000012]
[2.9600000000000013,620.63667200000009,1530.5594720785441,300,209.67455135135128,517.08090272923766,101.35135135135131,84.169600000000003,871.20332800000006,1491.8400000000001,207.99999999999977,503.99999999999989,2.9600000000000013]
[3.0400000000000014,627.35692800000015,1537.2797280785442,300,206.36741052631575,505.68412107846825,98.684210526315752,83.849600000000009,880.48307199999999,1507.8400000000001,191.99999999999977,495.99999999999989,3.0400000000000014]
[3.1200000000000014,634.05465600000014,1543.977456078544,300,203.22264615384611,494.86456925594337,96.153846153846104,83.606400000000008,888.50534400000026,1522.5600000000004,175.99999999999966,487.99999999999983,3.1200000000000014]
[3.2000000000000015,640.7360000000001,1550.6588000785441,300,200.22999999999993,484.58087502454481,93.749999999999957,83.44,895.26400000000035,1536.0000000000005,159.99999999999966,479.99999999999983,3.2000000000000015]
[3.2800000000000016,647.40710400000012,1557.3299040785441,300,197.38021463414628,474.79570246297055,91.463414634146304,83.350399999999993,900.75289600000019,1548.1600000000003,143.99999999999966,471.99999999999983,3.2800000000000016]
[3.3600000000000017,654.07411200000013,1563.996912078544,300,194.66491428571422,465.47527145194738,89.285714285714235,83.337600000000009,904.96588800000006,1559.0400000000002,127.99999999999966,463.99999999999983,3.3600000000000017]
[3.4400000000000017,660.7431680000002,1570.6659680785442,300,192.07650232558134,456.5889442088789,87.209302325581348,83.401599999999988,907.89683200000013,1568.6400000000003,111.99999999999966,455.99999999999983,3.4400000000000017]
[3.5200000000000018,667.42041600000016,1577.3432160785442,300,189.60807272727268,448.10886820413162,85.227272727272677,83.542400000000001,909.5395840000001,1576.9600000000003,95.999999999999659,447.99999999999983,3.5200000000000018]
[3.6000000000000019,674.11200000000008,1584.0348000785441,300,187.25333333333325,440.00966668848423,83.333333333333286,83.759999999999991,909.88799999999992,1584,79.999999999999659,439.99999999999983,3.6000000000000019]
[3.6800000000000019,680.82406400000013,1590.7468640785441,300,185.00653913043473,432.2681695865607,81.521739130434739,84.054400000000015,908.93593599999963,1589.7599999999998,63.999999999999659,431.99999999999983,3.6800000000000019]
[3.760000000000002,687.56275200000027,1597.4855520785443,300,182.86243404255316,424.86317874429346,79.787234042553152,84.425600000000003,906.67724799999996,1594.2400000000002,47.999999999999545,423.99999999999977,3.760000000000002]
[3.8400000000000021,694.33420800000022,1604.2570080785442,300,180.81619999999995,417.77526252045402,78.124999999999957,84.87360000000001,903.10579200000006,1597.4400000000003,31.999999999999545,415.99999999999977,3.8400000000000021]
[3.9200000000000021,701.14457600000014,1611.0673760785442,300,178.86341224489789,410.98657553024066,76.530612244897924,85.398400000000009,898.21542399999998,1599.3600000000001,15.999999999999545,407.99999999999977,3.9200000000000021]
[4.0000000000000018,708.00000000000011,1617.9228000785442,300,176.99999999999994,404.48070001963589,74.999999999999972,86.000000000000028,891.99999999999989,1600,0,399.99999999999983,4.0000000000000018]
[4.0800000000000018,714.90662400000019,1624.8294240785442,300,175.22221176470586,398.24250590160381,73.529411764705856,86.678400000000011,884.45337599999971,1599.36,-16.000000000000341,391.99999999999983,4.0800000000000018]
[4.1600000000000019,721.87059200000022,1631.7933920785442,300,173.52658461538459,392.25802694195755,72.115384615384585,87.433600000000013,875.56940799999961,1597.4399999999998,-32.000000000000341,383.99999999999983,4.1600000000000019]
[4.240000000000002,728.89804800000024,1638.8208480785443,300,171.90991698113206,386.51435096192063,70.754716981132049,88.26560000000002,865.34195199999999,1594.2400000000002,-48.000000000000455,375.99999999999977,4.240000000000002]
[4.3200000000000021,735.99513600000023,1645.9179360785442,300,170.3692444444444,380.99952224040356,69.444444444444414,89.174400000000048,853.76486399999953,1589.7599999999998,-64.000000000000455,367.99999999999977,4.3200000000000021]
[4.4000000000000021,743.16800000000023,1653.0908000785444,300,168.90181818181816,375.70245456330537,68.181818181818144,90.160000000000025,840.83199999999977,1584,-80.000000000000455,359.99999999999977,4.4000000000000021]
[4.4800000000000022,750.42278400000021,1660.3455840785441,300,167.50508571428568,370.61285358896055,66.96428571428568,91.222400000000022,826.5372159999996,1576.9599999999998,-96.000000000000455,351.99999999999977,4.4800000000000022]
[4.5600000000000023,757.76563200000021,1667.6884320785443,300,166.1766736842105,365.72114738564551,65.789473684210492,92.361600000000024,810.87436799999966,1568.6399999999999,-112.00000000000045,343.99999999999977,4.5600000000000023]
[4.6400000000000023,765.20268800000019,1675.1254880785441,300,164.91437241379307,361.01842415485845,64.655172413793068,93.577600000000075,793.83731199999932,1559.0399999999995,-128.00000000000045,335.99999999999977,4.6400000000000023]
[4.7200000000000024,772.74009600000022,1682.6628960785442,300,163.71612203389827,356.49637628782699,63.559322033898276,94.870400000000046,775.41990399999918,1548.1599999999994,-144.00000000000045,327.99999999999977,4.7200000000000024]
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[4.8800000000000026,788.1405440000002,1698.0633440785441,300,161.50420983606554,347.96380001609492,61.475409836065545,97.686400000000049,734.41945599999929,1522.5599999999995,-176.00000000000045,311.99999999999977,4.8800000000000026]
[4.9600000000000026,796.01587200000017,1705.9386720785442,300,160.48707096774189,343.93924840293209,60.4838709677419,99.20960000000008,711.82412799999952,1507.8399999999997,-192.00000000000057,303.99999999999972,4.9600000000000026]
[5.0400000000000027,804.01612800000032,1713.9389280785444,300,159.52700952380951,340.06724763463166,59.52380952380949,100.80960000000005,687.82387199999937,1491.8399999999997,-208.00000000000057,295.99999999999972,5.0400000000000027]
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