Anonymous
Anonymous asked in 科學數學 · 5 years ago

獨佔市場經濟學問題求解答!!!!!不懂如何計算

based on market research, a film production company in Ectenia obtains the

following information about the demand and production cost of its new DVD

P=1000-10Q

TR=1000Q-10Q(Q二次方)

MR=1000-20Q

MC=100+10Q

suppose, in addition to the cost above, the director of the film has to be paid.

the company is considering four options

a. A flat fee of 2000 Ectenian dollars

b. 50 percent of the profiles

c. 150 Ectenian dollars per unit sold

d. 50 percent of the revenue

for each option, calculate the profit maximizing price and quantity.

which, if any of these compensation schemes would alter the deadweight loss

from monopoly ?

C小題...為什麼新的MC=100+160Q???

其他題該怎麼計算???

1 Answer

Rating
  • 慈信
    Lv 4
    5 years ago
    Favorite Answer

    P = 1000 - 10Q

    TR = 1000Q - 10Q²

    MR = 1000 - 20Q

    MC = 100 + 10Q

    TC = 100Q + 5Q² + C

    原均衡

     MR = MC

     1000 - 20Q = 100 + 10Q , Q = 30

     P = 1000 - 10Q = 1000 - 10*30 = 700

     (P,Q) = ( 700 , 30 )

    π = TR - TC = 700*30 - (100*30 + 5*30² + C )

     = 7500 - C

    a. A flat fee of 2000 Ectenian dollars (定額費用)

     TC1 = TC + F = 100Q + 5Q² + C + 2000

     MC1 = 100+ 10Q = MC

     MR = MC1 = MC

     所以 (P1,Q1) = (P , Q) = (700,30)

     π1 = TR - ( TC + 2000 )

       = 700*30 - (100*30 + 5*30² + C + 2000 )

       = 5500 - C

     消費者剩餘沒有影響 , 但獨占廠商超額利潤減少

    b. 50 percent of the profiles

     πT = π/2 = ( TR - TC ) / 2

     dπT/dQ = 1/2 * dπ/dQ = (MR-MC)/2 = 0

     MR=MC

     所以 (P2,Q2) = (P , Q) = (700,30)

     πT= π/2 = (7500 - C)/2 = 3750 - C/2

    c. 150 Ectenian dollars per unit sold ( 從量費用)

     每單位產量 , 支付 t 元從量費用

     TC3 = TC + tQ = 100Q + 5Q² + C + tQ

     MC3 = 100 + 10Q + t = 100 + 10Q + 150 = 160 + 10Q

     MR = MC3

     1000 - 20Q3 = 160 + 10Q3 , Q3 = 28

     P3 = 1000 - 10Q3 = 1000 - 10*28 = 720

     所以 (P3,Q3) = ( 720 , 28 )

     π3 = TR - TC3 = P*Q - ( 100Q + 5Q² + C + tQ )

       = 720*28 - ( 100*28 + 5*28² + C + 150*28 )

       = 9240 - C

    d. 50 percent of the revenue

     π4 = TR/2 - TC

     dπ4/dQ = MR/2 - MC = 0

     MR/2 = MC

     (1000 - 20Q4)/2 = 100 + 10Q4 , Q4=20

     P4 = 1000 - 10Q4 = 1000 - 10*20 = 800

     所以 (P4,Q4) = ( 800 , 20 )

     π4 = TR/2 - TC = 800*20/2 - (100*20 + 5*20² + C )

       = 4000 - C

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