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經濟高手請救救我.....

我知道在這裡問功課不好, 只是我現在走投無路了...拜託哪個強者救救我...

一個人在外國求救無員.......


the dancing machine indusrty is a duopoly. the two firms, chuckie B.Corp. and

Gene gene dancing machines, compete through Cournot quantity setting

compeition. the demand curve for the indusrty is P=300 -Q, where Q is the total

quantity produced by Chuckie B and Gene Gene. Currently, each firm has

marginal cost of $30, and fixed cost of $100.


i. Compute the Cournot equilibrium price, qantity produced by each firm and

profit for each firm

ii. if the firms merged, what would be the resulting monopoly price, qantity, and

profit, (compare and contrast with you answer in a)


iii. in each case, would the equilibrium price or qantity change if the fixed cost

for each firm were 0?

Iv. suppose that Chuckie B. Corp developed a new process that lowers its

marginal cost to 21. Derive the new equilibrium price, qantities and profit.

how much would Chunkie B. pay to acquire this new process?





拜託哪個好心人教教我該怎麼做............
2006-08-21 15:27 發佈
文章關鍵字 經濟高手
妳確定題目沒抄錯?
P=300-Q 和 marginal cost = 30 的情況下我算出來的 equalibium 是 90unit(每一家), 售價 120, 利潤 8000.....
你自己看一下題目... 各生產20單位的話共40unit. P=300-40=260, 售價也不會是60元...
White bear wrote:
妳確定題目沒抄錯?P...(恕刪)


不好意思..我抄錯了! 我改過來了.........

請問你怎麼算出來的?

可否教我一下.........


fixed cost 不用算進去嘛?
1. 首先 P=300-Q, Marginal cost =30, 最大利益: Marginal cost = Marginal revenue
假設 A 公司產量 X, B 公司產量 Y. Q=X+Y
Total revenue (A公司)= P*X = X(300-X-Y) = 300X -X^2 -XY
Marginal revenue 就是把他微分: MR = 300 -2X -Y = MC =30
整理一下: 270 -2X -Y =0
用同樣方法算 B 公司, 的到 270 -X -2Y =0
270-2X-Y=0
270-X-2Y=0
解聯立方程式: X = 90, Y = 90
P = 300 -(90+90) = 120
Profit: 120 * 90 - 30*90 - 100 = 8000

2. 同上, 只是不必分 X 跟 Y, 直接代 Q 來算
P = 300 -Q, R = 300Q - Q^2, MR = 300 - 2Q = MC = 30
2Q = 270. Q = 135
Profit: P = 300-135 = 165. 165 *135 - 30 * 135 -100 = 18125
sorry, 剛剛算錯一個零

3. 不變

Fix cost 只會影響利潤, 不會影響 Marginal cost 或是 Marginal revenue
草莓夾心 wrote:
不好意思..我抄錯了...(恕刪)


fixed cost is never considered in production. Let suppose you built a factory and now want to decide on the level of production. Since the fixed cost of building it is already spent, the only cost that matter is the cost of producting an additional item(marginal cost).

Cournot Case:
let q1, q2 be the quantity produced by firm 1 and firm2, respectively.
c1, c1 be the marginal cost of firm 1&2. c1=c2 = 30
k1, k2 be the profits

P = 300 - Q = 300 - (q1 + q2)
(total output Q is just the total output of the two firms in duopoly models)

profit = total reveuce - total cost = quantity * price - quantity * cost
k1 = q1 * P - q1 * c1 = q1 * (300 - (q1 + q2)) - q1 * c1
= 300q1 - q1 ^2 + q1q2 - q1c1
k2 = q2 * P - q2 * c2 = = 300q2 - q2 ^2 + q1q2 - q2c2

using partial differentiation to find the optmial level of production for each firm to maximize profit for each firm
Please note that in Cournot model it's assumed that the firms are deciding the quantities being produced(as opposed to Bertrand where price being determined by firms) and firm 1 can only control output of itself.

∂k1/∂q1 = 300 - 2q1 + q2 - c1
∂k2/∂q2 = 300 - 2q2 + q1 - c1

let ∂k1/∂q1 = 0 and ∂k2/∂q2 = 0 to find the maximize level of output
∂k1/∂q1 = 0 => q2 = 300 - 2q1 - c1
∂k2/∂q2 = 0 => q1 = 300 - 2q2 - c2
these two equations are called the reaction function.
Since c1 = c2 = 30, solving the two equations together gives
q1 = 90 and q2 = 90
P = 300 - (q1 + q2) = 300 - 180 = 120
k1 = 90 * 120 - 90 * 30 = 90 * 90 = 8100
k2 = 90 * 120 - 90 * 30 = 90 * 90 = 8100


White bear wrote:
1. 首先 P=30...(恕刪)



在這邊感謝你了, 我用google 找了一天, 還是一點頭緒都沒有.......

謝謝你的幫忙...........
草莓夾心 wrote:
我知道在這裡問功課不...(恕刪)


這應該是microeconomic的題目.
你現在要學好喔.
不然到後面
你final會寫不出來.

奇怪了.....上面兩位大大! 你們算出來的答案是不是不一樣還是只是我個人眼花了?......




如果是firm X and Y, each has constant marginal cost of $20. demand fuction are

Qx=100-2Px+1 Py
Qy=100-2Py+1Px

calculate Bertrand Equilibrum price in this market......

請問算法是不是跟算Cournot 一樣.......??


哇~~~好久前的問題!!!!

這是大二的把?? 硬背他把...final都應該差不多...現在改去讀finance, 但還是不知讀到現在和我工作一點幫忙都沒有><
paradox1019 wrote:
fixed cost...(恕刪)



他少add 了fixed cost $100...


White bear大大..算對了..........



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