一題Stackelberg均衡(請幫我看答案) - 經濟

我有自己想答案，先附上題目～
請板友幫忙
感謝

題目大意為：
一島居民買魚，設關稅，利潤為CS＋關稅；<--沒說從量或從價
一獨佔者供魚，訂價格，
捕魚沒成本，
則：1.島主先訂關稅，獨佔者依關稅設價格，求均衡
2.順序顛倒過來的Stackelberg均衡

完整題目如下：
The residents of a certain island enjoy consuming a type of fish.
Unfortunately for these people this fish must be bought from a foreign a
foreign firm which has a monopoly over the fish. The leaders on the island
are considering placing a tariff on imports of the fish. Demand on the island
has been determined to be Q=D(p,t)=12-p-t, where p is the price set by the
foreign monopolist and t is the tariff. Model the situation as a same in
which the island leader move first and select a tariff and then given the
choice of the tariff the foreign monopoly selects its price. Assume the costs
of catching and shipping the fish are zero so that the firm sets price to
maximize total revenue. Assume that the island leaders select the tariff to
maximize total island surplus equal to consumer surplus plus tariff revenue.
What is the Stackelberg equilibrium outcome of this game? What is the
Stackelberg equilibrium if the order of moves is reversed?

-----------------------------------------------------
我的寫法

Max profit i = CS＋tariff = 0.5Q^2 + tQ .....island leader （*）

Max profit f = (12-Q)Q-C(Q)-tQ .......foreign follower （**）

（**）一階微分 12-Q-Q=t Q=(12-t)/2 代入 Max profit i （*）


Max profit i = -3t^2/8 + 3t + 18 （***）

（***）一階微分 => t = 4 = Q = P

Max profit i = 0.5*4^2 + 4*4 = 24

Max profit f = (12-4)*4 - 4*4 = 16

～～～～～～～～～～～～～～～
但是反過來，
賣魚廠商先定價，
（*）一階微分 Q + t = 0 這樣好像有點奇怪@@


請幫我看一下，可能利潤函數就沒設對了@@

我已經問題目到沒人願意回答我了orz

感謝

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法鼓八式 繪圖者 :　bryanwang86

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※ 編輯: luckysnow 來自: 140.112.86.133 (08/20 14:39)
※ 編輯: luckysnow 來自: 140.112.86.133 (08/20 14:45)