※ 引述《luckysnow (幸运雪+去冰珍绿)》之铭言： : 我有自己想答案，先附上题目～ : 请板友帮忙 : 感谢 : 题目大意为： : 一岛居民买鱼，设关税，利润为CS＋关税；<--没说从量或从价 : 一独占者供鱼，订价格， : 捕鱼没成本， : 则：1.岛主先订关税，独占者依关税设价格，求均衡 : 2.顺序颠倒过来的Stackelberg均衡 : 完整题目如下： : 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? : ----------------------------------------------------- : 我的写法 : Max profit i = CS＋tariff = 0.5Q^2 + tQ .....island leader （*） : Max profit f = (12-Q)Q-C(Q)-tQ .......foreign follower （**） : （**）一阶微分 12-Q-Q=t Q=(12-t)/2 代入 Max profit i （*） : Max profit i = -3t^2/8 + 3t + 18 （***） : （***）一阶微分 => t = 4 = Q = P : Max profit i = 0.5*4^2 + 4*4 = 24 : Max profit f = (12-4)*4 - 4*4 = 16 : ～～～～～～～～～～～～～～～ : 但是反过来， : 卖鱼厂商先定价， : （*）一阶微分 Q + t = 0 这样好像有点奇怪@@ : 请帮我看一下，可能利润函数就没设对了@@ : 我已经问题目到没人愿意回答我了orz : 感谢 这题算是变形题 因为两边所能决定的是价格(税)而非数量 方程式要化成t跟p的函数 ------------------------------------------------ 当岛主先订价时 Max profit i = CS+tariff revenue =0.5Q^2+tQ =0.5(12-p-t)^2+t(12-p-t) =72-12p+0.5p^2-0.5t^2 Max profit f =p(12-p-t) =12p-p^2-pt 对p做一阶偏微分=0 得厂商reaction function: p=0.5(12-t) 代入i得 72-72+6t+18-3t+0.125t^2-0.5t^2 =18+3t-0.375t^2 对t做一阶微分=0 得 3-0.75t=0 t=4 代入f的reaction function得p=4 p,t代入D(p,t)得Q=4 Stackelberg equilibrium为 p=4,t=4 此时Q=4，profit i=24,CS=8,tariff revenue=16 ----------------------------------------------------------------- 当独占厂商先订价时 i对t做一阶偏微分=0 得岛主reaction function:-t=0 代入f得 12p-p^2 对p做一阶微分=0 得 12-2p=0 p=6 代入i的reaction function得t=0 p,t代入D(p,t)得Q=6 Stackelberg equilibrium为 p=6,t=0 此时Q=6，profit i=36,CS=18,tariff revenue=0 --

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