[問題] 請教一題考題

[Allendd (===== =====凸)]

1. A firm in a competitive market has the poduction function

   Y = X1(1/3次方)X2(1/2次方), where Y is the amount of output

   and X1 and X2 are the amount of input.  The price of the output

   is P, and the price of both inputs are 1.  In the short run, the

   amount of X2 is fixed at 1.  To maximize its sort-run profit, the

   firm will employ X1(P) = aP(b次方) units of X1, where a and b are

   constant. What is the value of b ?  (93中興財金)

   註:1.第二行的Y是C-DUF函數,因為次方不知如何打 ><
      2.第六行的X1(P)表示"X1是P之函數"
      3.Ans: b = 2/3

  因為想了很久,也翻了不少次書,但是總是掌握不到解題的關鍵,加上或許自己的

  觀念不清楚所以在數學操作上也有問題(自己覺得應該是答案的"答案"數字超醜)

 ,所以想請各位高手幫忙解惑  謝謝<(_ _)>

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首次發問,如有不當之處請大家告知 謝謝

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推 dreambreaken:profit=PY-Px1*X1-Px2*X2，對x1微分可得
→ Allendd:了解了~~感恩感恩~~