Re: [其他] 考試 (研究所) 又到了, 唉!
假設 A 彩券有一半一半的機率拿到 (0,W-L)的報酬
B 彩券有一半一半的機率拿到 (W, -L)的報酬
W 和 L 都是正數
那一個人的 utility function 滿足 u''<0
iff 他喜歡 A 勝過 B,對所有的 W 和 L
假設 A 彩券有一半一半的機率拿到 (0,W+e)的報酬
B 彩券有一半一半的機率拿到 (e,W )的報酬
W 是正數,e 是期望值 0 的隨機變數
那一個人的 utility function 滿足 u'''>0
iff 他喜歡 A 勝過 B,對所有的 W 和 e
假設 A 彩券有一半一半的機率拿到 (e1, e2)的報酬
B 彩券有一半一半的機率拿到 (0,e1+e2)的報酬
e1 和 e2 是獨立的期望值 0 的隨機變數
那一個人的 utility function 滿足 u''''<0
iff 他喜歡 A 勝過 B,對所有的 e1 和 e2
以上這樣算是用很少數學在解釋何謂 u''<0 u'''>0 u''''<0
2006 年 AER 的文章,參考一下吧
就算要走實驗經濟學或行為經濟學或神經經濟學
還是要用到數學啊,現在經濟學裡面有什麼學門不用數學的嗎?
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