作者Zentigra (Regular Sloanie)
看板Economics
標題[作業] 請益對數有關的問題
時間Fri Jul 5 10:56:55 2013
Suppose the monthly demand for coffee is estimated as
ln(Q) = 7.5 - .1 ln(P) + .3 ln(I)
where Q is the quantity, P is the price, I is community income, and ln
denotes the natural logarithm. If price rises by 20 percent and income rises
by 10 percent, the quantity of coffee demanded will fall.
a. The above statement is true.
b. The above statement is false.
c. The above statement may be true or false.
原先第一次寫的時候沒有注意到logarithm這個字所以帶了兩組數字進去得到答案c XD
但是答案是B (表示Q應該要上升才對?) 請問這種含有ln的式子該怎麼看或者快速判讀?
感謝
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1F：→ larry1990:所得彈性0.3~看係數 07/05 12:59
2F：→ larry1990:彈性公式再看熟一點~ 07/05 13:00
3F：推 ChrisOvO:dlnQ=dQ/Q，也就是代表"變動量" 07/06 22:43
4F：→ ChrisOvO:若將題目的式子全微分，會得到:dln(Q)=-0.1dln(P)+0.3dln 07/06 22:45
5F：→ ChrisOvO:dln(Q)=-0.1dln(P)+0.3dln(I) 07/06 22:46
6F：→ ChrisOvO:再根據題意:P變動了0.2，I變動了0.1 07/06 22:47
7F：→ ChrisOvO:代入上式得dln(Q)=-0.1*0.2+0.3*0.1 07/06 22:48
8F：→ ChrisOvO:dln(Q)=0.01>0，代表Q的變動為正 07/06 22:49
9F：→ ChrisOvO:也就是Q會上升 07/06 22:50
10F：→ ChrisOvO:只要記得dlnX代表X的變動量 07/06 22:51
11F：→ Zentigra:感謝 07/07 07:50