作者Zentigra (Regular Sloanie)
看板Economics
标题[作业] 请益对数有关的问题
时间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.
原先第一次写的时候没有注意到logarithm这个字所以带了两组数字进去得到答案c XD
但是答案是B (表示Q应该要上升才对?) 请问这种含有ln的式子该怎麽看或者快速判读?
感谢
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1F：→ larry1990:所得弹性0.3~看系数 07/05 12:59
2F：→ larry1990:弹性公式再看熟一点~ 07/05 13:00
3F：推 ChrisOvO:dlnQ=dQ/Q，也就是代表"变动量" 07/06 22:43
4F：→ ChrisOvO:若将题目的式子全微分，会得到: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:再根据题意:P变动了0.2，I变动了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的变动为正 07/06 22:49
9F：→ ChrisOvO:也就是Q会上升 07/06 22:50
10F：→ ChrisOvO:只要记得dlnX代表X的变动量 07/06 22:51
11F：→ Zentigra:感谢 07/07 07:50