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chuziyang · 2022年05月22日

ΔQod /ΔPt爲何等於-0.16

NO.PZ2017100901000005

问题如下:

An individual’s demand for onions is given by the following equation:

Qod​=3−0.05P0​+0.009I−0.16Pt​

where Qod is the number of onions demanded, P0 is the price per pound of onions, I is the household income, and Pt​ is the price per pound of tomatoes. If the price of onions is $1.25, household income is $2,500, and the price of tomatoes is $3.75, the cross-price elasticity of demand for onions with respect to the price of tomatoes is closest to:

选项:

A.

1.0597.

B.

0.0242.

C.

0.0081

解释:

B is correct.

The cross-price elasticity of demand measures the responsiveness of the demand for onions in response to a change in the price of tomatoes. From the demand function equation:

Qod​=3−0.05P0​+0.009I−0.16Pt​

Qod​=3-0.05( 1.25 ) +0.009( 2,500 )-0.16( 3.75 ) = 24.8375

At a price of onions of $1.25 and a price of tomatoes of $3.75, the cross-price elasticity of demand is calculated as follows: Cross-price elasticity of demand = (ΔQod /ΔPt ) × ( P t / Qod ) Cross-price elasticity of demand = –0.16 × (3.75/24.8375) = –0.0242

考点:交叉价格弹性

解析:

把题目中给定的各项数据带入需求函数公式中,求解需求量。即

Qod​=3−0.05P0​+0.009I−0.16Pt​

Qod​=3-0.05( 1.25 ) +0.009( 2,500 )-0.16( 3.75 ) = 24.8375

接着利用需求交叉弹性公式计算结果,即:( (ΔQod /ΔPt ) × ( P t / Qod ) Cross-price elasticity of demand = –0.16 × (3.75/24.8375) = –0.0242

請問ΔQod /ΔPt爲何等於-0.16?

Qod​=3-0.05( 1.25 ) +0.009( 2,500 )-0.16( 3.75 ) = 24.8375

Qod​不是應該24.8375嗎?


那結果不應該是:ΔQod /ΔPt=24.8375/3.75(土豆價格)=6.623 ??


能説下ΔQod 與ΔPt的具體計算步驟嗎?謝謝

1 个答案

笛子_品职助教 · 2022年05月23日

嗨,努力学习的PZer你好:


請問ΔQod /ΔPt爲何等於-0.16?


角度一:从定义的角度

我们先根据定义:ΔQod /ΔPt表示,PT每变动1,QOD变动多少。


根据表达式Qod​=3−0.05P0​+0.009I−0.16Pt​,

PT每变动1,QOD变动-0.16。


所以ΔQod /ΔPt就是-0.16


角度二,从数学的角度

这道题涉及到导数的知识点。

ΔQod /ΔPt就是对PT求导。

导数公式


运用1和2公式,可以计算出对PT求导的导数 = -0.16

导数的计算和概念并不在CFA课程中,但是CFA默认考试者已经掌握导数这个数学概念。



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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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2021-07-06 09:57 2 · 回答

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2021-03-20 13:38 1 · 回答

我长的是这样弹性是价格变动引起的q变动,不应该是q除以p吗?????

2018-12-16 14:42 1 · 回答