设某消费者效用函数为,消费者的收入为M,x, y两商品的价格为
,求消费者对于x, y两商品的需求。
正确答案:消费者最大化效用:
约束条件为:![](https://img.274949.com/Images/2020-04/05/yubpdtkr.jpg)
拉格朗日函数为:![](https://img.274949.com/Images/2020-04/05/g6vd6cgn.jpg)
(1)对x求偏导得到:![](https://img.274949.com/Images/2020-04/05/239dkb3x.jpg)
(2)对y求偏导得到:![](https://img.274949.com/Images/2020-04/05/aqc7re39.jpg)
(3)对
求偏导得到:
联合(1)(2)(3)得到:![](https://img.274949.com/Images/2020-04/05/ojsnfvnn.jpg)
![](https://img.274949.com/Images/2020-04/05/2idjkwaj.jpg)
约束条件为:
![](https://img.274949.com/Images/2020-04/05/yubpdtkr.jpg)
拉格朗日函数为:
![](https://img.274949.com/Images/2020-04/05/g6vd6cgn.jpg)
(1)对x求偏导得到:
![](https://img.274949.com/Images/2020-04/05/239dkb3x.jpg)
(2)对y求偏导得到:
![](https://img.274949.com/Images/2020-04/05/aqc7re39.jpg)
(3)对
![](https://img.274949.com/Images/2020-04/05/s2799o95.jpg)
![](https://img.274949.com/Images/2020-04/05/psva0uvn.jpg)
![](https://img.274949.com/Images/2020-04/05/ojsnfvnn.jpg)
答案解析:有
![](/editor/images/201705/qrcode_for_gh_573e2a458573_258.jpg)
微信扫一扫手机做题
设某消费者效用函数为,消费者的收入为M,x, y两商品的价格为
,求消费者对于x, y两商品的需求。
微信扫一扫手机做题