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# System prepended metadata

title: 個經Hw3

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# 個經Hw3
## Problem 2 (2.7)

![](https://i.imgur.com/OK2LDhL.png)

$q_1=4\frac{p_2^2}{p_1^2}$

## Problem 4 (3.11)
由$MRS=MRT\ 可以得到\ \frac{U_1}{U_2}=\frac{\frac{0.5}{q_1}}{\frac{0.5}{q_2}}=\frac{q_2}{q_1}=\frac{p_1}{p_2}\Longrightarrow p_1q_1=p_2q_2$，接著求解$E(p_1,p_2,\bar U)$，可以先得到$q_1=e^{2\bar U-ln\ q_2}=\frac{e^{2\bar U}}{q_2}$ 
代回$E=p_1q_1+p_2q_2$可以得到$E=2\sqrt{p_1p_2e^{2\bar U}}$，對$p_1$微分後得到補償函數$H(p_1,p_2,\bar U)=q_1=\sqrt{\frac{p_2e^{2\bar U}}{p_1}}$

## Problem 5 (4.2)

![](https://i.imgur.com/mNvwQd8.png)

## Problem 6 (4.8)
![](https://i.imgur.com/I5QVRSB.jpg)
$L=tq_1^*$
So optimal utility of lump-sum tax >= specific tax
(Draw graph)

## Problem 7 Ch4 5.1

![](https://i.imgur.com/UlLNvgO.png)

## Problem 8 Ch4 5.3

bundle 1 is better 
Because bundle 2 is under buget constraint of bundle 1




