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# System prepended metadata

title: ECON HW5

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# ECON HW5
#### 3.
a. The price paid by buyers is the same as the price sellers received.
![](https://i.imgur.com/QY0zQeW.jpg =60%x)
b. The difference between price buyers pay and price sellers receive is the tax imposed and the quantity beer sold is decreased.

$P_{buyers}-P_{sellers}=tax=2dollars$

$Q_{beer}' \lt Q_{beer}$

![](https://i.imgur.com/UcTa3Lu.jpg =60%x)

#### 6.
By definition:

$e_D=\frac{\Delta Q_D}{\Delta P_D}\frac{P}{Q}$ and $e_S=\frac{\Delta Q_S}{\Delta P_S}\frac{P}{Q}$,

by rearranging we get

$\frac{\Delta P_D}{\Delta Q_D}=\frac{P}{e_DQ}$ and $\frac{\Delta P_S}{\Delta Q_S}=\frac{P}{e_SQ}$

When a good is taxed, the price buyers pay is not equal to the price sellers receive, but the quantity supplied is equal to the quantity demanded.
That is to say:

$\Delta Q_D = \Delta Q_S$ but $\Delta P_D \neq \Delta P_S$

The tax incidence for the buyers is:

$I_{buyers}=\frac{\Delta P_D}{\Delta P_D+\Delta P_S}=\frac{\frac{\Delta P_D}{\Delta Q_D}}{\frac{\Delta P_D}{\Delta Q_D}+\frac{\Delta P_S}{\Delta Q_D}}=\frac{\frac{\Delta P_D}{\Delta Q_D}}{\frac{\Delta P_D}{\Delta Q_D}+\frac{\Delta P_S}{\Delta Q_S}}=\frac{\frac{P}{e_DQ}}{\frac{P}{e_DQ}+\frac{P}{e_SQ}}=\frac{\frac{1}{e_D}}{\frac{1}{e_D}+\frac{1}{e_S}}=\frac{e_S}{e_D+e_S}$

Therefore, the tax incidence for the sellers is:

$I_{sellers}=1-I_{buyers}=1-\frac{e_S}{e_D+e_S}=\frac{e_D}{e_D+e_S}$