# ECON HW5
#### 3.
a. The price paid by buyers is the same as the price sellers received.
b. The difference between price buyers pay and price sellers receive is the tax imposed and the quantity beer sold is decreased.

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

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


#### 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:

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