Question

Suppose the demand for cigarettes is Q = 15 - 0.5Pand the supply of cigarettes is Q = P - 3, where P is the price per pack of cigarettes. Suppose the government imposes a cigarette tax of $3 per pack. 

 

(a) What is the price paid by producers? 

(b) What is the price faced by consumers? 

(c) What is the government revenue from the tax? 

(d) What is the total dollar amount of tax revenue that is ultimately paid by consumers (i.e. consumers' tax burden)? 

(e) What is the excess burden of the tax?

Answer 1

$Qd=15-0.5p\\p=\frac{15-Q}{0.5}=30-2Q\\Qs=p-3\\p=Q+3$

equilibrium is achieved when

$Qd=Qs\\Q+3=30-2Q\\Q=\frac{30-3}{1+2}=9 \space units\\p=9+3=\$12$

tax =$3

therefore after tax $QS=Q+3+3$

equition after tax

$Q+6=30-2Q\\Q^T=\frac{30-6}{1+2}=8\space units$

after tax

a.

price paid by consumers=30-2(8)=$14

b.

price recived by producers=8+3=$11

c.

government revenue after tax

$tax\times Q^t\\=3\times 8=\$24$

d.

consumer tax burden

$=(p^t-p)\times Q^t\\(14-12)\times 9=\$18$

e.

excess burden of the tax

$=\frac{1}{2}\times tax \times (Q-Q^T)\\=\frac{1}{2}\times 3\times (9-8)=\$1.5$