Question

Suppose that the demand curve is Qd = 120 - 6p and the supply curve is Qs = 18p. Calculate the effects of a specific tax of t=2 per unit on the equilibrium, government tax revenue,consumer surplus, producer surplus,welfare and deadweight loss?

Answer 1

Original equilibrium:

$Qs=Qd$

$120-6P=18P$

$P=5$

$120-6(5)$

$Q=90$

Finding new equilibrium:

Per tax reduces supplier by $t(P-t)$

Supply curve Qs$=18(P-2)=18P-36$

Qs$=$ Qd

$18P-36=120-6P$

$24P=156$

$P=6.5$

$Qs=Qd=120-6(6.5)$

$Q=81$

Prices that producers receive at new equilibrium $=$ $6.5-2=4.5$

Government tax revenue=Amount traded$×$ taxes

$=81×2=162$

CS and PS is calculated from the area represented on the supply and demand graph

Consumer Surplus.

$\frac {1}{2}\times 81\times 13.5=546.75$

Producer Surplus

$\frac{1}{2}\times 4.5\times 81=182.25$

Welfare and deadweight loss is calculated from the triangle area between the sandwich of original demand and supply curve

$=\frac{1}{2}×(6.5-4.5)×(90-81)=9$