Question

If tax is 4 units per quantity, new quantity added is 3 units ,what will be the tax revenue,consumer surplus,producer surplus,total surplus

Answer 1

The tax is a subsidy in form of tax reduction because it increases quantity supplied. In this case price paid by consumers decrease as price received by producers increase as shown in the graph below:

P_o=equilibrium price

Q_o=equilibrium quantity

P₁=price Consumers pay after tax

P₂=price producers receive after tax

Q₂=quantity supplied after tax

Therefore

(a) tax revenue=tax per unit × quantity sold

$=4×(Q_0+3)$

$=4Q_0+12$

(b) consumer surplus=area C and D

$\frac{1}{2}×sum \space of \space parallel \space sides× height$

$\frac{1}{2}×[Q_0+(Q_0+3)]×2$

$=2Q_0+3$

(c) producer surplus=area A and B

$\frac{1}{2}×sum \space of \space parallel \space sides× height$

$\frac{1}{2}×[Q_0+(Q_0+3)]×2$

$=2Q_0+3$

(d) Total surplus=Consumer surplus + producer surplus+ tax

$=2Q_0+3 +2Q_0+3+4$

$=4Q_0+10$

For example

If p_o= 20 and Q_o =10

Tax revenue$=4×13=52$

Consumer surplus$=\frac{1}{2}×10×13=65$

Producer surplus$=\frac{1}{2}×10×13=65$

Total surplus$=65+65+4=134$