Question

The demand and supply for a product is given by:

Qd: 300-5P Qs: 3P-100

Suppose the government imposes a tax T=$16

Calculate:

A) Consumer surplus after tax

B) Producer surplus after the tax

C) Government Revenue

D) Deadweight Loss

Answer 1

Demand Equation

Q = 300 -5P

Supply Equation

Q = 3P - 100

Equilibrium Price and Quantity before tax

3P - 100 = 300 -5P

P = 50 and Q = 50

To find equilibrium price and quantity after tax first we need to see demand and supply function in terms of price

Demand Equation

Q = 300 -5P

P = 300 - Q / 5

Supply Equation

Q = 3P - 100

P = 100 + Q / 3

If the government imposes the tax of $16 then the new supply equation will change

Supply Equation

P = 100 + Q / 3 + 16

Now we will equate the demand equation with this new supply equation.

300 - Q / 5 = 100 + Q / 3 + 16

300 - Q / 5 = 148 + Q / 3

Q = 20

As Q = 20 so P = 56

Equilibrium Price after Tax = $56

Equilibrium Quantity after Tax = 20

The above graph shows situation after tax so

Red Area = Consumer Surplus

Yellow Area = Tax Revenue

Brown Area = Producer Surplus

Blue Area = Deadweight Loss

Consumer Surplus

Area = 1/2 x base x height

Area = 1/2 x 20 x 4

Area = 40

Producer Surplus

Area = 1/2 x base x height

Area = 1/2 x 6.66 x 40

Area = 66.66

Tax Revenue

Area = Length x Breadth

Area = 20 x 16

Area = 320

Deadweight Loss

Area = 1/2 x base x height

Area = 1/2 x 16 x 30

Area = 240