Question

Exercise 5 In a competitive market the demand function is QD= 100 - P and the supply function is QS= P-20. In consequence of a new government decision there is a per unit tax on the good. How large is the tax if the consumer surplus decreased by 75 percent in consequence of the government decision? 1 D nerated i

Answer 1

In pre-tax equilibrium, Demand = Supply.

100 - P = P - 20

2P = 120

P = 60

Q = 100 - 60 = 40

From demand function, when QD = 0, P = 100

Consumer surplus (CS) = (1/2) x (100 - 60) x 40 = 20 x 40 = 800

When the tax lowers CS by 75%,

New CS = 800 x (100 - 75)% = 800 x 25% = 200

If required unit tax T, the after-tax supply function is:

QS1 = P - T - 20

Equating QD and QS1,

100 - P = P - T - 20

2P = 120 + T

P = 60 + 0.5T

Q = 100 - 60 - 0.5T = 40 - 0.5T

After-tax CS = (1/2) x [100 - (60 + 0.5T)] x (40 - 0.5T) = 200

(40 - 0.5T) (40 - 0.5T) = 400

(40 - 0.5T)² = 400

Taking square root,

40 - 0.5T = 20

0.5T = 20

T = 40