Question

Question 6 (1 point) Suppose that in a perfectly competitive market, demand and supply are given by QD = 100 – 6P QS = P - 20 where b=0.5. The government imposes a per-unit tax of $1 on the good. How large is the consumer share of the tax burden? If necessary, round to 2 decimals. Your Answer:

Answer 1

Answer 6

Equilibrium occurs when Quantity demand(Q_D) = Quantity supplied(Q_S).

Here Q_D = 100 - bP = 100 - 0.5P

Q_S = P - 20.

Equilibrium occurs when Q_D = Q_S

=> 100 - 0.5P = P - 20

=> 1.5P = 120

=> P = 80

Hence Initially before tax equilibrium or Market price = 80 and Equilibrium Quantity = Q_S = Q_D = 100 - 0.5*80 = 60.

According to tax incidence,

Share of Burden faced by a consumers = E_s/(E_s + E_d)

where E_s = Absolute value of elasticity of supply and E_s = Absolute value of elasticity of demand

Formula

Elasticity of supply = (dQ_S/dP)(P/Q_S) Here Q_S = P - 20 => dQ_S/dP = 1 and as calculated above P = 80 and Q_S = 60

Thus, Elasticity of supply = 1(80/60) = 4/3

=> E_s = Absolute value of elasticity of supply = 4/3

Elasticity of Demand = (dQ_D/dP)(P/Q_D) Here Q_D = 100 - 0.5P => dQ_D/dP = -0.5 and as calculated above P = 80 and Q_D = 60

Thus, Elasticity of Demand = -0.5(80/60) = -2/3

=> E_d = Absolute value of elasticity of demand = 2/3

Hence Using above Tax incidence formula we have :

Share of Burden faced by a consumers = E_s/(E_s + E_d) = (4/3)/(4/3 + 2/3) = 2/3

Thus, (2/3) of the per unit tax will borne by consumers and here Per unit tax = $1 thus, consumers will bear 2/3 = $0.67 of tax

Hence Consumer Share of this tax burden = 2/3 = 0.67