Question

Given the following information:

Demand: Qd = 200 – 5P

Supply: Qs = 5P

If a quantity tax of $2 per unit sold is imposed,

(a)Considering that the government will earn revenue, overall, do you think that the society benefits from the imposition of the tax? Explain.

(b) Calculate the equilibrium market price and the equilibrium quantity sold.

(c) Determine the demand and supply equation after the tax.

(d) What will be the new equilibrium price paid by the buyers and the new price received by the supplier?

(e) Calculate the new equilibrium quantity sold.

(f) Calculate the tax revenue earned by the government.

(g) Calculate the dead weight loss due to the tax.

(h) What determines whether the buyer of the seller bears the burden of the tax?

Answer 1

(a) Considering that the government will earn revenue, overall, the benefits from the imposition of the tax are smaller than the costs imposed in terms of efficiency loss, administration costs and cost of imposing and implementing the tax. Hence society is worse off due to tax

(b) At the equilibrium before the tax we have

Qd = Qs

200 - 5P = 5P

P = 200/10 = $10 per unit

Q = 5*10 = 50 units

This is the equilibrium market price and the equilibrium quantity sold respectively

(c) Demand equation is unchanged at Q = 200 - 5P and supply equation after the tax changes to Q = 5(P - 2) or Q = 5P - 10

(d) At the after tax equilibrium we have

Qd = New Qs

200 - 5P = 5P - 10

10P = 210

P = 21 (paid by sellers)

P = 19 (received by sellers)

Q = 200 - 5*21 = 95 units

The new equilibrium price paid by the buyers is $21 per unit and the new price received by the supplier is $19 per unit

(e) New equilibrium quantity sold is 95 units

(f) Tax revenue earned by the government = tax*quantity = 2*95 = $190

(g) Dead weight loss due to the tax = 0.5*tax*reduction in qty after tax = 0.5*2*5 = $5

(h) Elasticity of demand and supply determines whether the buyer of the seller bears the burden of the tax. The lesser is the elasticity of demand (supply), the greater the burden of tax falls on buyers (sellers).