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 deadweight loss due to the tax.

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

Answer 1

(a)

Even though government will earn tax revenue, the tax will increase market price and decrease market quantity. So social benefits will arise only if the tax revenue is higher than the efficiency loss caused by higher price and lower quantity.

(b)

In pre-tax equilibrium, Qd = Qs.

200 - 5P = 5P

10P = 200

P = 20

Q = 5 x 20 = 100

(c)

After-tax supply function is:

Qs = 5(P - 2) = 5P - 10

Demand function remains unchanged:

Qd = 200 - 5P

(d)

Equating with Qd,

200 - 5P = 5P - 10

10P = 210

P = 21 (Price paid by buyers)

Price received by sellers = 21 - 2 = 19

(e)

Q = 200 - (5 x 21) = 200 - 105 = 95

(f)

Tax revenue = Unit tax x After-tax quantity = 2 x 95 = 190

(g)

Deadweight loss = (1/2) x unit tax x Change in quantity = (1/2) x 2 x (100 - 95) = 1 x 5 = 5

(h)

Tax burden is determined by elasticity of demand and supply. If demand is more elastic than supply, sellers bear higher tax burden. If supply is more elastic than demand, buyers bear higher tax burden.