Answer to Question #42702 in Microeconomics for JoJo

Question

The ‘Tiny Island’ has a population of 5000 and currently has no tax on beer. However the government is considering a tax of $1.50 per dozen pack of beer. You are asked to conduct an economic analysis of the proposed tax, given the following estimates of demand and supply curves: Q = 2800 - 40P and Q =1600 + 60P, where the Q is quantity in dozen packs per week and P is the price per dozen pack.

(a) Calculate the equilibrium price and quantity in a free market (no tax).
(b) Calculate the demand and supply elasticities at the equilibrium price.
(c) Calculate the buyer’s price, seller’s price and the quantity of beer consumed/sold with the tax.
(d) What proportion of the tax is borne by the sellers? By consumers? Explain your answer in term of elasticities.
(e) Explain why the tax creates a deadweight loss. Explain what determines the size of the deadweight loss.

Answer 1

Population =5000, tax = $1.50 per dozen, Qd = 2800 - 40P, Pd = 70 - Q/40, Qs =1600 + 60P,
Ps = 80/3 - Q/60

(a)Calculate the equilibrium price and quantity in a free market (no tax).
In free market Qs = Qd, so:
2800 - 40P = 1600 + 60P
100P = 1200
Pe = $12
Qe = 1600 + 60*12 = 2320 units.


(b) Calculate the demand and supply elasticities at the equilibrium price.
Ed= P'(Qd) = 1/40 = 0.025, so demand is inelastic.
Es= P'(Qs) = 1/60 = 0.0167, so supply is inelastic too.
(c)Calculate the buyer’s price, seller’s price and the quantity of beer consumed/sold with the tax.

After implementation of the tax the sellers price will be the same, but the buyers will
pay 12+1.5 = 13.5 per dozen.
Quantity sold will be Q = 2320 dozens, but quantity bought will be Q = 2800 - 40*13.5 = 2260 dozens.
(d)What proportion of the tax is borne by the sellers? By consumers? Explain your
answer in term of elasticities.

As demand and supply are inelastic in our case, the main part of tax is borne by
the consumers, because they can't decrease their consumption significantly.

(e)Explain why the tax creates a deadweight loss. Explain what determines the size
of the deadweight loss. In economics, a deadweight loss (also known as excess burden or allocative inefficiency) is a loss of economic efficiency that can occur when equilibrium for a good or service is not Pareto optimal. Except in limiting special cases, a tax imposes a deadweight loss or excess burden on buyers and sellers. The deadweight loss is the amount by which the reduction in buyers' surplus and sellers' surplus exceeds the tax revenue.