Question

Suppose the demand for camping tents in the town of West Anderson is Qd=1000-8P, and the supply is Qs=12P.

In this example, the equilibrium price and Quantity is P= 50, Q = 600.

Also, here the consumer Surplus is =22500, Producer surplus= 1500. The $10 tax on purchase will in crease the price paid by buyers, therefore

Pc = Ps +$10 where Pc: Price paid by buyers and Ps: Price received by sellers

1. Find the new (after-tax) equilibrium quantity of tents, price paid by consumers, and price received by producers. (3 points)

2. How much consumer surplus is created by this market after the tax? How much producer surplus? (3 points)

3. How much tax revenue is generated for the West Anderson town government? How much deadweight loss does the tax cause? (3 points)

Answer 1

At equilibrium , Demand = Supply

1000 - 8P = 12P

P = 50

Q = 600

Thus consumer surplus before tax is sum of area A+B+C whose sum is (1/2) * (125 - 50 ) * 600 = 22,500

Producer surplus before tax is sum of area D+E+F whose sum is (1/2) * (50 - 0) * 600 = 15,000

A tax of $10 will fall on the ratio of 3:2 on consumer and producer as the elasticity of demand function is -8 and elasticity of supply function is 12. Less elasticity shows more inelastic and more tax tax falls on side which is more inelastic.

When price consumer pays is $56 and price sellers receive is $46. The consumer surplus after tax is A whose sum is (1/2) * (125 - 56) * 552 = 19,044

Producer surplus after tax is area F whose sum is (1/2) * (46 - 0) * 552 = 12,696

Government revenue is sum of area B+D which is (56 - 46) * 552 = 5,520

Deadweight loss is sum of area C+E which is (1/2) * (56 - 46) * 48 = 240