Question

Consider the market for mountain bikes. The following graph shows the demand and supply for mountain bikes before the government imposes any taxes. First, use the black point (plus symbol) to indicate the equilibrium price and quantity of mountain bikes in the absence of a tax. Then use the green point (triangle symbol) to shade the area representing total consumer surplus (CS) at the equilibrium price. Next, use the purple point (diamond symbol) to shade the area representing total producer surplus (PS) at the equilibrium price.

Suppose the government imposes an excise tax on mountain bikes. The black line on the following graph shows the tax wedge created by a tax of $60 per bike.

First, use the tan quadrilateral (dash symbols) to shade the area representing tax revenue. Next, use the green point (triangle symbol) to shade the area representing total consumer surplus after the tax. Then, use the purple point (diamond symbol) to shade the area representing total producer surplus after the tax. Finally, use the black point (plus symbol) to shade the area representing deadweight loss.

Complete the following table by using the previous graphs to determine the values of consumer and producer surplus before the tax, and consumer surplus, producer surplus, tax revenue, and deadweight loss after the tax.

Answer 1

(1) Since I can't access your graph tool, I've labelled the areas you need to shade in.

Consumer surplus (CS) = Area between demand curve & equilibrium price = Area AEP0

Producer surplus (PS) = Area between supply curve & equilibrium price = Area BEP0

(2) After the tax,

Price paid by buyers = P1

Price received by sellers = P2

CS = Area ACP1

PS = Area BDP2

Tax revenue = Area P1CDP2

Deadweight loss = Area CDE

(3)

CS before tax = (1/2) x $(120 - 90) x 280 = 140 x $30 = $4,200

CS after tax = (1/2) x $(120 - 105) x 140 = 70 x $15 = $1,050

PA before tax = (1/2) x $(90 - 0) x 280 = 140 x $90 = $12,600

PS after tax = (1/2) x $(45 - 0) x 140 = 70 x $45 = $3,150

Tax revenue = $60 x 140 = $8,400

Deadweight loss = (1/2) x $60 x (280 - 140) = $30 x 140 = $4,200