Solutions to Problems
Chapter 8
1a. The gain to domestic producers is the increase in producer surplus of $25,000 per year The area abgh in figure 1.
The increase in producer surplus = 0.50 x 40,000 + ½ x 0.50 x 20,000
= $25,000 per year
1b. The government collects $10,000a year in tax revenue from T-shirt imports. The area bcef in figure 1.
Tax revenue = (80,000 - 60,000) x 0.50
= $10,000 per year
1c. The loss of consumer surplus is $45,000 per year. The area acdh in figure 1.
The loss of consumer surplus = 80,000 x 0.50 + ½ x 20,000 x .50
= $45,000 per year.
1d. The DWL is $10,000 per year. The area bfg + area cde in figure 1.
DWL = ½ x 20,000 x .50 + ½ x 20,000 x .50
= $10,000 per year
With $1 DWL per tax dollar raised the tariff on T-shirts has a considerable impact on the allocation of resources and would not be considered an efficient way of raising revenue for the government. Most Australian tariffs however were imposed to protect Australian industry and not as revenue raising instruments.
3a. To maintain the same level of imports as occurred with the tariff the import quota will need to be set at 20,000 per year. The Australian supply curve for T-shirts SA moves to the right by 20,000 to SA/ (see figure 4).
3b. Domestic prices will rise to $5.50 and domestic production will be 60,000 per year.
3c. Domestic producers have increased their sales by 20,000 and receive an extra 50c per unit.
Consumers lose area acdh of consumer surplus.
= (80,000 x $0.50) + ½(20,000 x $0.50)
= $45000 per year
Domestic producers gain area abgh in producer surplus
= (40,000 x $0.50) + ½(20,000 x $0.50)
= $25,000 per year
3d. The total value of the import quota is 20,000 x .50 = $10,000 per year. This is the area bcef in figure 3 which was the tariff revenue in question 1. The government can still capture this ‘value of the import quota’ by selling the right to import a quota (an import licence) at auction.
3e Of the surplus lost by consumers, area acdh, abgh is gained by domestic producers, bcef is gained by the government if the licensing system is used, but areas bfg and cde are DWL. Of the $45,000 in consumer surplus lost each year due to the quota $25,000 goes to domestic producer surplus, $10,000 to the government for import licences and $10,000 is deadweight loss.
DWL = ½(60,000 - 40,000) (.50) + ½(100,00 - 80,000) (.50)
= $10,000 per year.
5a. With no tax on icecreams, the price is 60 cents an icecream and 4 million a day are consumed. (see figure 4)
5b. The price increases to 70 cents an icecream, and 3 million a day are consumed. (see figure 4)
The tax decreases the supply of icecreams and raises the price. With a 20 cent tax, producers are willing to sell 3 million icecreams a day only if the price is 20 cents higher at 70 cents an icecream.
5c Consumers and producers each pay 10 cents of the tax. The government collects $0.20 x 3m = $600,000 in tax revenue. (see figure 4)