Elementary Microeconomics Chapter 8
The Deadweight Loss of Taxation
The ultimate impact of a tax on a market is the same whether the tax is levied on buyers or sellers.
A tax on buyers shifts the demand curve downward by the size of the tax; a tax on sellers shifts the supply curve upward by that amount.
As a result, how the tax burden is distributed between producers and consumers depends not on how the tax is levied but on the elasticities of supply and demand.
The tax places a wedge between the price buyers pay and the price sellers receive. Because of this wedge, the quantity sold is less than it would be if there were no tax.
In other words, a tax on a good shrinks the size of the market for it.
How a Tax Affects Market Participants
There are three market participants: buyers, sellers, and the government.
T is the size of the tax and Q is the quantity of the good sold, then the government takes in tax revenue of T × Q.
The government’s tax revenue is represented by the rectangle between the supply and demand curves. The height of this rectangle is the size of the tax, T, and its width is the quantity of the good sold, Q.
Because a rectangle’s area is its height multiplied by its width, this rectangle’s area is T × Q, which equals the tax revenue.
Welfare Without a Tax
Without a tax, the equilibrium price and quantity are found at the intersection of the supply and demand curves. The price is P1, and the quantity sold is Q1.
Because the demand curve reflects buyers’ willingness to pay, consumer surplus is the area between the demand curve and the price, A + B + C.
Similarly, because the supply curve reflects sellers’ costs, producer surplus is the area between the supply curve and the price, D + E + F. Because there is no tax, tax revenue is zero.
Welfare with a Tax
The price paid by buyers rises from P1 to PB, so consumer surplus equals only area A (the area below the demand curve and above the buyers’ price, PB).
The price received by sellers falls from P1 to PS, so producer surplus equals only area F (the area above the supply curve and below the sellers’ price, PS).
The quantity sold falls from Q1 to Q2, and the government collects tax revenue equal to the area B + D.
To find total surplus with the tax, add consumer surplus, producer surplus, and tax revenue. Thus, total surplus is area A + B + D + F.
Changes in Welfare
The change in total welfare includes the change in consumer surplus (which is negative), the change in producer surplus (which is also negative), and the change in tax revenue (which is positive).
Total surplus in the market falls by the area C + E when tax is imposed. The losses to buyers and sellers from a tax exceed the revenue raised by the government.
The fall in total surplus that results when a tax (or some other policy) distorts the outcome in an otherwise efficient market is called a deadweight loss.
People respond to incentives and competitive markets typically allocate scarce resources efficiently.
When the government imposes a tax, it raises the price buyers pay and lowers the price sellers receive, giving incentives to buyers to consume less and sellers to produce less.
As a result, the market shrinks below its optimum. Thus, because taxes distort incentives, they cause markets to allocate resources inefficiently.
Practice Questions
A tax on a good has a deadweight loss if
A. the reduction in consumer and producer surplus is greater than the tax revenue.
B. the tax revenue is greater than the reduction in consumer and producer surplus.
C. the reduction in consumer surplus is greater than the reduction in producer surplus.
D. the reduction in producer surplus is greater than the reduction in consumer surplus.
Answer: A. the reduction in consumer and producer surplus is greater than the tax revenue.
Donna runs an inn and charges $300 a night for a room, which equals her cost. Sam, Harry, and Bill are three potential customers willing to pay $500, $325, and $250, respectively. When the government levies a tax on innkeepers of $50 per night of occupancy, Donna raises her price to $350. The deadweight loss of the tax is
A. $25.
B. $50.
C. $100.
D. $150.
Answer: A. $25. (Harry is the only one affected by the tax)
Sophie pays Sky $50 to mow her lawn every week. When the government levies a mowing tax of $10 on Sky, he raises his price to $60. Sophie continues to hire him at the higher price. What is the change in producer surplus, the change in consumer surplus, and the deadweight loss?
A. $0, $0, $10
B. $0, 2$10, $0
C. 1$10, 2$10, $10
D. 1$10, 2$10, $0
Answer: B. $0, 2$10, $0
The Determinants of Deadweight Loss
What determines whether the deadweight loss from a tax is large or small? The answer is to be found in the price elasticities of supply and demand, which measure how much the quantity supplied and quantity demanded respond to changes in the price.
In panel (a), the supply curve is relatively inelastic: The quantity supplied responds only slightly to changes in the price. In panel (b), the supply curve is relatively elastic: The quantity supplied responds substantially to changes in the price.
Notice that the deadweight loss, the area of the triangle between the supply and demand curves, is larger when the supply curve is more elastic.
In panel (c), the demand curve is relatively inelastic, and the deadweight loss is small.
In panel (d), the demand curve is more elastic, and the deadweight loss from the tax is larger.
A tax has a deadweight loss because it induces buyers and sellers to change their behavior. The tax raises the price paid by buyers, so they consume less.
At the same time, the tax lowers the price received by sellers, so they produce less. Because of these changes in behavior, the equilibrium quantity in the market shrinks below the optimal quantity for economic efficiency.
The more responsive buyers and sellers are to changes in the price, the more the equilibrium quantity shrinks. Hence, the greater the elasticities of supply and demand, the larger the deadweight loss of a tax.
Practice Questions
If policymakers want to raise revenue by taxing goods while minimizing the deadweight losses, they should look for goods with ________ elasticities of demand and ________ elasticities of supply.
A. small; small
B. small; large
C. large; small
D. large; large
Answer: A. small; small
In the economy of Agricola, tenant farmers rent the land they use. If the supply of land is perfectly inelastic, then a tax on land would have _________ deadweight losses, and the burden of the tax would fall entirely on the _________.
A. sizable; farmers
B. sizable; landowners
C. no; farmers
D. no; landowners
Answer: D. no; landowners
Suppose the demand for grape jelly is perfectly elastic (because strawberry jelly is a good substitute), while the supply is unit elastic. A tax on grape jelly would have __________ deadweight losses, and the burden of the tax would fall entirely on the __________ of grape jelly.
A. sizable; consumers
B. sizable; producers
C. no; consumers
D. no; producers
Answer: B. sizable; producers
Deadweight Loss and Tax Revenue as Taxes Vary
The deadweight loss—the reduction in total surplus that results when the tax reduces a market’s size below the optimum—equals the area of the triangle between the supply and demand curves.
For the small tax in panel (a), the area of the deadweight loss triangle is quite small. But as the size of the tax rises in panels (b) and (c), the deadweight loss grows larger and larger.
This occurs because the deadweight loss is the area of a triangle, and the area of a triangle depends on the square of its size.
If we double the size of a tax, for instance, the base and height of the triangle double, so the deadweight loss rises by a factor of four.
If we triple the size of a tax, the base and height triple, so the deadweight loss rises by a factor of nine.