# Elasticity and tax revenue

## Key points

• Tax incidence is the manner in which the tax burden is divided between buyers and sellers.
• The tax incidence depends on the relative price elasticity of supply and demand. When supply is more elastic than demand, buyers bear most of the tax burden. When demand is more elastic than supply, producers bear most of the cost of the tax.
• Tax revenue is larger the more inelastic the demand and supply are.

## The burden of tax

Depending on the circumstance, the burden of tax can fall more on consumers or on producers.
In the case of cigarettes, for example, demand is inelastic—because cigarettes are an addictive substance—and taxes are mainly passed along to consumers in the form of higher prices.
The analysis, or manner, of how the burden of a tax is divided between consumers and producers is called tax incidence.

## Elasticity and tax incidence

Typically, the incidence, or burden, of a tax falls both on the consumers and producers of the taxed good. But if we want to predict which group will bear most of the burden, all we need to do is examine the elasticity of demand and supply.
In the tobacco example above, the tax burden falls on the most inelastic side of the market. If demand is more inelastic than supply, consumers bear most of the tax burden. But, if supply is more inelastic than demand, sellers bear most of the tax burden.
Think about it this way—when the demand is inelastic, consumers are not very responsive to price changes, and the quantity demanded remains relatively constant when the tax is introduced. In the case of smoking, the demand is inelastic because consumers are addicted to the product. The seller can then pass the tax burden along to consumers in the form of higher prices without much of a decline in the equilibrium quantity.
When a tax is introduced in a market with an inelastic supply—such as, for example, beachfront hotels—sellers have no choice but to accept lower prices for their business. Taxes do not greatly affect the equilibrium quantity. The tax burden in this case is on the sellers. If the supply were elastic and sellers had the possibility of reorganizing their businesses to avoid supplying the taxed good, the tax burden on the sellers would be much smaller, and the tax would result in a much lower quantity sold instead of lower prices received. You can see the relationship between tax incidence and elasticity of demand and supply represented graphically below.
Two graphs that represent the relationship between elasticity and tax incidence. Graph A shows the situation that occurs when demand is elastic and supply is inelastic— tax incidence is lower on consumers. Graph B shows the situation that occurs when demand is inelastic and supply is elastic—tax incidence is lower on producers.
Image credit: Figure 3 in "Elasticity and Pricing" by OpenStaxCollege, CC BY 4.0
In diagram A, above on the left, the supply is inelastic and the demand is elastic—as it was in the beachfront hotels example. While consumers may have other vacation choices, sellers can’t easily move their businesses. By introducing a tax, the government essentially creates a wedge between the price paid by consumers, $\text{Pc}$, and the price received by producers, $\text{Pp}$. In other words, of the total price paid by consumers, part is retained by the sellers and part is paid to the government in the form of a tax. The distance between $\text{Pc}$ and $\text{Pp}$ is the tax rate. The new market price is $\text{Pc}$, but sellers receive only $\text{Pp}$ per unit sold since they pay $\text{Pc}-\text{Pp}$ to the government. Since a tax can be viewed as raising the costs of production, this could also be represented by a leftward shift of the supply curve. The new supply curve would intercept the demand at the new quantity $\text{Qt}$. For simplicity, the diagram above omits the shift in the supply curve.
The tax revenue is given by the shaded area, which is obtained by multiplying the tax per unit by the total quantity sold, $\text{Qt}$. The tax incidence on the consumers is given by the difference between the price paid, $\text{Pc}$, and the initial equilibrium price, $\text{Pe}$. The tax incidence on the sellers is given by the difference between the initial equilibrium price, $\text{Pe}$, and the price they receive after the tax is introduced, $\text{Pp}$.
In diagram A, above on the left, the tax burden falls disproportionately on the sellers, and a larger proportion of the tax revenue—the shaded area—is due to the resulting lower price received by the sellers than by the resulting higher prices paid by the buyers.
On the other hand, if we go back to our example of cigarette taxes, the situation would look more like diagram B—above on the right—where the supply is more elastic than demand. The tax incidence now falls disproportionately on consumers, as shown by the large difference between the price they pay, $\text{Pc}$, and the initial equilibrium price, $\text{Pe}$. Sellers receive a lower price than before the tax, but this difference is much smaller than the change in consumers’ price.
Using this type of analysis, we can also predict whether a tax is likely to create a large revenue or not. The more elastic the demand curve, the easier it is for consumers to reduce quantity instead of paying higher prices. The more elastic the supply curve, the easier it is for sellers to reduce the quantity sold instead of taking lower prices. In a market where both the demand and supply are very elastic, the imposition of an excise tax generates low revenue.
People often think that excise taxes hurt mainly the specific industries they target. But ultimately, whether the tax burden falls mostly on the industry or on the consumers depends simply on the elasticity of demand and supply.

## Review question

Under which circumstances does the tax burden fall entirely on consumers?

## Critical-thinking question

In a market where the supply curve is perfectly inelastic, how does an excise tax affect the price paid by consumers and the quantity bought and sold?