Taxes, mandatory payments made by members of society to finance government operations disrupt what otherwise would be an efficiently functioning market. This disruption is seen as a tax wedge between the demand price and the supply price. Changes in the demand and supply prices after a tax when compared to the equilibrium price before the tax is incidence or burden of the tax. The tax incidence identifies who ultimately pays the tax.
While one side of the market or the other might superficially appear to pay a tax, that is, the ones writing the check, more often than not both sides of the market share the tax burden. They share the burden by way of changes in their demand and supply prices. If a $10 tax, for example, results in an $8 increase in the demand price and a $2 decrease in the supply price, then buyers pay 80% of the tax and sellers pay the remaining 20%.
The division of the tax payment between buyers and sellers depends on the relative price elasticities of demand and supply. If the demand curve is less elastic (more inelastic) than the supply curve, then buyers pay a relatively larger share of the tax. If the supply curve is less elastic (more inelastic) than the demand curve, then sellers pay a relatively larger share of the tax. In the extreme, buyers pay the entire tax only if the demand curve is perfectly inelastic or the supply curve is perfectly elastic. Alternatively, sellers pay the entire tax only if the supply curve is perfectly inelastic or the demand curve is perfectly elastic.
The Tax Wedge
The starting place for analyzing the incidence of a tax is to review an efficient market for a private good. In the exhibit to the right the market equilibrium intersection of the demand curve (D) and supply curve (S) generates an efficient allocation of resources -- assuming no market control, no external costs or benefits, and perfect information.
This equilibrium is efficient because the demand price and supply price are equal at $3. The value of the good produced is equal to the value of goods not produced. It is not possible to produce more or less of this good such that society's level of satisfaction increases.
Placing a tax on an efficient market disrupts this efficiency. While a tax can be imposed on this market from either the demand side or the supply side, for the present discussion the easiest way to do this is to treat the tax as a cost of production. While a tax is not really an opportunity cost from the economy's perspective, if paying the tax is the responsibility of the suppliers, then it can be viewed as a "cost of doing business" for the suppliers.
For this reason, we can identify a new "supply" curve that is the original supply curve plus the tax. Suppose that a per unit tax of $1 is added to supply. The result is a new "supply" curve, which lies above and to the left of the original supply curve. This new supply curve, labeled S + T, can be revealed by a click of the [Add the Tax] button. The inclusion of a tax has much the same affect as an increase in any resource price or the cost of production, technically termed a decrease in supply.
Before getting to the new equilibrium achieved with the tax, take a closer look at exactly what the tax does. The tax drives a "wedge" between the price buyers pay (the demand price) and the price sellers receive (the supply price). The demand price is the price corresponding with the demand curve (D) and the supply price is the price corresponding with the original supply curve (S).
To illustrate this tax wedge, click the [Tax Wedge] button. Doing so highlights that a $1 per unit tax effectively creates a $1 difference between the demand price and supply price. This position of this wedge effectively determines the after-tax equilibrium for this market.
Tax IncidenceThe next step in this analysis is to identify the incidence of the tax, how much is of the tax is paid by buyers and how much by sellers. To do so, it is necessary to identify the new equilibrium, the market equilibrium achieved with the tax. This is found at the intersection of the original demand curve (D) and the new "supply curve" (S + T). A click of the [Equilibrium] button reveals this result.
The market achieves equilibrium with a price of $3.50 and a quantity of 3.75. The result of this per unit tax is a higher price and a decrease in the quantity exchanged, just like any decrease in supply. In fact, the inclusion of a tax has much the same affect on a market as an increase in any resource price. The price goes up and the quantity goes down.
However, while the market equilibrium price is higher and the buyers are paying a higher price to purchase this good, the sellers are not receiving this higher price. Part of the higher price goes to government as the tax. So, who is really paying the tax? Buyers? Or sellers?
As a general rule, both buyers and sellers pay a share of the tax. The question of who pays the tax and how much is termed tax incidence, the division of a tax between buyers and sellers. Tax incidence is found as the difference between the pre-tax market equilibrium price and the demand and supply prices that result after the tax is imposed.
Tax incidence is the difference between the original price and these two prices. Because buyers pay a higher price after the tax than before ($3.50 versus $3), they pay a portion of the tax ($0.50). Because sellers receive a lower price after the tax than before ($2.50 versus $3), they also pay a portion of the tax ($0.50).
- Demand Price: The demand price is the price paid by the buyers at the new equilibrium intersection of the demand curve, D, and the new supply curve, S + T, a price of $3.50. This is the maximum price that buyers are willing and able to pay for the new equilibrium quantity.
- Supply Price: The supply price is the price received by the sellers, which is the difference between the new equilibrium price ($3.50) and the tax ($1), or $2.50. This is the minimum price that sellers are willing and able to accept for the new equilibrium quantity.
In this example, $0.50 of the $1 per unit tax is paid by buyers and $0.50 is paid by sellers. A tax is seldom equally divided among buyers and sellers, as in this simplistic example. The actual tax incidence is based on the shapes, slopes, and elasticities of the demand and supply curves.
Bring On Elasticity
The incidence or burden of a tax depends on the relative price elasticities of demand and supply. Here are the general rules for elasticity and tax incidence.
The incidence of the tax ultimately rests with the RELATIVE elasticities of the two markets. If both demand and supply are relatively elastic, hence both sides essentially refuse to pay the tax, then tax incidence rests with which side is the most elastic. If demand is more elastic than supply, then sellers bear a larger tax burden. If supply is more elastic than demand, then buyers bear a larger burden.
- Inelastic: If one side of the market is relatively inelastic, then it tends to bear a relatively greater tax burden. The inelastic side of the market is essentially "unconcerned" about the price, with the primary focus on the quantity. This side will pay the tax if needed to maintain the quantity.
- Elastic: However, if one side of the market is relatively elastic, then the other side of market tends to bear a relatively greater tax burden. In this case, the elastic side of the market is focused on the price and "unconcerned" about the quantity. It simply refuses to pay the tax, pushing the burden to the other side.
Alternatively, if both demand and supply are relatively inelastic, with both sides willing to pay the tax, the tax incidence rests with which side is the most inelastic. If demand is more inelastic than supply, then buyers bear a larger tax burden. If supply is more inelastic than demand, then sellers bear a larger burden.
The incidence of a tax is much like two rival siblings, each willing to accept the blame for a broken lamp, or shifting the blame to their sibling, to different degrees. Inelastic demand or supply means the sibling is willing to accept the blame (and pay the tax). Elastic demand and supply means sibling is more willing to pass the blame on to the other (and not pay the tax).
The exhibit to the right helps to illustrate how different demand and supply elasticities affect tax incidence. Click the [Buyers Pay] button to show how a relatively inelastic demand combine with a relatively elastic supply places a relatively greater tax burden on buyers. The $1 tax wedge increases the demand price to $3.80 and decreases the supply price to $2.80. The differences between the pre-tax equilibrium price and the new demand and supply prices mean that buyers pay a larger 80% of the tax and sellers pay a smaller 20%.
Now click the [Sellers Pay] button to show that a relatively elastic demand and relatively inelastic supply places a relatively greater tax burden on sellers. In this case the $1 tax wedge increases the demand price only to $3.20 and decreases the supply price all of the way to $2.20. The differences between the pre-tax equilibrium price and the new demand and supply prices mean that sellers pay a larger 80% of the tax and sellers pay a smaller 20%.
TAX INCIDENCE, AmosWEB Encyclonomic WEB*pedia, http://www.AmosWEB.com, AmosWEB LLC, 2000-2013. [Accessed: May 21, 2013].