Sales tax

Definition

A sales tax is a tax imposed by a government on final sales or purchases.

A sales tax is a kind of consumption tax, and it differs from a value-added tax in that the tax is collected only at the point of final purchase rather than at intermediate steps on the value added at each step.

A sales tax may be of either of these two forms:

A price-proportional sales tax: Here, the sales tax is specified as a fraction of the total pre-tax price and added to it. The buyer pays a post-tax price which is the sum of the pre-tax price and the sales tax. The seller keeps the pre-tax price and the sales tax is remitted to the taxing authority.
A quantity-proportional sales tax: Here, the sales tax is specified per unit of the quantity being sold. For instance, a sales tax on wheat flour might specify a tax in money units per unit mass of wheat flour.

Interpretation of percentages for price-proportional sales tax

Note that unlike the income tax, the sales tax is computed as a percentage of the pre-tax price and added to the pre-tax price to determine how much the buyer will pay. Thus, the interpretation of percentages for the sales tax is somewhat different from that for income taxes.

For instance, for a sales tax of 25%, the post-tax price is $1.25$ times the pre-tax price. The taxing authority collects $0.25$ times the pre-tax price, which is $0.20$ times, or $20\%$ of, the post-tax price. Note that the percentage 20% is different from the sales tax percentage. In general, the percentage of post-tax price collected by the taxing authority is lower than the percentage of sales tax. However, for small values of price-proportional sales tax, these two percentages are almost the same.

The explicit formula is this. In fractional term, if the sales tax fraction of pre-tax price is $x$ , the fraction of post-tax price is:

$\!{\frac {x}{1+x}}$

Effects of sales tax

The effect of a sales tax is understood to mean the effect of introducing the sales tax on a good where there was none before. The analysis of such effects is an example of comparative statics.

Effect on market price and quantity traded

Further information: effect of sales tax on market price and quantity traded

Consider the simplifying assumptions of a competitive market, and assume that the sales tax is levied only on a particular good and not on the various substitute goods and complementary goods. Also, we assume that the law of demand and law of supply hold (these assumptions are usually valid in the short run). Under these assumptions, the following are the effects of introducing or increasing a sales tax:

The pre-tax price (which is what the seller gets to keep) either stays the same or goes down. The extreme case of it staying the same arises in either of two cases:
- The demand curve is vertical, i.e., the price-elasticity of demand is zero. Intuitively, what this means is that the quantity demanded is unaffected by price, so the entire burden of the sales tax is passed on to buyers (consumers).
- The supply curve is horizontal, i.e., the price-elasticity of supply is infinite.
The post-tax price (which is what the buyer needs to pay) either stays the same or goes up. The extreme case of it staying the same arises in either of these two cases:
- The supply curve is vertical, i.e., the price-elasticity of supply is zero. Intuitively, what this means is that the quantity supplied is unaffected by price, so the entire burden of the sales tax is absorbed by sellers.
- The demand curve is horizontal, i.e., the price-elasticity of demand is infinite.
The quantity traded goes down.

Effect on social surplus and its distribution

Further information: effect of sales tax on social surplus

In the absence of a sales tax, the social surplus arising from the sale of a good is captured by two types of parties -- sellers/producers (in the form of producer surplus) and buyers/consumers (in the form of consumer surplus).

Once a sales tax is introduced, there are generally two important effects:

Now, the social surplus is captured by three types of parties -- producers (producer surplus), consumers (consumer surplus), and the taxing authority (government surplus).
The total social surplus goes down: The new total social surplus, even including the portion captured by the taxing authority, is less than the original social surplus. Both the producer surplus and the consumer surplus go down. While part of the reduction in their surpluses is captured by the taxing authority, part of it is lost. The loss can be attributed to the trades that do not occur because of the decline in quantity traded, and is an example of a deadweight loss due to taxation. Geometrically, it can be measured as the area of a Harberger triangle.

More explicitly, we have:

Social surplus in absence of sales tax = Producer surplus in absence of sales tax + Consumer surplus in absence of sales tax

Social surplus in presence of sales tax = Producer surplus in presence of sales tax + Consumer surplus in presence of sales tax + Government surplus in presence of sales tax

Social surplus in absence of sales tax = Social surplus in presence of sales tax + Deadweight loss due to taxation = Producer surplus in presence of sales tax + Consumer surplus in presence of sales tax + Government surplus in presence of sales tax + Deadweight loss due to taxation

Producer surplus in absence of sales tax = Producer surplus in presence of sales tax + Part of government surplus in presence of sales tax that is collected at the expense of producers + Part of deadweight loss due to taxation experienced by producers

Consumer surplus in absence of sales tax = Consumer surplus in presence of sales tax + Part of government surplus in presence of sales tax that is collected at the expense of consumers + Part of deadweight loss due to taxation experienced by consumers

The tax incidence question is: how is the burden of taxation (both in terms of the part captured through government surplus and the deadweight loss) distributed between producers and consumers? The answer depends on the relative price-elasticities of the demand and supply curves.