## Excise Taxes and Changes in Total Surplus

© 1999-2020, Douglas A.Ruby (06-04-2020)

An Excise Tax is a per-unit tax placed on the sale of a good (usually goods rather than services). These taxes often are imposed to generate revenue for federal, state and local governments and sometimes take the place of a per-use fee as in the case of a gasoline tax used to pay for roads, bridges and infrastructure. Excise taxes are sometimes considered to be Sin taxes in that they raise the price of certain products (tobacco and alcohol) with the goal of deterring use.

We often model the imposition of such taxes on the supply-side of the market. This corresponds to the administrative ease in collecting tax revenue -- fewer business relative to the number of consumers and business firms tend to keep better accounts. When an excise tax is imposed on the market, it cuts into both consumer surplus and producer surplus as the market price increases and consumer buy less of the product.

In the diagram below, move the Excise Tax slider to the right -- say a \$10 exicse tax. Pay attention to the numbers in the status boxes. Notice that the supply curve S is modified to read S + T. The vertical distance between 'S' and 'S+T' is the amount of the exicse tax. Also note the change in Consumer Surplus and Producer Surplus. In the absence of the tax consumer surplus is equal to \$80,000 (\$90 - \$50) x (4,000 units) and producer surplus is equal to \$60,000 (\$50 - \$20) x (4,000 units). The combined value of consumer and producer surplus (\$140,000) is known as Total Surplus and represents total surplus value to consumers and producers for participating in the market. As a tax is imposed the value of total surplus decreases. Some of it goes to the government in the form of Tax revenue, specifically the amount of the tax multiplied by the new equilibrium quantity.

For example with an excise tax (T) of \$10.00:

New equilibrium quantity: 3,444.4 units
New (remaining) Consumer Surplus: [(\$90.00 - \$55.60) x 3,444.40]/2 = \$59,243.68
New (remaining) Producer Surplus: [(\$45.60 - \$20) x 3,444.4]/2 = \$44,088.32
New (remaining) Total Surplus: \$59,243.68 + \$ 44,088.32 = \$103,332.00

The Deadweight Loss in this example is equal to the change in total surplus: \$140,000 - \$103,332.00 = \$36,668.00 less the tax revenue collected:

Change in Total Surplus: \$140,000 - \$120,554 = \$36,668.00
Tax Revenue collected: \$10.00 x 3,444.4 units = \$34,444.00
Difference or Deadweight Loss: \$36,668.00 - \$34,444.00 = \$2,224.00

Deadweight loss is a meaure if inefficiency in resource allocation due to a distortion in the market -- in this case: imposing an excise tax. The need to generate government revenue comes with a cost in the form of lost consumer surplus that isn't recovered by any agent in the market-place

 Demand Excise tax

The relative steepness or flatness (more inelastic / more elastic) of the demand curve compared to the supply curve, affects the amount and split of revenue generated. If supply is relatively more elastic than demand, then the split (tax burden} of revenue generated falls more on the consumer.

It is useful to note that the imposition of the \$10.00 per-unit tax only raised the market price by \$5.60 -- consumers will substitute away from this good as it becomes relatively more expensive. So. \$56.60 is paid to the seller (producer), but this seller needs to pay \$10.00 per-unit, or \$34,444.40 to the taxing-jurisdiction. Thus, the seller keeps \$45.60 per-unit or \$4.40 per-unit less than the market price in the absence of the tax.

For example:

Excise Tax: \$10.00 per unit
Price paid by the consumer: \$56.60, an increase of \$5.60
Price received by the producer: \$46.60, a reduction of \$4.40
Tax paid by the consumer: \$5.60 x 3,444.4 units = \$19,288.64
Tax paid by the producer: \$4.40 x 3,444.4 units = \$15,155.36

In the example above, the change in price paid by the consumer (\$5.60) is more than half of the per-unit tax of \$10.00. If demand were to be relative flatter (demand is more price sensitive) when compared to supply, the increase in price to the consumer would be less and the seller would receive less net of taxes paid.

Concepts for Review:
• Change in Consumer Surplus
• Change in Producer Surplus
• Excise Tax
• Tax Burden
• Tax Revenue
• Total Surplus