Elasticity, Taxes, and Deadweight Loss Lesson

Per-unit taxes and subsidies affect the total price consumers pay, net price firms receive, equilibrium quantity, consumer and producer surpluses, deadweight loss, and government revenue or cost. The impact of change depends on the price elasticity of supply and demand. Lump-sum taxes and lump-sum subsidies do not change either marginal cost or marginal benefit; only fixed costs will be affected (that will be important later). Binding price ceilings and floors affect prices and quantities differently depending on the price elasticities of supply and demand.

Elasticity plays a major role in determining the impact a tax will have on a market. In a market that is otherwise operating appropriately, taxes tend to decrease efficiency and create deadweight loss to society by moving away from the socially optimal level of production and decreasing consumer and producer surplus. So, if these negative effects occur, why would the government want to levy a tax? At this juncture in the course, there are two main reasons for taxation. The most obvious reason a government imposes a tax is to generate a flow of income. Tax revenue is used to provide for many of the public goods we all enjoy. In addition, taxes are used to discourage the production of consumption of goods that produce harmful effects (this includes harmful environmental or social effects - for instance, pollution). The most common form of taxation in these instances is an excise tax. An excise tax is a per-unit tax on specific items. It is attached to the production of a good and not the sale of the good. However, the impact of the tax may show up in a change of price for the good in the market. The degrees to which the market price changes and the degree to which consumption/production changes are both based on the elasticity of the demand and supply curves.

Impact of Tax

Impact of Tax Graph

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Impact of Tax Graph

X-axis – Quantity
Y-axis – Price

Three curves are included on the graph - Stax, Supply, and Demand. The demand decreases as the price increases.

Demand intersects Stax at point F. Demand intersects Supply at point B.

These two curves (Stax and Supply) run parallel to each other, separated by the amount of the tax ($2).

Original Equilibrium Price = $4

Original Equilibrium Quantity = 4 unit

In the above graph, the original supply curve is labeled S. The original equilibrium price and quantity are $4.00 and 4 units, respectively. A tax of $2.00 per unit is levied. To properly show the impact on the supply curve, it should be shifted up vertically at every point by the amount of the tax. For example, the point associated with a price of $1.00 and a quantity of 1 unit would shift up to a price of $3.00 at a quantity of 1 unit. Since each point shifts upward by the amount of the tax, the new supply curve, S_tax, is separated from the original supply curve by $2.00 at each point. That means the two curves run parallel to each other. This upward shift is viewed as a decrease in supply (and should be considered a leftward shift if you are reading quantities).

After some market adjustment, the new equilibrium price and quantity would settle at $5.00 and 3 units.

Comparing the original and new equilibrium prices, you can see that consumers will be paying a higher price because of the tax. However, the new price doesn't reflect the full amount of the tax (that would only happen if the demand curve was perfectly inelastic - or vertical).

If the consumers were paying $4.00 and now they are paying $5.00, then they are bearing $1.00 of the tax burden in the form of a higher price. Sellers are receiving $5.00 per unit, but they must send the $2.00 tax to the government. Therefore, they only get to keep $3.00 per unit. Before the tax, suppliers were receiving and keeping $4.00, so suppliers are also bearing $1.00 of the tax in the form of a lower price they get to keep. As you can see from the graph, the original supply curve shows that when suppliers receive $3.00 per unit, they are only willing to supply 3 units (which happens to be the new equilibrium quantity).

In this particular instance, the tax burden or tax incidence was split evenly between consumers and producers. However, that is not always the case. If the demand curve had been more elastic (flatter), less of the tax could have been passed off to the consumer. That's because consumers would be very sensitive to a change in price and the quantity demanded would drop significantly if the supplier tried to push too much of the tax off on the consumer. If the demand for the good had been less elastic (or inelastic), the producers could have thrown the bulk of the tax off on consumers to pay for in the form of a higher price. When the demand for a good is less elastic (or inelastic), the quantity demanded will not change much in response to a change in price and consumers will bear more of the tax incidence. The same rationale applies to the elasticity of the supply curve in regard to the amount of the tax that will fall on the producers of a good.

Impact of Tax

Impact of Tax Graph

Full text available below image.

View the full text from the image above.

Impact of Tax Graph

X-axis – Quantity
Y-axis – Price

Three curves are included on the graph - Stax, Supply, and Demand. The demand decreases as the price increases.

Demand intersects Stax at point F. Demand intersects Supply at point B.

These two curves (Stax and Supply) run parallel to each other, separated by the amount of the tax ($2).

Original Equilibrium Price = $4

Original Equilibrium Quantity = 4 unit

Let's look a little more closely at what happens in the market when this tax is levied. The tax will create a deadweight loss to society because it results in production which is less than the socially optimal level. As a matter of fact, a market with a rather elastic demand curve will incur a larger deadweight loss when a tax is levied.

Before the tax, consumers purchased 4 units and had an area of consumer surplus equal to ΔABD. After the tax, consumers are paying $5.00 per unit and consume only 3 units (less than the socially optimal level). Consumer surplus has been reduced to ΔAFE.

Before the tax, producers supplied 4 units and had a producer surplus equal to ΔCBD. After the tax, suppliers are only keeping $3.00 per unit and sell only 3 units. Producer surplus has been reduced to ΔCGH. To find the dollar amount of the consumer or producer surplus triangles, you simply calculate the area of the triangle that represents the surplus.

What happened to the lost consumer and producer surpluses? Part of it was lost to everyone and is considered deadweight loss (because the 4^th unit that was desired was never produced and consumed). Deadweight loss equals ΔFBG and contains some lost consumer surplus and some lost producer surplus. The other lost portions of consumer and producer surpluses were actually transferred to the government in the form of tax revenue. Tax revenue is found by multiplying the tax by the quantity sold ($2 x 3 units = $6.00). Graphically, it is rectangle EFGH. If you calculate the area of that rectangle, it should reveal that the tax revenue collected was, indeed, $6.00.

Review

Practice what you've learned with the review activity below.

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