Question

The state needs to raise money, and the governor has a choice of imposing an excise tax of the same amount on one of two previously untaxed goods: the state can tax sales of either restaurant meals or gasoline. Both the demand for and the supply of restaurant meals are more elastic than the demand for and the supply of gasoline. If the governor wants to minimize the deadweight loss caused by the tax, which good should be taxed? For each good, draw a diagram that illustrates the deadweight loss from taxation.

Short answer

Answer: To minimize the deadweight loss caused by the tax, the governor should tax gasoline rather than restaurant meals.

Step-by-step solution

Understand elasticity and deadweight loss

First, we need to understand that when demand and supply are more elastic, the burden of the tax is more sensitive to changes in price due to the tax. This will affect the deadweight loss, which is the difference between the consumer and producer surplus before and after taxation.

Draw the pre-taxation equilibrium for each good

For each good, draw the demand and supply curves on a graph with price on the vertical axis and quantity on the horizontal axis. Label the pre-taxation equilibrium points, prices, and quantities for both gasoline and restaurant meals.

Add the tax for each good

Now, add the excise tax to the supply curve for both goods. This will lead to a vertical shift of the supply curve upward by the amount of the tax. Label this new supply curve as S_new for both restaurant meals and gasoline.

Find the new equilibrium

With the new supply curves for both goods, determine the new equilibrium points (price and quantity) after the imposition of the tax. Label these points on the graphs.

Determine the deadweight loss for each good

To find the deadweight loss, look for the difference between the two triangle-shaped areas that used to be part of consumer and producer surplus before the tax and now are not part of any surplus (neither consumer nor producer). For each good, shade the deadweight loss area on the graph.

Compare the deadweight losses between two goods

Choose the good that has a smaller deadweight loss area on the graph. This will be the good that the governor should tax to minimize the deadweight loss caused by the tax. As the demand and supply of restaurant meals are more elastic than gasoline, it can be inferred that taxing gasoline will result in a smaller deadweight loss when compared to restaurant meals. To minimize the deadweight loss caused by the tax, the governor should tax gasoline rather than restaurant meals.

Key concepts

Elasticity of Demand

Elasticity of demand describes how sensitive the quantity demanded of a good is to a change in its price. If demand is highly elastic, a small change in price will lead to a large change in the quantity demanded. In other words, consumers are very responsive to price changes. Conversely, if demand is inelastic, quantity demanded does not change much with price shifts. This concept is crucial when considering excise taxes. When a good with elastic demand is taxed, consumers significantly reduce their purchases, leading to greater economic inefficiency or deadweight loss. To minimize deadweight loss, policymakers often prefer to tax goods with inelastic demand, where quantity demanded changes minimally with price changes.

Elasticity of Supply

Elasticity of supply measures how sensitive the quantity supplied of a good is to a change in its price. When supply is elastic, suppliers can adjust their production levels quickly in response to price changes, meaning they have more flexibility. In contrast, an inelastic supply implies producers do not change their quantity supplied much, even when prices fluctuate. In the context of excise taxes, if a good has an elastic supply, producers will reduce the quantity they provide significantly when faced with a tax-induced price increase. Therefore, to avoid a substantial loss of economic welfare, goods with inelastic supply are often chosen for taxation, as the quantity supplied remains relatively stable, minimizing the deadweight loss.

Excise Tax

An excise tax is a fee imposed on a specific good, usually targeting goods that generate negative externalities or are deemed luxury items. This tax shifts the supply curve upward, as the cost of supplying each unit increases. After the imposition of an excise tax, the equilibrium price consumers pay increases, while the price producers receive decreases. The difference results in tax revenue for the government but also leads to a potential deadweight loss in the market. Excise taxes can reduce both consumer and producer surplus, but when applied to inelastic goods, the overall efficiency loss is minimized as the consumer and producer behaviors exhibit less change.

Consumer Surplus

Consumer surplus represents the difference between what consumers are willing to pay for a good and what they actually pay. It measures the additional benefit that consumers receive from purchasing a good at its market price. When an excise tax is applied, the consumer surplus decreases because the price consumers pay increases, reducing the amount of benefit they derive. In economic terms, some portion of consumer surplus gets converted into government revenue through taxes. However, with highly elastic goods, the loss in consumer surplus can be substantial as the price increase leads to a significant reduction in quantity demanded.

Producer Surplus

Producer surplus is the difference between what producers are willing to accept for a good and the price they actually receive. It reflects the additional profit producers make over the minimum amount they need to supply the good. Imposing an excise tax reduces producer surplus, as it increases the cost of providing the good, subsequently lowering the effective price producers receive after tax. For goods with elastic supply, this reduction is pronounced, as producers tend to cut back on production significantly when their profit margins shrink. Thus, when supply elasticity is high, an excise tax can cause substantial losses in producer surplus, contributing to a larger deadweight loss.