Application: The Costs of Taxation

Deadweight Loss of Taxation Tax on a good Levied on buyers Demand curve shifts downward by the size of tax Levied on sellers Supply curve shifts upward by the size of tax Same outcome: price wedge Price paid by buyers rises Price received by sellers falls Lower quantity sold

Deadweight Loss of Taxation Tax burden Distributed between producers and consumers Determined by elasticities of supply and demand Market for the good becomes smaller

The effects of a tax Price Demand Price buyers pay Supply Quantity with tax Size of tax Price without tax Quantity without tax Price sellers receive Quantity A tax on a good places a wedge between the price that buyers pay and the price that sellers receive. The quantity of the good sold falls.

The Deadweight Loss of Taxation How a tax affects market participants Gains and losses from a tax on a good Buyers: consumer surplus Sellers: producer surplus Government: total tax revenue Tax times quantity sold Public benefit from the tax

Tax revenue Price Demand Supply Price buyers pay Quantity with tax Size of tax (T) Supply Price buyers pay Quantity with tax Tax revenue T ˣ Q Quantity without tax Price sellers receive Quantity sold (Q) Quantity The tax revenue that the government collects equals T × Q, the size of the tax T times the quantity sold Q. Thus, tax revenue equals the area of the rectangle between the supply and demand curves

The Deadweight Loss of Taxation Welfare without a tax Maximum Consumer Surplus Maximum Producer Surplus Total tax revenue = zero Welfare with tax Smaller Consumer Surplus Smaller Producer Surplus Total tax revenue > zero Smaller overall welfare

How a tax affects welfare Price Demand Price buyers pay =PB Q2 Supply A A tax on a good reduces consumer surplus (by the area B + C) The tax reduces producer surplus (by the area D + E). Because the fall in producer and consumer surplus exceeds tax revenue (area B + D), the tax is said to impose a deadweight loss (area C + E). C B Price without tax =P1 E Q1 D Price sellers receive =PS F Quantity Without Tax With Tax Change Consumer Surplus Producer Surplus Tax Revenue Total Surplus A+B+C D+E+F None A+B+C+D+E+F A F B+D A+B+D+F -(B+C) -(D+E) +(B+D) -(C+E) The area C + E shows the fall in total surplus and is the deadweight loss of the tax

The Deadweight Loss of Taxation Losses of surplus to buyers and sellers from a tax exceeds the revenue raised by the government Deadweight loss: The fall in total surplus that results from a market distortion, such as a tax Taxes distort incentives Markets now allocate resources inefficiently

How a tax affects welfare Hamburger Market Price Demand Price buyers pay =$11 90 Supply Tax ($2 times 90) = $180 C+E = $20 Government revenue increased by $180 but the tax damaged the market by $200 If the government fails to take $180 and create $200 or more in value, then policy lowered overall economic value $180 $20 Price without tax =$10 100 Price sellers receive =$9 Quantity Hamburger sellers create a lower price Hamburger consumers pay a higher price The hamburger market is now smaller Even if the government manages to create economic value buyers and sellers in the hamburger market are unlikely to be better off (redistribution of income)

Determinants of the Deadweight Loss Price elasticities of supply and demand When the supply curve is more elastic Deadweight loss is larger When the demand curve is more elastic The greater the elasticities of supply and demand The greater the deadweight loss of a tax

Tax distortions and elasticities Inelastic Supply Elastic Supply When supply is relatively inelastic, the deadweight loss of a tax is small Price Price When supply is relatively elastic, the deadweight loss of a tax is large Demand Supply Demand Supply Size of tax Size of tax Quantity Quantity In the above illustrations the demand curve and the size of the tax are the same, but the price elasticity of supply is different. Notice that the more elastic the supply curve, the larger the deadweight loss of the tax.

Tax distortions and elasticities Inelastic Demand Elastic Demand When demand is relatively inelastic, the deadweight loss of a tax is small When demand is relatively elastic, the deadweight loss of a tax is large Price Price Supply Supply Demand Demand Size of tax Size of tax Quantity Quantity In the above illustrations, the supply curve and the size of the tax are the same, but the price elasticity of demand is different. Notice that the more elastic the demand curve, the larger the deadweight loss of the tax.

The deadweight loss debate Size of Government The larger the deadweight loss of taxation The larger the cost of any government program If taxes cause a large deadweight losses Strong argument for a leaner government Do less and taxes less If taxes cause a small deadweight losses Government programs are less costly

Deadweight Loss & Tax Revenue As the tax increases Deadweight loss increases Even more rapidly than the size of the tax Tax revenue Increases initially Then decreases Higher tax – drastically reduces the size of the market

Deadweight Loss & Tax Revenue Small tax Medium tax Large tax Price Price Price Deadweight loss Deadweight loss Deadweight loss Demand Demand PB Supply Supply Demand Q2 Supply PB Q2 PB Tax revenue Q2 Tax revenue Q1 Q1 Tax revenue Q1 PS PS PS Quantity Quantity Quantity The deadweight loss is the reduction in total surplus due to the tax. Tax revenue is the amount of the tax times the amount of the good sold. A small tax has a small deadweight loss and raises a small amount of revenue. A somewhat larger tax has a larger deadweight loss and raises a larger amount of revenue. A very large tax has a very large deadweight loss, but because it has reduced the size of the market so much, the tax raises only a small amount of revenue.

Deadweight Loss & Tax Revenue 1974, economist Arthur Laffer Tax rates were so high Reducing them would actually raise tax revenue Ronald Reagan ran for president in 1980 Taxes were so high that they were discouraging hard work Lower taxes would give people the proper incentive to work Raise economic well-being Perhaps increase tax revenue

Deadweight Loss & Tax Revenue Tax size Laffer curve Tax revenue first increases then decreases