Application: The Costs of Taxation Chapter 8 1 IN THIS CHAPTER • A tax affect − Consumer surplus, producer surplus, and total surplus − Total surplus = economic well-being • Maximized at equilibrium • Deadweight loss(DWL) of a tax • Factors determine the size of the deadweight loss − Elastic vs inelastic • Tax revenue depends on the size of the tax 2 A tax? (an amount of) money paid to the government that is based on your income or the cost of goods or services you have bought. 3 The effects of a tax • Total surplus = Consumer surplus + Producer surplus − Maximized at equilibrium • With taxes: − CS decreases (higher PB, lower QT) − PS decreases (lower PS, lower QT) − Government gains tax revenue (per unit tax * QT) • What happens to total surplus? 4 How a Tax Affects Market Participants P A. Equilibrium with no tax: • Price = PE • Quantity = QE B. Equilibrium with tax = $T per unit: • Buyers pay PB • Sellers receive PS • Quantity = QT Revenue from tax: $T x QT Size of tax = $T S PB PE PS D QT QE Q 5 How a Tax Affects Market Participants: without a tax P Without a tax, CS = A + B + C PS = D + E + F Tax revenue = 0 A S B C E PE Total surplus = CS + PS =A+B+C +D+E+F D D F QT QE Q 6 How a Tax Affects Market Participants: with a tax With the tax, • CS = A • PS = F • Tax revenue = B + D • Total surplus = CS + PS + tax revenue =A+B+D+F C + E is called the deadweight loss (DWL) of the tax, the fall in total surplus that results from a market distortion, such as a tax. P A PB S B D The tax reduces total surplus by C+E • QE – QT = units not sold because of the tax C E PS D F QT QE Q 7 Deadweight loss(DWL)? A loss occurs when a government raises taxes to get more money, but then loses money as a result. 8 Deadweight Loss of Taxation • Tax on a good levied on buyers − Demand curve shifts to the left(=downward) • By the size of tax • Tax on a good levied on sellers − Supply curve shifts to the left(=upward) • By the size of tax • Lower quantity sold 9 Deadweight Loss of Taxation • A tax on sellers (Chapter 6) 10 Deadweight Loss of Taxation • A tax on buyers (Chapter 6) 11 Example 1: Analysis of a tax A. Compute CS, PS, and total surplus without a tax. P $ 400 350 300 B. If a $200 tax per unit is imposed, compute CS, PS, tax revenue, total surplus, and DWL. S 250 200 150 D 100 50 0 0 25 50 Q 75 100 125 12 Example 1: A. Without a tax P A. Without tax: • CS = ½ x $200 x 100 = $10,000 $ 400 350 300 CS 250 • PS = ½ x $200 x 100 = $10,000 • TS = $20,000 S P = 200 PS 150 D 100 50 0 0 25 50 Q 75 100 125 13 Example 1: B. With $200 tax B. With $200 tax: • CS = ½ x $100 x 50 = $2,500 • PS = $2,500 • Tax revenue = $200 x 50 = $10,000 • TS = $15,000 • DWL = $5,000 P $ 400 350 CS PB = 300 S 250 Tax 200 DWL revenue 150 D PS = 100 PS 50 0 0 25 50 Q 75 100 125 14 EXAMPLE 2: DWL and the gains from trade Tom is taking his laundry to Jerry’s dry cleaning and laundry services business. For this arrangement, each month, Tom is willing to pay $165, and Jerry’s cost is $140. They agree on a price of $150 per month. A. Calculate CS, PS, and TS. B. The government imposes a $35 tax on all laundry service providers. What happens to CS, PS, and TS? 15 EXAMPLE 2: Solutions Tom’s WTP = $165; Jerry’s cost = $140 P = $150 per month. A. Calculate CS, PS, and TS. • Tom’s CS = WTP – P = 165 – 150 = $15 • Jerry’s PS = P – cost = 150 – 140 = $10 • TS = CS + PS = $25 16 EXAMPLE 2: Solutions Tom’s WTP = $165;Jerry’s cost = $140 P = $150 per month. B. $35 tax • Jerry needs 140 + 35 = $175 to provide laundry services to Tom, but Tom’s WTP = $165 • Trade doesn’t happen! • The tax has made both worse off: DWL = $25 • How about the government? The government gets $0 in tax revenue because Jerry and Tom are not trading. 17 The Determinants of the Deadweight Loss • Price elasticities of supply and demand − More elastic supply curve • Larger deadweight loss − More elastic demand curve • Larger deadweight loss • The greater the elasticities of supply and demand − The greater the deadweight loss of a tax 18 DWL and elasticity of supply P S When supply is inelastic, A change in price leads to a small change in quantity supplied. DWL is small. Size of tax D Q 19 DWL and elasticity of supply P The more elastic is the supply, The greater the change in quantity supplied due to a change in price... The greater the DWL. S Size of tax D Q 20 Tax Distortions and Elasticities (a, b) 21 DWL and elasticity of demand P When demand is inelastic, A change in price leads to a small change in quantity demanded. DWL is small. S Size of tax D Q 22 DWL and elasticity of demand The more elastic is demand, The greater the change in quantity demanded due to a change in price… and the greater the DWL. P S Size of tax D Q 23 Tax Distortions and Elasticities (c, d) 24 DWL and Tax Revenue as Taxes Vary • As the tax increases − Deadweight loss increases • Even more rapidly than the size of the tax − Tax revenue • Increases initially • Then decreases • The higher tax: drastically reduces the size of the market 25 DWL and the size of the tax P new DWL Initially, the tax is T per unit. S Increasing the tax to 2T per unit… causes the DWL to more than double. 2T T D initial DWL Q2 Q1 Q 26 DWL and the size of the tax P new DWL Initially, the tax is T per unit. Increasing the tax even more, to 3T per unit… S T 3T causes the DWL to more than triple. D initial DWL Q3 Q1 Q 27 Revenue and the size of the tax P When the tax is small, increasing it causes tax revenue to rise. When the tax is larger, increasing it causes tax revenue to fall. PB3 PB2 S PB1 3T 2T PS1 T D PS2 PS3 Q3 Q2 Q1 Q 28 How Deadweight Loss and Tax Revenue Vary with the Size of a Tax (a, b, c) 29 Deadweight Loss and tax revenue as taxes vary Tax revenue DWL The Laffer curve Tax size When a tax increases, DWL rises even more. Tax size When a tax increases, tax revenue initially increases, then decreases. 30 CHAPTER IN A NUTSHELL • A tax on a good reduces the welfare of buyers and sellers, and the reduction in CS and PS usually exceeds the revenue raised by the government. − The fall in total surplus is DWL of a tax. • Taxes have deadweight losses. − Buyers consume less and pay a higher P. − Sellers produce less and receive a lower P. 31 CHAPTER IN A NUTSHELL • Large S and D elasticities: larger DWL • As a tax grows larger − Distorts incentives more − Its DWL grows larger − Tax revenue first rises with the size of a tax, but if the tax gets large enough, tax revenue starts to fall. 32