The Costs of Taxation

The Costs of Taxation (Chapter 8)

Introduction

• This chapter explores the impact of taxation on consumer surplus, producer surplus, and total surplus.
• It defines the deadweight loss of a tax and the factors that determine its size.
• It examines the relationship between tax revenue and the size of the tax.

Review from Chapter 6

• A tax:
  • Creates a wedge between the price buyers pay and the price sellers receive.
  • Increases the price buyers pay and decreases the price sellers receive.
  • Reduces the quantity bought and sold.
• These effects are the same whether imposed on buyers or sellers.

The Effects of a Tax

• Equilibrium without tax:
  • Price = $P_E$
  • Quantity = $Q_E$
• Equilibrium with tax = $T$ per unit:
  • Sellers receive $P_S$
  • Buyers pay $P_B$
  • Quantity = $Q_T$
  • Size of tax = $T$
• Revenue from tax: $T \,!x \,!Q_T$
• Welfare economics measures gains and losses from a tax.
• Includes consumer surplus (CS), producer surplus (PS), tax revenue, and total surplus with and without the tax.
• Tax revenue can fund beneficial services (e.g., education, roads, police), so is included in total surplus.

Without a Tax

• Consumer Surplus (CS) = A + B + C
• Producer Surplus (PS) = D + E + F
• Tax revenue = 0
• Total surplus = CS + PS = A + B + C + D + E + F

With the Tax

• Consumer Surplus (CS) = A
• Producer Surplus (PS) = F
• Tax revenue = B + D
• Total surplus = A + B + D + F
• The tax reduces total surplus by C + E.

Deadweight Loss (DWL)

• C + E is the deadweight loss (DWL) of the tax.
• DWL is the fall in total surplus that results from a market distortion, such as a tax.
• Because of the tax, the units between $Q<em>T$ and $Q</em>E$ are not sold.
• The value of these units to buyers is greater than the cost of producing them, so the tax prevents some mutually beneficial trades.

Example: Analysis of a Tax

• The Market for Airplane Tickets
• Compute CS, PS, and total surplus without a tax.
• With $100 tax per ticket, compute the CS, PS, tax revenue, total surplus, and DWL.</li> </ul> <h5 id="answerstoawithouttax">Answers to A (Without Tax)</h5> <ul> <li>CS =$\frac{1}{2} \times 200 \times 100 = $10,000$</li> <li>PS =$\frac{1}{2} \times 200 \times 100 = $10,000$</li> <li>Total surplus =$10,000 + $10,000 = $20,000

Answers to B (With $100 Tax)

• CS = \frac{1}{2} \times 150 \times 75 = $5,625$</li> <li>PS =$5,625$</li> <li>Tax revenue =$100 \times 75 = $7,500$</li> <li>Total surplus =$18,750$</li> <li>DWL =$1,250$</li> </ul> <h4 id="whatdeterminesthesizeofthedwl">What Determines the Size of the DWL?</h4> <ul> <li>The government should tax goods/services with the smallest DWL.</li> <li>DWL size depends on the price elasticities of supply and demand.</li> <li>The price elasticity of demand (or supply) measures how much$QD$(or$QS$) changes when P changes.</li> </ul> <h5 id="dwlandtheelasticityofsupply">DWL and the Elasticity of Supply</h5> <ul> <li>When supply is inelastic, it’s harder for firms to leave the market when the tax reduces PS.</li> <li>The tax only reduces Q a little, and DWL is small.</li> <li>The more elastic is supply, the easier for firms to leave the market when the tax reduces PS.</li> <li>The greater Q falls below the surplus-maximizing quantity, the greater the DWL.</li> </ul> <h5 id="dwlandtheelasticityofdemand">DWL and the Elasticity of Demand</h5> <ul> <li>When demand is inelastic, it’s harder for consumers to leave the market when the tax raises$P_B$.</li> <li>The tax only reduces Q a little, and DWL is small.</li> <li>The more elastic is demand, the easier for buyers to leave the market when the tax increases$P_B$$.
• The more Q falls below the surplus-maximizing quantity, and the greater the DWL.

Example: Elasticity and the DWL of a Tax

A. Breakfast Cereal vs. Sunscreen

• Breakfast cereal has more close substitutes than sunscreen, so demand for breakfast cereal is more price-elastic than demand for sunscreen.
• A tax on breakfast cereal would cause a larger DWL than a tax on sunscreen.

B. Hotel Rooms in the Short Run vs. Long Run

• The price elasticities of demand and supply for hotel rooms are larger in the long run than in the short run.
• A tax on hotel rooms would cause a larger DWL in the long run than in the short run.

C. Groceries vs. Meals at Fancy Restaurants

• Groceries are more of a necessity and therefore less price-elastic than meals at fancy restaurants.
• A tax on restaurant meals would cause a larger DWL than a tax on groceries.

How Big Should the Government Be?

• A bigger government provides more services but requires higher taxes, which cause DWLs.
• The larger the DWL from taxation, the greater the argument for smaller government.
• The tax on labor income is the biggest source of government revenue.
• For the typical worker, the marginal tax rate (the tax on the last dollar of earnings) is about 40%.
• If labor supply is inelastic, then this DWL is small.
• Some economists believe labor supply is inelastic, arguing that most workers work full-time regardless of the wage.
• Other economists believe labor taxes are highly distorting because some groups of workers have elastic supply and can respond to incentives:
  • Many workers can adjust their hours, e.g., by working overtime.
  • Many families have a 2nd earner with discretion over whether and how much to work.
  • Many elderly choose when to retire based on the wages they earn.
  • Some people work in the “underground economy” to evade high taxes.

The Effects of Changing the Size of the Tax

• Policymakers often change taxes, raising some and lowering others.
• What happens to DWL and tax revenue when taxes change?

DWL and the Size of the Tax

• Doubling the tax causes the DWL to more than double.
• Tripling the tax causes the DWL to more than triple.

Summary

• When a tax increases, DWL rises even more.
• When tax rates are low, raising them doesn’t cause much harm, and lowering them doesn’t bring much benefit.
• When tax rates are high, raising them is very harmful, and cutting them is very beneficial.

Revenue and the Size of the Tax

• When the tax is small, increasing it causes the tax revenue to rise.
• When the tax is larger, increasing it causes tax revenue to fall.

Laffer Curve

• The Laffer curve shows the relationship between the size of the tax and tax revenue.

Summary

• A tax on a good reduces the welfare of buyers and sellers. This welfare loss usually exceeds the revenue the tax raises for the govt.
• The fall in total surplus (consumer surplus, producer surplus, and tax revenue) is called the deadweight loss (DWL) of the tax.
• A tax has a DWL because it causes consumers to buy less and producers to sell less, thus shrinking the market below the level that maximizes total surplus.
• The price elasticities of demand and supply measure how much buyers and sellers respond to price changes. Therefore, higher elasticities imply higher DWLs.
• An increase in the size of a tax causes the DWL to rise even more.
• An increase in the size of a tax causes revenue to rise at first, but eventually revenue falls because the tax reduces the size of the market.