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 QT and QE 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.
Answers to A (Without Tax)
CS = \frac{1}{2} \times 200 \times 100 = $10,000
PS = \frac{1}{2} \times 200 \times 100 = $10,000
Total surplus = 10,000 + $10,000 = $20,000
Answers to B (With $100 Tax)
CS = \frac{1}{2} \times 150 \times 75 = $5,625
PS = 5,625
Tax revenue = 100 \times 75 = $7,500
Total surplus = 18,750
DWL = 1,250
What Determines the Size of the DWL?
The government should tax goods/services with the smallest DWL.
DWL size depends on the price elasticities of supply and demand.
The price elasticity of demand (or supply) measures how much QD (or QS) changes when P changes.
DWL and the Elasticity of Supply
When supply is inelastic, it’s harder for firms to leave the market when the tax reduces PS.
The tax only reduces Q a little, and DWL is small.
The more elastic is supply, the easier for firms to leave the market when the tax reduces PS.
The greater Q falls below the surplus-maximizing quantity, the greater the DWL.
DWL and the Elasticity of Demand
When demand is inelastic, it’s harder for consumers to leave the market when the tax raises P_B.
The tax only reduces Q a little, and DWL is small.
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.