Chapter 8: The Costs of Taxation

Why taxes shrink the pie — and how much depends on elasticity

Running Example

The Gasoline Market

We'll use the market for gasoline throughout this chapter. Buyers have a downward-sloping demand (they buy less as price rises), and sellers have an upward-sloping supply (they produce more as price rises). A straight-line model captures all the essential economics.

Demand: P = 50 − 2Q buyers' willingness to pay
Supply: P = 10 + 2Q sellers' minimum acceptable price
Equilibrium: Q* = 10,  P* = $30 where both lines cross

Without any tax, 10 units trade at $30 each. Total surplus = ½×10×20 + ½×10×20 = $200. Now suppose the government places a $10 per-unit tax on sellers. What happens?

Section 1

The Tax Wedge

A tax drives a wedge between what buyers pay and what sellers receive. If the government collects $10 per gallon, and buyers pay Pb, then sellers only keep Ps = Pb − $10.

With a $10 tax, the new equilibrium quantity falls to QT = 7.5 units. Buyers pay Pb = $35, sellers receive Ps = $25, and the government collects $10 × 7.5 = $75 in revenue.

Tax wedge = Pb − Ps = T  |  Tax Revenue = T × QT

Notice how the tax splits the market into four regions: CS (blue triangle), PS (orange triangle), Tax Revenue (purple rectangle), and DWL (gold triangle). The DWL is the part nobody gets — it simply disappears.

Section 2

Why Deadweight Loss Exists

Before the tax, 10 units were traded. After the tax, only 7.5 are traded. What happened to the 2.5 units that used to trade?

Consider a buyer willing to pay $32 and a seller whose cost is $28. Without tax, they'd happily trade — the buyer gains $2, the seller gains $2, total gain = $4. But with a $10 tax, the seller needs to charge at least $38 ($28 + $10), and the buyer won't pay $38 for something worth $32 to them. The trade doesn't happen. That $4 of gains is destroyed — nobody captures it. That's deadweight loss.

Key insight: DWL is not a transfer. It's not that government takes it, or that buyers/sellers lose it to each other. It's economic value that simply ceases to exist — mutually beneficial trades that don't happen because the tax made them unprofitable.

The DWL triangle has:

  • Base = lost quantity = Q* − QT = 10 − 7.5 = 2.5 units
  • Height = tax size = T = $10
  • Area = DWL = ½ × T × ΔQ = ½ × $10 × 2.5 = $12.50
DWL = ½ × T × ΔQ   (area of the triangle)

Let's verify with the full surplus table:

Before tax: CS = $100, PS = $100, Total = $200
After tax: CS = $56.25, PS = $56.25, Tax Rev = $75
DWL: $200 − ($56.25 + $56.25 + $75) = $12.50

Section 3

Elasticity Determines the Size of DWL

A $10 tax always creates a $10 wedge — but the DWL it causes depends entirely on how much quantity falls. That depends on elasticity.

If buyers and sellers are very inelastic (they barely respond to price changes), quantity barely falls and DWL is small. If they're very elastic (they respond strongly to prices), the same $10 tax kills many more trades and DWL is large.

0 10 20 30 40 50 0 5 10 15 7.5 Quantity (gallons) Price ($) Demand Supply DWL Pb=$35 Pₛ=$25

Inelastic Curves

Q (no tax) 10.00
Q (with $10 tax) 8.75
Lost quantity 1.25
CS $153.13
PS $153.13
Tax Revenue $87.50
DWL $6.25

Toggle above to compare elastic vs inelastic — same $10 tax, very different DWL.

With inelastic curves (steep), the same $10 tax barely reduces quantity. Buyers and sellers grudgingly absorb the wedge, DWL is small, and tax revenue is large. With elastic curves (flat), the $10 tax causes a big drop in quantity — many trades are killed, DWL is large, and tax revenue actually falls.

Policy implication: If you want to minimize deadweight loss, tax goods with inelastic demand or supply (cigarettes, gasoline, alcohol). If you want to maximize tax revenue, the same principle applies — inelastic goods generate more revenue per dollar of DWL.

Section 4

How DWL Grows as Tax Size Increases

DWL grows with the square of the tax rate. Double the tax? DWL quadruples. Meanwhile, tax revenue first rises (more tax per unit) but eventually falls (too few units traded). Drag the slider to see both effects in real time.

$10
0 10 20 30 40 50 0 5 10 15 7.5 Quantity (gallons) Price ($) Demand Supply Pb=$35 Pₛ=$25 DWL

Market Outcomes

Tax (T) $10.00
Pb (buyer pays) $35.00
Pₛ (seller gets) $25.00
Q traded 7.50
CS $56.25
PS $56.25
Tax Revenue $75.00
DWL $12.50

Set T = $20 and watch DWL = $50 (4× the DWL at T = $10)

Tax revenue vs. tax size — the Laffer curve shape

The revenue curve is an inverted parabola — called the Laffer curve (even though Mankiw focuses on the DWL version). Revenue peaks at T = $20 in this model, then falls to zero at T = $40 (when no one trades). Meanwhile, DWL grows as T² — doubling the tax quadruples the deadweight loss.

Summary

Key Takeaways

  • Taxes create a wedge between buyer price (Pb) and seller price (Ps). The difference is the tax: T = Pb − Ps.
  • Deadweight loss = ½ × T × ΔQ. It's the triangle of mutually beneficial trades that don't happen because of the tax.
  • DWL grows with the square of the tax rate. Double the tax ⇒ quadruple the DWL. This is why large taxes are especially costly.
  • More elastic markets suffer more DWL. When buyers/sellers respond strongly to price changes, the same tax kills more trades.
  • Tax revenue eventually falls as the tax gets very large — the Laffer curve insight. Beyond a point, higher rates yield lower revenue.
  • Tax incidence (who actually bears the tax) depends on elasticities, not on whether the tax is legally placed on buyers or sellers.

Ready to test yourself?

Work through problems on tax wedges, deadweight loss, and the Laffer curve.

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