Enter Values

Qd = a - bP; quantity when P = 0
Units decrease per $1 price increase
Qs = -c + dP; minimum supply price = c/d
Units increase per $1 price increase
$
Dollar amount of tax per unit sold
Curve Equations
Demand: Qd = a - bP
Supply: Qs = -c + dP
Equilibrium: P* = (a + c) / (b + d)
Tax Wedge: Pbuyer - Pseller = T
Model Assumptions
  • Linear supply and demand curves
  • Per-unit tax (not ad valorem / percentage tax)
  • Tax incidence is independent of statutory incidence (economic burden splits the same way regardless of who legally pays)
  • Perfectly competitive market (no market power)
  • DWL arises from units that would have been traded but are not due to the tax

For educational purposes. Not financial advice. Market conventions simplified.

Ryan O'Connell, CFA
Calculator by Ryan O'Connell, CFA

Tax Analysis Results

Pre-Tax Equilibrium
Price (P*) $24.00
Quantity (Q*) 52.00
Post-Tax Equilibrium
Buyers Pay $27.00
Sellers Get $22.00
Quantity 46.00
Tax Wedge $5.00
Quantity Change -6.00
Tax Burden Split
Buyer's Burden 60% ($3.00/unit)
Seller's Burden 40% ($2.00/unit)
Revenue & Welfare Effects
Tax Revenue $230.00
Deadweight Loss $15.00
Change in CS -$147.00
Change in PS -$98.00
Welfare Identity Check
|ΔCS| + |ΔPS| = $245.00 = $230.00 + $15.00 = Revenue + DWL ✓

Supply & Demand Diagram

Supply and demand diagram with tax wedge visualization
Demand (D) Supply (S) S + T Tax Revenue DWL

Formula Breakdown

DWL = ½ × T × (Q* − Qtax)
Buyer's Share = d / (b + d)  |  Seller's Share = b / (b + d)

Understanding Tax Incidence & Deadweight Loss

What Is Tax Incidence?

Tax incidence refers to how the burden of a tax is distributed between buyers and sellers. A key insight from economics is that the statutory incidence (who legally pays the tax) does not determine the economic incidence (who actually bears the burden). The economic burden is determined entirely by the relative elasticities of supply and demand.

Tax Incidence Formulas
Buyer's Share = d / (b + d) = PES / (PES + PED)
Seller's Share = b / (b + d) = PED / (PES + PED)
Source: Mankiw, Principles of Economics, Ch. 6

What Is Deadweight Loss?

Deadweight loss (DWL) represents the reduction in total economic surplus caused by a tax. It measures the value of mutually beneficial trades that no longer occur because the tax drives a wedge between the price buyers pay and the price sellers receive. The DWL triangle on the supply and demand diagram captures this lost surplus.

Importantly, DWL grows with the square of the tax rate for linear curves: doubling the tax quadruples the deadweight loss. This result supports the economic principle that broad, low-rate taxes are more efficient than narrow, high-rate taxes.

How Elasticity Determines Tax Burden

The more inelastic side of the market bears a larger share of the tax burden:

  • Inelastic demand (small b): Buyers cannot easily reduce purchases, so they absorb most of the price increase.
  • Inelastic supply (small d): Sellers cannot easily reduce production, so they absorb most of the price decrease.
  • Perfectly inelastic demand (b = 0): Buyers pay the entire tax. No quantity change. DWL = 0.
Verification Example (Mankiw Ch. 8 style): Qd = 100 - 2P, Qs = -20 + 3P, T = $5.
P* = $24, Q* = 52. Buyer pays $27, seller gets $22, Q = 46.
Revenue = $230, DWL = $15, |ΔCS| + |ΔPS| = $245 = Revenue + DWL ✓

Frequently Asked Questions

Deadweight loss is the reduction in total economic surplus caused by a tax. It represents the value of transactions that would have occurred in a free market but don't happen because the tax raises the price buyers pay above the price sellers receive. The "tax wedge" between buyer and seller prices eliminates trades where the buyer's willingness to pay exceeds the seller's cost but falls within the wedge. Graphically, DWL is the triangle between the supply and demand curves from the post-tax quantity to the free-market quantity.

The economic burden of a tax is determined by the relative elasticities of supply and demand, not by who legally pays the tax. The side of the market that is more inelastic (less responsive to price changes) bears a larger share of the tax burden. Mathematically, the buyer's share equals the price elasticity of supply divided by the sum of the elasticities. With linear curves Qd = a - bP and Qs = -c + dP, the buyer's share is d/(b+d) and the seller's share is b/(b+d).

No. This is one of the most important results in public finance: the economic incidence of a tax is independent of its statutory (legal) incidence within the standard competitive, per-unit-tax model. Whether the government collects the tax from buyers or sellers, the equilibrium prices paid and received, the quantity traded, tax revenue, and deadweight loss are all identical. Only the relative elasticities of supply and demand determine who bears the economic burden.

The more inelastic side of the market bears a larger share because they cannot easily adjust their behavior. If demand is inelastic (steep demand curve, small b), buyers can't easily reduce purchases, so they absorb most of the price increase. If supply is inelastic (steep supply curve, small d), sellers can't easily reduce production, so they absorb most of the price decrease. In the extreme, perfectly inelastic demand (b = 0) means buyers pay the entire tax with no deadweight loss.

Deadweight loss increases more than proportionally with the tax rate. Since DWL = ½ × T × ΔQ and ΔQ itself increases with T (for linear curves, ΔQ = T × bd/(b+d)), DWL grows with the square of the tax rate: DWL = ½ × T² × bd/(b+d). Doubling the tax rate quadruples the deadweight loss. This is why economists generally favor broad-based taxes with low rates over narrow taxes with high rates.

When demand is inelastic (holding supply elasticity fixed), buyers continue purchasing nearly the same quantity despite the higher price, so fewer transactions are lost. In the extreme case of perfectly inelastic demand (b = 0), quantity doesn't change at all, and DWL is zero — the tax is fully absorbed by buyers with no efficiency loss. This is why economists sometimes advocate taxing goods with inelastic demand (like cigarettes or gasoline) if the goal is to raise revenue with minimal distortion.

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Disclaimer

This calculator is for educational purposes only. Results are based on linear supply and demand curves with a per-unit tax. Real-world markets involve nonlinear curves, multiple taxes, externalities, and other factors not captured here. This tool should not be used for business, investment, or policy decisions.