Microeconomics Essentials: Taxes—Tax Incidence, Wedges, and Efficiency Costs

Per-Unit Taxes as a “Wedge” Between Buyers and Sellers

A per-unit tax (also called a specific tax) is a fixed dollar amount charged on each unit traded (e.g., $2 per gallon, $50 per ticket). The key idea is that the tax creates a wedge between the price buyers pay and the price sellers receive.

Let:

• t = per-unit tax
• P_b = price paid by buyers (consumer price)
• P_s = price received by sellers (producer price, net of tax)

The wedge condition is:

P_b = P_s + t

So a tax does not just “raise the price.” It splits the transaction price into two linked prices separated by exactly t.

Legal incidence vs economic incidence

Legal incidence is who is required to send the tax payment to the government (buyers or sellers). Economic incidence is who actually bears the burden through higher prices paid or lower prices received. A central result: the economic incidence does not depend on who legally pays (holding supply and demand fixed). The market adjusts so that the wedge holds either way.

Continue in our app.

• Listen to the audio with the screen off.
• Earn a certificate upon completion.
• Over 5000 courses for you to explore!

Or continue reading below...

Download the app

(1) Graph the Tax Wedge

On a standard price–quantity graph, the wedge can be shown in two equivalent ways:

• Tax on sellers: the supply curve shifts upward by t (because sellers require t more from buyers to keep the same net price).
• Tax on buyers: the demand curve shifts downward by t (because buyers are willing to pay t less to sellers for any total price they face).

Both representations produce the same traded quantity and the same pair (P_b, P_s) satisfying P_b - P_s = t.

(2) Find the New Equilibrium (Step-by-Step)

To solve for the post-tax outcome, you need three objects:

• Demand: Q_d(P_b) depends on the price buyers pay.
• Supply: Q_s(P_s) depends on the price sellers receive.
• The wedge: P_b = P_s + t.

Step-by-step method (algebra):

1. Write equilibrium condition in quantities: Q_d(P_b) = Q_s(P_s).
2. Use the wedge to eliminate one price: substitute P_b = P_s + t into demand (or P_s = P_b - t into supply).
3. Solve for the remaining price (either P_s or P_b).
4. Compute the other price using the wedge.
5. Compute the new quantity by plugging the relevant price into demand or supply.

Interpretation: after the tax, the traded quantity typically falls. Buyers pay more than before, sellers receive less than before, and the gap equals the tax.

Economic incidence: who bears the burden?

Define the pre-tax equilibrium price as P*. Then:

• Buyer burden per unit = P_b - P*
• Seller burden per unit = P* - P_s

These two burdens add up to the tax:

(P_b - P*) + (P* - P_s) = P_b - P_s = t

Who bears more depends on relative elasticities:

• If demand is inelastic (buyers are not very responsive), buyers tend to bear more: P_b rises a lot.
• If demand is elastic (buyers are very responsive), sellers tend to bear more: P_s falls a lot.
• Similarly, if supply is inelastic, sellers bear more; if supply is elastic, buyers bear more.

(3) Compute Tax Revenue (Rectangle)

Tax revenue equals the tax per unit times the number of units traded after the tax:

Tax Revenue = t × Q_tax

Graphically, this is a rectangle:

• Height = t (the wedge)
• Width = Q_tax (post-tax quantity)

Important: revenue depends on the post-tax quantity. If the tax causes a large drop in quantity (high responsiveness), revenue may be smaller than expected.

(4) Compute Deadweight Loss (Triangle)

The tax reduces trades that would have created gains from trade. The lost gains from the “missing” units show up as deadweight loss (DWL).

Let:

• Q* = pre-tax equilibrium quantity
• Q_tax = post-tax equilibrium quantity

The reduction in quantity is ΔQ = Q* - Q_tax. Under the standard linear-curve case, the deadweight loss is the area of a triangle:

DWL = 1/2 × t × (Q* - Q_tax)

Graphically:

• Height = t
• Base = Q* - Q_tax

How elasticity affects DWL

DWL is larger when the tax causes a larger reduction in quantity. That tends to happen when:

• Demand is more elastic (buyers cut back a lot when P_b rises), or
• Supply is more elastic (sellers cut back a lot when P_s falls).

So, even if two markets raise the same revenue per unit tax, the market with more elastic supply and/or demand typically generates a larger efficiency cost.

Comparative Incidence Examples (Inelastic vs Elastic Demand)

Example A: Inelastic demand (buyers bear more)

Consider a product with few substitutes in the short run (e.g., a necessary medication). A per-unit tax raises the buyer price substantially because buyers do not reduce quantity much. Since quantity barely falls, the wedge is mostly absorbed by buyers via higher P_b, and tax revenue can be relatively high with a relatively small quantity reduction (though equity concerns may be severe).

Example B: Elastic demand (sellers bear more)

Consider a product with many substitutes (e.g., a brand in a competitive category). If a tax raises the buyer price, buyers switch away quickly. To keep sales, sellers must accept a much lower net price P_s. Quantity falls more, so DWL tends to be larger, and revenue may be limited by the sharp contraction in trade.

Numerical Problems: Post-Tax Prices, Quantity, Revenue, and DWL

Use the wedge method. In each problem, treat demand as a function of P_b and supply as a function of P_s.

Problem 1 (compute full post-tax outcome)

Demand: Q_d = 100 - 2P_b
Supply: Q_s = 20 + 3P_s
Per-unit tax: t = 10

Step 1: Impose equilibrium and wedge

Q_d = Q_s  and  P_b = P_s + 10

Step 2: Substitute wedge into demand

100 - 2(P_s + 10) = 20 + 3P_s

Step 3: Solve for P_s

100 - 2P_s - 20 = 20 + 3P_s  →  80 - 2P_s = 20 + 3P_s  →  60 = 5P_s  →  P_s = 12

Step 4: Compute P_b and Q_tax

P_b = 12 + 10 = 22

Q_tax = 20 + 3(12) = 56

Step 5: Compute pre-tax equilibrium (for DWL)

Without tax, P_b = P_s = P:

100 - 2P = 20 + 3P  →  80 = 5P  →  P* = 16

Q* = 100 - 2(16) = 68

Step 6: Tax revenue and DWL

Revenue = t × Q_tax = 10 × 56 = 560

DWL = 1/2 × t × (Q* - Q_tax) = 1/2 × 10 × (68 - 56) = 60

Incidence check (per unit):

Buyer burden = P_b - P* = 22 - 16 = 6

Seller burden = P* - P_s = 16 - 12 = 4

6 + 4 = 10 = t

Problem 2 (same tax, more elastic demand; compare incidence)

Demand: Q_d = 160 - 8P_b
Supply: Q_s = 40 + 2P_s
Tax: t = 10

Task: Find P_s, P_b, Q_tax, and split the burden relative to P*.

Work:

160 - 8(P_s + 10) = 40 + 2P_s

160 - 8P_s - 80 = 40 + 2P_s  →  80 - 8P_s = 40 + 2P_s  →  40 = 10P_s  →  P_s = 4

P_b = 4 + 10 = 14

Q_tax = 40 + 2(4) = 48

Pre-tax equilibrium:

160 - 8P = 40 + 2P  →  120 = 10P  →  P* = 12

Incidence:

Buyer burden = P_b - P* = 14 - 12 = 2

Seller burden = P* - P_s = 12 - 4 = 8

This illustrates the pattern: with more elastic demand (steeper responsiveness), sellers end up bearing more of the tax through a much lower net price.

Problem 3 (compute revenue and DWL quickly)

Suppose a market has Q* = 1,000. A per-unit tax of t = 3 reduces quantity to Q_tax = 900.

• Tax revenue: 3 × 900 = 2,700
• Deadweight loss: 1/2 × 3 × (1,000 - 900) = 150

Problem 4 (find post-tax quantity only)

Demand: Q_d = 300 - 3P_b
Supply: Q_s = 60 + 6P_s
Tax: t = 12

Task: Find Q_tax.

300 - 3(P_s + 12) = 60 + 6P_s

300 - 3P_s - 36 = 60 + 6P_s  →  264 - 3P_s = 60 + 6P_s  →  204 = 9P_s  →  P_s = 22.666...

Q_tax = 60 + 6(22.666...) = 196