Tax incidence and deadweight loss calculator

Enter a tax per unit and the demand and supply lines. The graph shows the wedge the tax drives between the price buyers pay and the price sellers keep, colours the part each side bears, and works out the revenue and the deadweight loss.

Inputs

A fixed amount on every unit sold, such as a gasoline or cigarette tax. A tax of 0 means no tax.

Try both: the numbers do not change. Who bears the tax depends on the slopes, not on who hands over the money.

The price at which buyers want nothing (a in P = a − bQ).

How much the price falls for each extra unit (b). Positive; the bigger it is, the less buyers respond to price.

The lowest price at which sellers offer anything (c in P = c + dQ). It can be negative.

How much the price must rise for each extra unit sellers offer (d).

Deadweight loss

37.5

The tax cuts trade from 30 to 25 units. Buyers bear 67% of it and sellers 33%.

Price buyers pay
50
Price sellers keep
35
Quantity traded
25
Who bears the tax
Buyers 67% · sellers 33%
Tax revenue
375
Consumer surplus
625
Producer surplus
312.5
Elasticities at equilibrium
demand −0.667 · supply 1.33
Demand
P = 100 − 2Q
Supply
P = 10 + Q
Who pays a 15 per-unit tax
DS
  • Demand (D)
  • Supply (S)
  • Consumer surplus 625
  • Producer surplus 312.5
  • Buyers’ part of the tax 250
  • Sellers’ part of the tax 125
  • Deadweight loss 37.5

Drag a line, its round knob or its ring to move it. On a keyboard, tab to a knob and use the arrow keys.

Without a tax, demand P = 100 − 2Q and supply P = 10 + Q cross at a price of 40 and a quantity of 30. A tax of 15 per unit (sellers send the tax to the government) opens a gap between the price buyers pay, 50, and the price sellers keep, 35, and 25 units trade instead of 30. Buyers pay 10 more per unit and sellers keep 5 less, so buyers bear 67% of the tax and sellers 33%. The government collects 375 and 37.5 of surplus is lost as deadweight loss. It would come out the same whichever side the law taxed.

How to read this graph

  • Price goes up the side, quantity along the bottom. The blue line is demand and the orange line is supply; drag either one, or type its equation.
  • The tax opens a wedge at the new quantity. The top of the bracket is the price buyers pay (Pb). The bottom is the price sellers keep after paying the tax (Ps). The faint dashed lines mark the old equilibrium.
  • The two coloured rectangles are the tax split. The blue one, between the old price and Pb, is the part buyers bear. The orange one, between Ps and the old price, is the part sellers bear. Together they make the tax revenue.
  • The hatched triangle is the deadweight loss: trades that no longer happen.
  • The blue and orange triangles above and below are what is left of consumer and producer surplus.
  • Drag a line to see incidence move. Make demand steeper and buyers’ rectangle grows. Make supply steeper and sellers’ grows.

How it works

demand   P = a − b × Q        supply   P = c + d × Q        tax t per unit
quantity      Q = (a − c − t) ÷ (b + d)
buyers pay    Pb = a − b × Q         sellers keep   Ps = Pb − t
buyers bear   (Pb − P*) = t × b ÷ (b + d)       sellers bear   (P* − Ps) = t × d ÷ (b + d)
tax revenue       = t × Q
deadweight loss   = ½ × t × (Q* − Q) = ½ × t² ÷ (b + d)
  • a is where demand meets the price axis and c is where supply does; b and d are the slopes. Enter slopes as positive numbers.
  • In terms of elasticity, buyers’ share is Es ÷ (Es + |Ed|), evaluated at the equilibrium. The more elastic side escapes more of the tax.
  • “Incidence” two ways. Per unit, it is the change in the price each side faces. As totals, multiplying by the quantity traded gives each side’s share of the tax revenue.
  • A tax of a − c or more ends all trade. Nothing is collected and the whole surplus is lost.
  • Nothing has units. Use dollars and units, euros and tonnes, or whatever your problem uses.

Worked example

Wisconsin’s hot chocolate: supply Qs = 5P − 5 (P = 1 + 0.2Q) and demand Qd = 100 − 10P (P = 10 − 0.1Q), with a $3 tax. Open it in the calculator.

  • Without the tax: 10 − 0.1Q = 1 + 0.2Q gives Q* = 30 and P* = 7.
  • With the tax: Q = (10 − 1 − 3) ÷ 0.3 = 20. Buyers pay 10 − 0.1 × 20 = 8 and sellers keep 8 − 3 = 5.
  • Who bears it: buyers pay 8 − 7 = $1 more per unit and sellers get 7 − 5 = $2 less, so buyers bear 1 ÷ 3 of the tax. That matches b ÷ (b + d) = 0.1 ÷ 0.3.
  • Totals: revenue 3 × 20 = 60, split $20 from buyers and $40 from sellers. Deadweight loss ½ × 3 × (30 − 20) = 15.

More to try:

  • UW–Madison soft drinks: a 4 tax on Q = 20 − P and Q = 3P cuts quantity from 15 to 12. Buyers pay 8, sellers keep 4, revenue 48, deadweight loss 6, and buyers bear three quarters.
  • Kansas State gasoline: equal slopes, so the tax is split evenly: buyers pay 6 and sellers keep 4, revenue 4, deadweight loss 1.

Tips

  • Switch “who the law makes pay it” back and forth. Not one number moves. That is the point of incidence: where the law puts the bill tells you nothing about who ends up paying.
  • Flatten a line to shift the burden. A nearly flat demand line means buyers can walk away, so sellers absorb almost all of the tax.
  • Raise the tax slowly and watch the loss. Revenue grows, then shrinks: a tax near a − c collects little because almost nothing is traded.
  • Add a subsidy instead? The Supply & Demand Studio handles subsidies, and the same wedge logic applies with the sign reversed.
  • The model is a simplification. It assumes straight lines, a competitive market and no other distortions. Real tax incidence depends on real elasticities, which are estimated from data.

FAQ

Who really pays a per-unit tax, buyers or sellers?

Both, in proportion to how little each side can avoid it. Buyers bear b ÷ (b + d) of the tax and sellers d ÷ (b + d), where b and d are the slopes of demand and supply. The steeper line, the side with fewer alternatives, bears more. With demand P = 100 − 2Q and supply P = 10 + Q, buyers bear two thirds.

Does it matter whether the law taxes buyers or sellers?

No. The price buyers pay, the price sellers keep, the quantity, the revenue and the deadweight loss come out the same either way. The Wisconsin discussion handout makes this point, and you can check it with the selector above. Who hands the money over is an accounting matter, not an economic one.

Why is there a deadweight loss?

Because the tax stops some trades that were worth making. Between the new quantity and the old one, buyers value a unit more than it costs to make, but the tax makes the sale unprofitable. That lost surplus goes to nobody, neither the buyers, the sellers nor the government. It is the triangle on the graph.

What happens to the deadweight loss if I double the tax?

It quadruples, as long as some trade remains. The loss is ½ × t × (Q* − Q), and Q* − Q is itself proportional to t. The formula works out to ½ × t² ÷ (b + d). Shifting a curve sideways does not change it.

My homework says the tax incidence is $20 and $40, but the tool shows $1 and $2 per unit. Which is right?

Both describe the same thing. Per unit, consumers bear (Pb − P*) and producers (P* − Ps), $1 and $2 in the Wisconsin hot chocolate problem. Multiply each by the quantity traded and you get each side's share of the revenue, $20 and $40. The chips show both.

Sources

  1. ECON 101 Spring 2015, Homework #3 (answers), question 1g to 1i, University of Wisconsin–Madison, Economics 101 (Emily Kelly). A $3 excise tax on Qs = 5P − 5 and Qd = 100 − 10P gives price 8, quantity 20, producers net 5, revenue 60, deadweight loss 15, and tax incidence of 20 for consumers and 40 for producers.
  2. ECON 101: Principles of Microeconomics, Discussion Section Week 5 (handout with solutions), University of Wisconsin–Madison, TA Kanit Kuevibulvanich (Fall 2013). A $4 tax on Q = 20 − P and Q = 3P gives quantity 12, prices 8 and 4, revenue 48, deadweight loss 6, consumers bearing 3/4, and the answer that the legal side does not matter.
  3. The Economics of Food and Agricultural Markets, 2.5 Taxes, Andrew Barkley, Kansas State University (New Prairie Press), via LibreTexts. A gasoline tax (P = 8 − Q, P = 2 + Q, t = 2) with each change in surplus, elasticities of −5/3 and +5/3, and a pass-through fraction of 0.5.

Formula and sources last checked September 30, 2026. How we test formulas.

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