Tax Incidence Worksheet with Answers and Deadweight Loss

This tax incidence worksheet asks students to calculate who bears a per-unit tax, distinguish tax revenue from lost gains from trade, and compare a $3 tax with a $6 tax. The original market equations, student questions, and worked teacher key are all below. Use the written equations for every numerical answer. Any interactive graph displayed with this page is for exploration and may use different default data.

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Supply and demand at equilibrium, drawn by the interactive graph. Tap it to drag the curves, open the full version, or put it on your own site free, or turn it into a five-minute class activity.

Teacher setup

Suggested duration is 35 minutes: five for the untaxed market, ten for the first tax, ten for the larger tax, and ten for elasticity and explanation. Students need paper and a calculator. Copy the student section without the visible key for independent work. Before beginning, students should be comfortable with equilibrium and triangle areas; the consumer and producer surplus worksheet supplies practice with both.

Assume a competitive market with linear demand and supply, no external costs or benefits, no other taxes or subsidies, full tax compliance, and no collection or transaction costs. Demand measures marginal willingness to pay and supply measures marginal resource cost. All mutually feasible trades occur, with goods going to the highest-value buyers and coming from the lowest-cost sellers. Count each dollar of government revenue as a transfer in total surplus; do not add any separate benefit from spending it. These are modeling assumptions, not claims about every real tax.

Student worksheet

A. Find the untaxed market

The invented market sells reusable containers. Quantity Q is containers per day, treated as continuous in the graph model. Prices are dollars per container. Inverse demand is Pb = 20 - 0.2Q. Inverse supply is Ps = 2 + 0.1Q. Pb is the amount paid by buyers; Ps is the amount sellers keep after tax. Without a tax, Pb = Ps.

1. Solve for the untaxed equilibrium price and quantity.

2. Draw demand and supply with price on the vertical axis. Label both vertical intercepts and equilibrium.

3. Calculate consumer surplus, producer surplus, and total surplus before tax.

B. Impose a $3 per-unit tax

The government collects $3 from sellers for every container sold. The buyer price and seller net price therefore satisfy Pb - Ps = 3.

1. Substitute the two inverse curves into that tax-wedge equation. Solve for quantity, buyer price, and seller net price.

2. Relative to the untaxed price, calculate the buyers' burden per traded unit and the sellers' burden per traded unit. Express each as a share of the $3 tax.

3. Calculate daily government revenue. Why is the tax multiplied by the new quantity rather than the original quantity?

4. Calculate consumer surplus and producer surplus after tax. Add government revenue and compare with the original total surplus.

5. Draw the vertical tax wedge at the new quantity. Shade the revenue rectangle and the triangle of lost gains from trade. Check the triangle using one-half x tax x reduction in quantity.

C. Compare a $6 tax

Replace the $3 tax with a $6 tax. This is a separate policy, not an additional $6 on top of the first tax. Repeat the calculations for quantity, both prices, both per-unit burdens, revenue, and deadweight loss.

Does doubling the tax double revenue? Does it double deadweight loss? Explain each answer with the calculated quantities and areas.

D. Interpret incidence

At the original equilibrium, demand's price-elasticity magnitude is 2/3 and supply's is 4/3. Which side is less responsive? Does the division of the tax match that comparison?

A classmate says, 'Sellers send the entire tax to the government, so sellers bear the entire burden.' Correct the statement. Under the same assumptions, would collecting the same per-unit tax from buyers instead change the wedge between buyers' total payment and sellers' net receipt?

Teacher answer key

Untaxed: Set 20 - 0.2Q = 2 + 0.1Q. Then 18 = 0.3Q, so Q = 60 and P = $8. The graph's intercepts are $20 for demand and $2 for supply, with equilibrium at (60, 8). Consumer surplus is one-half x 60 x (20 - 8) = $360 per day. Producer surplus is one-half x 60 x (8 - 2) = $180 per day. Total surplus is $540 per day.

$3 tax: The wedge equation is (20 - 0.2Q) - (2 + 0.1Q) = 3. Thus 18 - 0.3Q = 3 and Q = 50. Buyers pay 20 - 0.2(50) = $10; sellers keep 2 + 0.1(50) = $7. The difference is exactly $3. Buyers bear $10 - $8 = $2 per traded unit, or two-thirds of the tax. Sellers bear $8 - $7 = $1, or one-third. These are price-incidence measures on traded units, not the full changes in each group's surplus.

Revenue is $3 x 50 = $150 per day. Only the 50 completed sales are taxed. Consumer surplus is one-half x 50 x (20 - 10) = $250; producer surplus is one-half x 50 x (7 - 2) = $125. Including revenue gives $525 per day, so deadweight loss is $540 - $525 = $15 per day. The triangle check is one-half x 3 x (60 - 50) = $15. Government revenue is transferred purchasing power, not part of that lost-gains triangle.

$6 tax: Solve 18 - 0.3Q = 6 to obtain Q = 40. Substitution gives Pb = $12 and Ps = $6. Revenue is $6 x 40 = $240. Surplus triangles are one-half x 40 x 8 = $160 for buyers and one-half x 40 x 4 = $80 for sellers. Total surplus is $160 + $80 + $240 = $480. Deadweight loss is $60, also one-half x 6 x 20.

Doubling the tax raises revenue by $90, or 60%, rather than doubling it, because the taxed quantity falls. Deadweight loss quadruples from $15 to $60: both the tax wedge and the quantity reduction double. This exact relationship follows from these unchanged linear curves while positive trade continues; it is not a universal prediction for all tax systems.

Incidence: Demand is less elastic than supply at the original equilibrium, and buyers bear the larger share. The stated elasticities follow from Qd = 100 - 5Pb and Qs = 10Ps - 20: at P = 8 and Q = 60, magnitudes are 5 x 8/60 = 2/3 and 10 x 8/60 = 4/3. Statutory remittance identifies who sends the payment, not who experiences the price change. Collecting from buyers instead leaves the same tax wedge and the same equilibrium in this model.

Follow-up and concept references

Use the tax incidence explanation for a second treatment of legal versus economic burden. Explore the supply and demand sandbox separately; its default values are not the worksheet data. The original equations and answers above use incidence principles checked against OpenStax, Elasticity and Pricing and surplus-area definitions checked against OpenStax, Demand, Supply, and Efficiency.