AP Microeconomics: Taxes and Incidence (Per‑unit Tax, Tax Burden, Deadweight Loss)

AP Microeconomics – Taxes and Incidence (Per‑unit Tax, Tax Burden, Deadweight Loss)

AP Microeconomics – Taxes & Incidence (Per‑unit Tax, Tax Burden, Dead‑weight Loss)

What This Is

A per‑unit tax is a fixed amount the government adds to the price of a good (e.g., a $0.10 tax on every soda can). The tax creates a tax burden (who pays what) and a dead‑weight loss (the lost surplus from reduced trade). Understanding these pieces lets you predict how a tax changes prices, quantities, and welfare— a staple of AP‑Micro multiple‑choice and FRQ questions.

Key Terms & Formulas

• Per‑unit tax (t) – a fixed dollar amount levied on each unit of a good; shown as a vertical distance between the supply curve and the “tax‑inclusive” supply curve.
• Supply with tax (S_tax) – the original supply curve shifted upward by t (price sellers must receive = P_buyer – t).
• Demand curve (D) – price (vertical) vs. quantity (horizontal) relationship for buyers; unchanged by a tax unless the tax also changes consumer preferences.
• Tax incidence – the division of the tax burden between buyers and sellers; measured by the difference between the price buyers pay (P_B) and the price sellers receive (P_S).
• Consumer surplus (CS) – area above price and below demand curve; shrinks after a tax.
• Producer surplus (PS) – area below price and above supply curve; also shrinks after a tax.
• Dead‑weight loss (DWL) – ½ · t · ΔQ, where ΔQ is the reduction in quantity traded because of the tax. It is the triangular area between the original and new equilibrium.
• Elasticity of demand (|ε_D|) – %ΔQ_D / %ΔP; the steeper (more inelastic) the demand, the larger the buyer’s share of the tax burden.
• Elasticity of supply (|ε_S|) – %ΔQ_S / %ΔP; the steeper (more inelastic) the supply, the larger the seller’s share of the tax burden.
• Incidence graph (price‑quantity diagram) – Axes: Price on vertical, Quantity on horizontal. Plot the original supply (S) and demand (D). Draw a second supply curve S_tax parallel to S but t units higher. The vertical distance between the two equilibrium prices (P_B – P_S) is the tax.
• Tax revenue (TR) – t · Q_tax, where Q_tax is the quantity sold after the tax.

Step‑by‑Step Process (Typical AP Problem)

1. Identify the tax type – per‑unit (fixed dollar amount) vs. ad‑valorem (percentage). For this guide we assume a per‑unit tax t.
2. Draw the basic D‑S diagram – label the original equilibrium (E₀) with price P₀ and quantity Q₀.
3. Shift the supply curve upward by t – draw S_tax parallel to the original supply; label the new equilibrium (E₁) with buyer price P_B, seller price P_S, and quantity Q₁.
4. Calculate the tax burden –
5. Buyer’s share = P_B – P₀
6. Seller’s share = P₀ – P_S
   
   (Use elasticity intuition: the side with the flatter curve bears more of the tax.)
7. Compute dead‑weight loss – use DWL = ½ · t · (Q₀ – Q₁). Shade the triangle between D, S, and S_tax.
8. Answer the prompt – state who bears the larger burden, give the numerical DWL, and explain why the loss occurs (reduced mutually beneficial trades).

Common Mistakes

AP Exam Insights

1. Multiple‑choice focus: Look for the phrase “who bears the larger burden?” – you must compare elasticities, not just read the graph.
2. FRQ tip: You’ll often be asked to draw the tax diagram, label the three prices (buyer, seller, pre‑tax), and compute DWL. Remember to shade the dead‑weight loss triangle and write the formula.
3. Tricky distinction: A tax creates a movement along the original supply curve (sellers receive less) and a parallel shift of the supply curve; only the shift is the tax itself.
4. Graphing requirement: The AP rubric awards points for (a) correct labeling of axes, (b) clear identification of the original and new equilibria, and (c) correct calculation of the tax burden and DWL. Missing any label can cost you points.

Quick Check Questions

1. MC: A $0.25 per‑unit tax is imposed on cigarettes. Demand is relatively inelastic, supply is elastic. Who bears the larger share of the tax?

2. Answer: Buyers. Because the more inelastic side (demand) cannot avoid the tax by reducing quantity much, so price paid by consumers rises more.

3. FRQ‑style: A $1 tax on bottled water reduces the equilibrium quantity from 100 million to 80 million units. Calculate the dead‑weight loss.

4. Answer: DWL = ½ · $1 · (100 – 80) = $10 million. The triangle’s base is the 20‑million‑unit drop; height is the $1 tax.

5. MC: Which of the following statements is always true after a per‑unit tax is imposed?
   
   A) Consumer surplus falls, producer surplus rises.
   
   B) Tax revenue equals the dead‑weight loss.
   
   C) The price buyers pay rises, the price sellers receive falls.
   
   D) Quantity demanded stays the same.

6. Answer: C. Buyers pay more, sellers receive less; the other statements are false.

Last‑Minute Cram Sheet (10 One‑liners)

1. Per‑unit tax (t) = vertical distance between original supply and S_tax.
2. Tax burden = (P_buyer – P_seller) = split of t based on relative elasticities.
3. DWL = ½ · t · ΔQ – always a triangle between D, S, and S_tax.
4. Elastic side = smaller tax share; inelastic side = larger tax share.
5. Supply shift for a per‑unit tax: parallel upward, not rightward. ⚠️
6. Tax revenue = t × quantity after tax (Q₁).
7. Consumer surplus = area above price, below demand; shrinks after tax.
8. Producer surplus = area below price, above supply; shrinks after tax.
9. When demand is perfectly inelastic, buyers bear 100 % of the tax.
10. When supply is perfectly elastic, sellers bear 0 % of the tax (price to buyers rises by the full amount).

Good luck—remember to draw clean graphs, label every point, and always tie the math back to the economic intuition!