AP Microeconomics: Price Elasticity of Supply (PES) and Cross?Price/Income Elasticity

AP Microeconomics – Price Elasticity of Supply (PES) and Cross?Price/Income Elasticity

## What This Is
Price Elasticity of Supply (PES) measures how much the quantity supplied of a good responds to a change in its price. Cross?price elasticity (XED) gauges how the quantity demanded of one good reacts to a price change of another good, while income elasticity of demand (YED) shows how demand changes as consumer income shifts. These elasticities are core AP?Micro concepts because every FRQ that involves a tax, subsidy, or market shock asks you to predict who “bears the burden,” how producers adjust, or whether two goods are substitutes or complements.
Real?world example: When the U.S. government raised the federal excise tax on cigarettes, manufacturers’ supply curves shifted left (higher cost per unit) while the quantity supplied fell; the size of the shift depended on the PES of cigarettes (relatively inelastic in the short run because factories cannot instantly change output).

## Key Terms & Formulas

• PES (Price Elasticity of Supply) = %?Qs / %?P – measures responsiveness of quantity supplied (Qs) to a price change (P).
• Elastic Supply: PES?>?1 – producers can quickly increase output when price rises (e.g., software services).
• Inelastic Supply: PES?<?1 – output changes little with price (e.g., oil drilling rigs).
• Unit?Elastic Supply: PES?=?1 – percentage change in quantity equals percentage change in price.
• Supply Curve (S): Graph with price (P) on the vertical axis and quantity supplied (Qs) on the horizontal axis; upward?sloping because higher prices incentivize more production.
• Cross?Price Elasticity of Demand (XED) = %?Qd? / %?P? – measures how the quantity demanded of good?1 changes when the price of good?2 changes.
• XED?>?0-Substitutes (e.g., butter vs. margarine).
• XED?<?0-Complements (e.g., printers vs. ink cartridges).
• Income Elasticity of Demand (YED) = %?Qd / %?Y – shows how demand reacts to changes in consumer income (Y).
• YED?>?1-Luxury Good (e.g., high?end smartphones).
• 0?<?YED?<?1-Necessity (e.g., bread).
• YED?<?0-Inferior Good (e.g., generic instant noodles).

## Step?by?Step / Process Flow

1. Identify the shock (tax, subsidy, input?price change, etc.) and decide which curve(s) shift.
2. Determine the elasticity of the relevant market:
3. If PES is elastic, draw a large leftward shift of the supply curve for a cost?increase shock.
4. If PES is inelastic, draw a modest shift.
5. Sketch the graph:
6. Plot the original Supply (S?) and Demand (D) curves.
7. Shift the supply curve to S? (left for higher costs, right for lower costs).
8. Mark the original equilibrium (E?) and the new equilibrium (E?).
9. Calculate the new equilibrium price and quantity (use the given equations or percentage changes).
10. Interpret the result:
11. State who bears the burden (consumers vs. producers) based on relative elasticities.
12. For XED/YED questions, plug the percentage changes into the formulas and label the relationship (substitutes, complements, normal, luxury, inferior).

## Common Mistakes

• Mistake: Treating a “change in price” as a shift of the supply curve.
  Correction: A price change causes a movement along the existing supply curve; only changes in production costs, technology, or input prices shift the curve.

• Mistake: Forgetting that PES is calculated with percentage changes, not absolute changes.
  Correction: Use %?Qs ÷ %?P (or the midpoint formula) to avoid sign errors and to compare across different price levels.

• Mistake: Assuming XED is always positive because “more price = more demand.”
  Correction: XED can be negative for complements; always check the sign to classify the relationship.

• Mistake: Mixing up income elasticity with price elasticity when a question mentions “as income rises, demand falls.”
  Correction: That scenario describes a negative YED (inferior good), not a price?elastic response.

• Mistake: Ignoring the time?frame qualifier (short?run vs. long?run) when judging PES.
  Correction: Supply is usually more elastic in the long run because firms can adjust plant size, hire workers, or adopt new technology.

## AP Exam Insights

1. FRQ Prompt Pattern: “A tax is imposed on good?X. Explain how the tax burden is divided between buyers and sellers, and illustrate the effect on equilibrium using a supply?and?demand diagram.” – You must state the relative elasticities, draw the supply shift, label the tax wedge, and identify the incidence.
2. Multiple?Choice Trick: Questions often give a numeric PES (e.g., 0.4) and ask whether a price increase will cause a large or small change in quantity supplied. Remember: PES?<?1-small change.
3. Cross?Price vs. Income: AP?Micro frequently pairs XED with YED in a single item. Be ready to compute both and then label the goods (substitutes/complements; normal/luxury/inferior).
4. Graphing Requirement: The exam expects a clearly labeled supply curve shift (S?-S?) and the resulting equilibrium points (E?, E?). Include the axes, the tax wedge (if applicable), and a brief caption.

## Quick Check Questions

1. MC: If the PES for wheat is 0.2 in the short run, a 10?% rise in wheat price will cause quantity supplied to
2. A) Increase by 2?%
3. B) Increase by 5?%
4. C) Increase by 10?%

5. D) Increase by 20?%
   Answer: A) Increase by 2?% – PES?=?%?Qs / %?P-%?Qs?=?0.2?×?10?%?=?2?%.

6. FRQ?style: The price of coffee beans rises 15?%. The cross?price elasticity of demand for tea with respect to coffee is –0.6. What happens to the quantity demanded of tea?
   Answer: %?Qd=?XED?×?%?P_coffee?=?(–0.6)?×?15?%?=?–9?%; tea demand falls, confirming that tea and coffee are complements.

7. MC: A 5?% increase in consumer income leads to a 12?% increase in demand for concert tickets. The income elasticity of demand is

8. A) 0.42
9. B) 2.4
10. C) 5.0
11. D) 17.0
    Answer: B) 2.4 – YED?=?%?Qd / %?Y?=?12?% / 5?%?=?2.4 (a luxury good).

## Last?Minute Cram Sheet

1. PES = %?Qs / %?P – use the midpoint formula for precision.
2. Supply curve: P (vertical) vs. Qs (horizontal); upward?sloping.
3. Elastic supply (PES?>?1)-producers can quickly adjust output.
4. Inelastic supply (PES?<?1)-output changes little with price.
5. XED?>?0-substitutes; XED?<?0-complements.
6. YED?>?1-luxury; 0?<?YED?<?1-necessity; YED?<?0-inferior.
7. Short?run PES is usually lower than long?run PES because firms need time to change capacity.
8. Tax incidence: The side with the more inelastic curve bears a larger share of the tax burden.
9. “Supply increases” means the curve shifts right, not up. A price rise moves you along the existing curve.
10. When a cost?increase shock hits, shift the supply curve left; when a cost?decrease (subsidy) hits, shift it right.