How to Solve: IB Economics – Supply/Demand Diagrams & Elasticity Calculations (PED, XED, YED, PES)

How to Solve: IB Economics – Supply/Demand Diagrams & Elasticity Calculations (PED, XED, YED, PES)

Introduction

"Mastering supply/demand diagrams and elasticity calculations can earn you 12–15% of your IB Economics SL/HL exam score—and it’s the skill that lets you predict real-world price wars, tax impacts, and even why your favorite coffee shop raises prices when wages go up. Today, you’ll learn the exact steps to draw perfect diagrams and calculate elasticity like a pro."

What You Need To Know First

1. Basic supply and demand curves: What shifts them (non-price determinants) vs. movements along them (price changes).
2. Market equilibrium: Where supply meets demand, and how to find it graphically.
3. Percentage change formula: (New – Old) / Old × 100% (given on exam sheet, but you must know how to use it).

KEY TERMS & FORMULAS

Key Terms

Formulas

1. Price Elasticity of Demand (PED) [ PED = \frac{\%\ \text{Change in Quantity Demanded}}{\%\ \text{Change in Price}} ]
2. MEMORISE THIS: Use the midpoint (arc elasticity) formula for accuracy: [ PED = \frac{(Q_2 - Q_1) / \left(\frac{Q_1 + Q_2}{2}\right)}{(P_2 - P_1) / \left(\frac{P_1 + P_2}{2}\right)} ]

3. Interpretation:

   • |PED| > 1 → Elastic
   • |PED| < 1 → Inelastic
   • PED = 0 → Perfectly inelastic (vertical demand curve)
   • PED = ∞ → Perfectly elastic (horizontal demand curve)

4. Cross Elasticity of Demand (XED) [ XED = \frac{\%\ \text{Change in Quantity Demanded of Good A}}{\%\ \text{Change in Price of Good B}} ]

5. MEMORISE THIS: Use the midpoint formula for XED too.

6. Interpretation:

   • XED > 0 → Substitutes
   • XED < 0 → Complements
   • XED = 0 → Unrelated goods

7. Income Elasticity of Demand (YED) [ YED = \frac{\%\ \text{Change in Quantity Demanded}}{\%\ \text{Change in Income}} ]

8. MEMORISE THIS: Midpoint formula applies here as well.

9. Interpretation:

   • YED > 0 → Normal good
   • YED < 0 → Inferior good
   • YED > 1 → Luxury good (income elastic)
   • 0 < YED < 1 → Necessity (income inelastic)

10. Price Elasticity of Supply (PES) [ PES = \frac{\%\ \text{Change in Quantity Supplied}}{\%\ \text{Change in Price}} ]

11. MEMORISE THIS: Midpoint formula applies.
12. Interpretation:
    • PES > 1 → Elastic supply
    • PES < 1 → Inelastic supply
    • PES = 0 → Perfectly inelastic (vertical supply curve)
    • PES = ∞ → Perfectly elastic (horizontal supply curve)

Step-by-Step Method

Part 1: Drawing Supply/Demand Diagrams

Step 1: Label axes - X-axis: Quantity (Q) - Y-axis: Price (P) - Always label both axes with units (e.g., "Price ($)", "Quantity (units)").

Step 2: Draw demand curve - Downward-sloping (negative relationship between P and Q). - Label it D.

Step 3: Draw supply curve - Upward-sloping (positive relationship between P and Q). - Label it S.

Step 4: Mark equilibrium - Where D and S intersect = equilibrium price (Pe) and quantity (Qe). - Label Pe on the Y-axis and Qe on the X-axis.

Step 5: Show shifts (if required) - Demand shifts: Right (increase), Left (decrease). - Supply shifts: Right (increase), Left (decrease). - Label the new equilibrium (P1, Q1) and show arrows for the shift.

Step 6: Add annotations - Write 1–2 sentences explaining the shift (e.g., "Increase in consumer income → Demand shifts right → Higher Pe and Qe").

Part 2: Calculating Elasticity

Step 1: Identify the formula needed - PED? XED? YED? PES? Check the question.

Step 2: Extract data from the question - Write down initial and new values for price, quantity, income, etc.

Step 3: Calculate percentage changes - Use the midpoint formula for accuracy: [ \% \text{Change} = \frac{\text{New} - \text{Old}}{\left(\frac{\text{New} + \text{Old}}{2}\right)} \times 100\% ]

Step 4: Plug into the elasticity formula - Example for PED: [ PED = \frac{\%\ \text{Change in Qd}}{\%\ \text{Change in P}} ]

Step 5: Interpret the result - State whether it’s elastic/inelastic, substitute/complement, normal/inferior, etc. - Always include units (e.g., "PED = -1.5 → Demand is elastic").

Step 6: Link to real-world meaning - Example: "Since PED is elastic, a price increase will reduce total revenue."

Worked Examples

Example 1 – Basic PED Calculation

Question: The price of a coffee increases from $3 to $4. Quantity demanded falls from 100 to 80 cups per day. Calculate PED and interpret the result.

Solution:
1. Formula: PED = %ΔQd / %ΔP
2. Data: - P1 = $3, P2 = $4 - Q1 = 100, Q2 = 80
3. Calculate %ΔQd: [ \%ΔQd = \frac{80 - 100}{\left(\frac{80 + 100}{2}\right)} \times 100\% = \frac{-20}{90} \times 100\% = -22.22\% ]
4. Calculate %ΔP: [ \%ΔP = \frac{4 - 3}{\left(\frac{4 + 3}{2}\right)} \times 100\% = \frac{1}{3.5} \times 100\% = 28.57\% ]
5. Calculate PED: [ PED = \frac{-22.22\%}{28.57\%} = -0.78 ]
6. Interpretation: - |PED| = 0.78 < 1 → Inelastic demand. - A 1% price increase leads to a 0.78% decrease in quantity demanded.

What we did and why: - Used the midpoint formula to avoid bias from starting point. - Interpreted the absolute value of PED to determine elasticity.

Example 2 – Medium XED Calculation

Question: The price of tea increases from $2 to $3. As a result, the quantity demanded of coffee increases from 50 to 60 cups per day. Calculate XED and state whether the goods are substitutes or complements.

Solution:
1. Formula: XED = %ΔQd (Coffee) / %ΔP (Tea)
2. Data: - P1 (Tea) = $2, P2 (Tea) = $3 - Q1 (Coffee) = 50, Q2 (Coffee) = 60
3. Calculate %ΔQd (Coffee): [ \%ΔQd = \frac{60 - 50}{\left(\frac{60 + 50}{2}\right)} \times 100\% = \frac{10}{55} \times 100\% = 18.18\% ]
4. Calculate %ΔP (Tea): [ \%ΔP = \frac{3 - 2}{\left(\frac{3 + 2}{2}\right)} \times 100\% = \frac{1}{2.5} \times 100\% = 40\% ]
5. Calculate XED: [ XED = \frac{18.18\%}{40\%} = 0.45 ]
6. Interpretation: - XED = 0.45 > 0 → Substitute goods.

What we did and why: - Recognized that coffee and tea are related goods, so XED applies. - A positive XED confirms they are substitutes.

Example 3 – Exam-Style YED & Diagram

Question: A country’s average income rises from $30,000 to $36,000. As a result, the demand for organic apples increases from 200 to 250 kg per week. a) Calculate YED and state whether organic apples are a normal or inferior good. b) Draw a demand and supply diagram showing the effect of this income change on the market for organic apples.

Solution (a):
1. Formula: YED = %ΔQd / %ΔIncome
2. Data: - Income1 = $30,000, Income2 = $36,000 - Q1 = 200 kg, Q2 = 250 kg
3. Calculate %ΔQd: [ \%ΔQd = \frac{250 - 200}{\left(\frac{250 + 200}{2}\right)} \times 100\% = \frac{50}{225} \times 100\% = 22.22\% ]
4. Calculate %ΔIncome: [ \%ΔIncome = \frac{36,000 - 30,000}{\left(\frac{36,000 + 30,000}{2}\right)} \times 100\% = \frac{6,000}{33,000} \times 100\% = 18.18\% ]
5. Calculate YED: [ YED = \frac{22.22\%}{18.18\%} = 1.22 ]
6. Interpretation: - YED = 1.22 > 0 → Normal good. - YED > 1 → Luxury good (income elastic).

Solution (b):
1. Draw initial diagram: - X-axis: Quantity (kg) - Y-axis: Price ($) - Draw D1 and S intersecting at Pe, Qe.
2. Shift demand right (income increase → demand increases for normal goods).
3. Label new equilibrium (P1, Q1).
4. Annotation: - "Increase in income → Demand shifts right → Higher Pe and Qe."

What we did and why: - Calculated YED to classify the good (normal vs. inferior). - Drew the correct shift (right for normal goods) and labeled everything clearly.

Common Mistakes

Exam Traps

1-Minute Recap

"Here’s your 60-second crash course:
1. Diagrams: Label axes, draw D (down) and S (up), mark equilibrium. Shifts? Right for increase, left for decrease.
2. PED: Midpoint formula → %ΔQd / %ΔP. |PED| > 1 = elastic, < 1 = inelastic.
3. XED: Positive = substitutes, negative = complements.
4. YED: Positive = normal, negative = inferior. >1 = luxury.
5. PES: Same as PED but for supply. >1 = elastic, <1 = inelastic.
6. Exam traps: Watch for % changes given directly, unrelated goods in XED, and unlabeled diagrams. Now go ace that exam!