Price & Income Elasticity Calculator

Calculate PED & YED step-by-step with zero formula confusion. Specifically built for Cambridge IGCSE Economics (0455).

⚠️ Classic Exam Trap: Percentage Change must be calculated as $\frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100\%$. Always divide by the initial starting value!

IGCSE Economics (0455) Topic 2.5 & 2.6 Key Summary

Elasticity Concept Formula Numerical Value Economic Meaning
Price Elastic Demand $$\text{PED} = \frac{\% \Delta Q_d}{\% \Delta P}$$ $|\text{PED}| > 1$ Quantity demanded is highly responsive to price changes. (e.g., luxury goods, items with close substitutes).
Price Inelastic Demand $$\text{PED} = \frac{\% \Delta Q_d}{\% \Delta P}$$ $|\text{PED}| < 1$ Quantity demanded is unresponsive to price changes. (e.g., necessities, addictive goods).
Unitary Elasticity $$\text{PED} = \frac{\% \Delta Q_d}{\% \Delta P}$$ $|\text{PED}| = 1$ Proportional change in quantity equals the proportional change in price. Total revenue remains constant.
YED: Normal Good $$\text{YED} = \frac{\% \Delta Q_d}{\% \Delta \text{Income}}$$ $\text{YED} > 0$ Demand increases as consumer income rises. ($\text{YED} > 1$ = Luxury, $0 < \text{YED} < 1$ = Necessity).
YED: Inferior Good $$\text{YED} = \frac{\% \Delta Q_d}{\% \Delta \text{Income}}$$ $\text{YED} < 0$ Demand decreases as consumer income rises (consumers switch to higher quality alternatives).

PED & Total Revenue (TR) Matrix

Demand Elasticity Price Change Impact on Total Revenue (TR = P × Q)
Price Elastic ($|\text{PED}| > 1$) Price Increases ($\uparrow$) Total Revenue Falls ($\downarrow$)
Price Cuts ($\downarrow$) Total Revenue Rises ($\uparrow$)
Price Inelastic ($|\text{PED}| < 1$) Price Increases ($\uparrow$) Total Revenue Rises ($\uparrow$)
Price Cuts ($\downarrow$) Total Revenue Falls ($\downarrow$)
Cambridge Exam Worked Example (Paper 2)
Official Cambridge Mark Scheme Structure

Question: A bus operator increases single fare tickets from $\$4.00$ to $\$5.00$. The number of daily passengers decreases from $1,200$ to $1,050$.
(a) Calculate the Price Elasticity of Demand (PED). [3 marks]
(b) Explain whether the bus company should increase prices to raise revenue. [2 marks]

Official Cambridge Marking Steps:
  • $\% \Delta Q_d$: $\frac{1050 - 1200}{1200} \times 100\% = -12.5\%$ [1 mark]
  • $\% \Delta P$: $\frac{5 - 4}{4} \times 100\% = +25\%$ [1 mark]
  • PED Answer: $\text{PED} = \frac{-12.5\%}{+25\%} = \mathbf{-0.5}$ [1 mark]
  • Analysis (b): Demand is price inelastic ($|-0.5| < 1$). Raising prices will increase total revenue because the percentage drop in passengers is smaller than the percentage price increase.

4 Common Mistakes Highlighted by Examiners

❌ Confusing New vs Original

Always divide by the original starting figure ($P_1$ or $Q_1$). Dividing by the new figure is the #1 reason students lose marks.

❌ Removing Signs in YED

While minus signs in PED are often ignored, the $+$ or $-$ sign in YED is crucial for defining Normal vs Inferior goods.

❌ Forgetting the Percentage Symbol

Do not divide absolute changes ($\Delta Q / \Delta P$). You must divide percentage changes ($\% \Delta Q / \% \Delta P$).

❌ Confusing Slope & Elasticity

Elasticity changes along a straight-line demand curve. Never assume a straight line has constant elasticity!

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