calculation of price, income and promotional elasticity of demand
8.1 Marketing Analysis – Elasticity
What is Elasticity? 🤔
Elasticity measures how much the quantity demanded of a product changes when a factor (price, income, or promotion) changes. Think of it like a rubber band: the more elastic, the more it stretches for a small push. 📏
Price Elasticity of Demand (PED) 📉
The % change in quantity demanded divided by the % change in price. $$PED = \frac{\% \Delta Q_d}{\% \Delta P}$$
- Find the initial price and quantity.
- Find the new price and quantity after the change.
- Calculate the percentage changes:
- $\% \Delta P = \frac{P_{\text{new}}-P_{\text{old}}}{P_{\text{old}}} \times 100$
- $\% \Delta Q_d = \frac{Q_{\text{new}}-Q_{\text{old}}}{Q_{\text{old}}} \times 100$
- Divide the two percentages to get PED.
Interpretation:
- |PED| > 1 : Demand is elastic (big reaction to price).
- |PED| < 1 : Demand is inelastic (small reaction).
- |PED| = 1 : Unit‑elastic.
| Scenario | Initial Price (P₀) | New Price (P₁) | Initial Qty (Q₀) | New Qty (Q₁) | PED |
|---|---|---|---|---|---|
| Candy price drop | $1.00 | $0.80 | 100 units | 150 units | 1.5 |
| Premium coffee price rise | $5.00 | $6.00 | 200 units | 180 units | -0.5 |
Income Elasticity of Demand (YED) 💰
$$YED = \frac{\% \Delta Q_d}{\% \Delta I}$$
- Measure the change in consumer income.
- Measure the resulting change in quantity demanded.
- Calculate the percentage changes and divide.
Interpretation:
- YED > 0 : Normal good (demand rises with income).
- YED > 1 : Luxury good (demand rises more than income).
- 0 < YED < 1 : Necessity (demand rises but less than income).
- YED < 0 : Inferior good (demand falls as income rises).
| Scenario | Initial Income (I₀) | New Income (I₁) | Initial Qty (Q₀) | New Qty (Q₁) | YED |
|---|---|---|---|---|---|
| Students buying textbooks | $30,000 | $32,000 | 500 units | 520 units | 0.8 |
| Luxury cars | $50,000 | $55,000 | 200 units | 240 units | 2.0 |
Promotional Elasticity of Demand (PED) 📣
Measures how quantity demanded changes when promotional effort (e.g., advertising spend, discount rate) changes. $$PE = \frac{\% \Delta Q_d}{\% \Delta P_{\text{promo}}}$$
- Record the initial promotional spend and sales.
- Increase the spend and record new sales.
- Compute the percentage changes and divide.
Interpretation:
- PE > 1 : Demand is highly responsive to promotion.
- PE < 1 : Demand is less responsive.
| Scenario | Initial Promo Spend (P₀) | New Promo Spend (P₁) | Initial Sales (Q₀) | New Sales (Q₁) | PE |
|---|---|---|---|---|---|
| Social media campaign for sneakers | $10,000 | $15,000 | 1,000 units | 1,500 units | 1.5 |
| Email discount for coffee | $2,000 | $2,200 | 3,000 cups | 3,100 cups | 0.5 |
Quick Summary ??
- Price Elasticity: How much buyers change quantity when price changes.
- Income Elasticity: How much buyers change quantity when their income changes.
- Promotional Elasticity: How much buyers change quantity when promotion changes.
Remember: the higher the absolute value, the more responsive the demand. Use these tools to decide pricing, target markets, and marketing budgets. 🚀
Revision
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