Relationship between PED and the amount spent by consumers and revenue raised by firms
The Allocation of Resources – Price Elasticity of Demand (PED)
What is Price Elasticity of Demand?
Price Elasticity of Demand measures how much the quantity demanded of a good changes when its price changes. It tells us whether consumers are elastic (very responsive) or inelastic (not very responsive) to price changes.
Formula (written in LaTeX): $PED = \frac{\% \Delta Q_d}{\% \Delta P}$
How to Interpret PED Values
- Elastic demand (|PED| > 1) – Quantity changes more than price. Example: 🍕 pizza, a small price drop leads to a big jump in orders.
- Unit‑elastic demand (|PED| = 1) – Quantity changes proportionally with price.
- Inelastic demand (|PED| < 1) – Quantity changes less than price. Example: 🚗 fuel – people still need it even if the price rises.
Analogy: The Rubber‑Band Test
Imagine a rubber band. If you pull it (increase price) and it stretches a lot (quantity falls a lot), the demand is elastic. If it barely stretches, demand is inelastic.
Example Calculation
Pizza price rises from $8 to $9 (a 12.5% increase). Quantity sold falls from 100 to 90 (a 10% decrease).
PED = $\frac{-10\%}{12.5\%} = -0.8$ → inelastic demand (|PED| < 1).
Impact on Consumer Spending
Total amount spent by consumers = price × quantity.
| Scenario | Price ($) | Quantity (units) | Total Spending ($) |
|---|---|---|---|
| Before price rise | 8 | 100 | 800 |
| After price rise | 9 | 90 | 810 |
Even though fewer pizzas were sold, total spending increased because the price increase outweighed the drop in quantity – a typical result when demand is inelastic.
Impact on Firm Revenue
Firm revenue (TR) = price × quantity. The effect of a price change on revenue depends on PED.
| Elasticity Type | Effect of Lowering Price | Effect of Raising Price |
|---|---|---|
| Elastic (|PED| > 1) | Revenue increases (quantity rises more than price falls). | Revenue decreases (quantity falls more than price rises). |
| Unit‑elastic (|PED| = 1) | Revenue stays unchanged. | Revenue stays unchanged. |
| Inelastic (|PED| < 1) | Revenue decreases (quantity rises less than price falls). | Revenue increases (quantity falls less than price rises). |
Quick Check: What Would Happen?
- Price of a popular video game drops by 20%. The quantity sold increases by 50%. Is the demand elastic or inelastic?
- Fuel prices rise by 10%, but quantity demanded falls by only 5%. What does this say about consumer spending on fuel?
Answers: 1️⃣ Elastic (|PED| = 2.5). 2️⃣ Inelastic – consumers still buy almost the same amount, so total spending on fuel goes up.
Key Takeaways
- Elasticity tells us how sensitive demand is to price changes.
- Consumer spending (total amount spent) = price × quantity.
- Firm revenue changes with price depending on whether demand is elastic, unit‑elastic, or inelastic.
- Use the PED formula to predict whether a price change will raise or lower revenue.
Revision
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