To determine the elasticity of demand based on the given information, we will use the formula for the price elasticity of demand (PED), which measures how much the quantity demanded of a good responds to a change in its price. The formula is:
[
\text{Price Elasticity of Demand (PED)} = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}}
]
Step 1: Calculate the Changes in Quantity and Price
- Initial Quantity Demanded (Q1): 20
- New Quantity Demanded (Q2): 30
- Initial Price (P1): N4
- New Price (P2): N5
Now, we calculate the changes:
-
Change in Quantity Demanded (ΔQ):
[
ΔQ = Q2 - Q1 = 30 - 20 = 10
]
-
Change in Price (ΔP):
[
ΔP = P2 - P1 = 5 - 4 = 1
]
Step 2: Calculate the Percentage Changes
Next, we calculate the percentage changes in quantity demanded and price.
-
Percentage Change in Quantity Demanded:
[
\text{Percentage Change in Quantity} = \frac{ΔQ}{Q1} \times 100 = \frac{10}{20} \times 100 = 50\%
]
-
Percentage Change in Price:
[
\text{Percentage Change in Price} = \frac{ΔP}{P1} \times 100 = \frac{1}{4} \times 100 = 25\%
]
Step 3: Calculate the Price Elasticity of Demand
Now we can substitute these values into the elasticity formula:
[
\text{PED} = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}} = \frac{50\%}{25\%} = 2
]
Conclusion
The elasticity of demand is
2, which means that the demand is elastic. This indicates that the quantity demanded changes by a larger percentage than the price change.
Explanation of Options
-
Option A: Zero - This would imply that the quantity demanded does not change at all with a change in price, which is not the case here since the quantity demanded increased significantly.
-
Option B: 1 - This indicates unitary elasticity, where the percentage change in quantity demanded is equal to the percentage change in price. However, we calculated that the percentage change in quantity demanded (50%) is greater than the percentage change in price (25%).
-
Option C: 2 - This is the correct answer. It indicates that the demand is elastic, meaning consumers are quite responsive to price changes.
-
Option D: 5 - This would suggest an extremely elastic demand, where the quantity demanded changes five times as much as the price change. Our calculations show that the elasticity is 2, not 5.
Revision Summary
- The price elasticity of demand measures how quantity demanded responds to price changes.
- The formula for PED is: (\text{PED} = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}}).
- In this case, the PED calculated is 2, indicating elastic demand.
- Understanding the relationship between price changes and quantity demanded is crucial for analyzing consumer behavior.