Suppose that quantity demanded falls by 30% as a result of a 5% increase in price. The price elasticity of demand for this good is
a. inelastic and equal to 6.
b. elastic and equal to 6.
c. inelastic and equal to 0.17.
d. elastic and equal to 0.17.
The correct answer and explanation is :
To calculate the price elasticity of demand (PED), we use the following formula:
$$
\text{Price Elasticity of Demand (PED)} = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in price}}
$$
From the question:
- The percentage change in quantity demanded = −30% (it falls)
- The percentage change in price = +5%
Now substitute these values into the formula:
$$
\text{PED} = \frac{-30\%}{5\%} = -6
$$
Elasticity is usually expressed as a positive number (absolute value), so:
$$
|\text{PED}| = 6
$$
Interpretation:
A PED of 6 means that for every 1% increase in price, the quantity demanded falls by 6%. This indicates a very responsive or highly elastic demand.
Correct Answer:
b. elastic and equal to 6
Detailed Explanation (300+ words):
Price elasticity of demand (PED) is a key concept in economics that measures how much the quantity demanded of a good responds to changes in its price. The basic formula compares the percentage change in quantity demanded to the percentage change in price. If the absolute value of PED is greater than 1, demand is considered elastic, meaning consumers are highly responsive to price changes. If it is less than 1, demand is inelastic, showing that consumers are less sensitive to price changes.
In this case, the quantity demanded decreased by 30% when the price increased by just 5%. This large change in demand relative to a small change in price results in a price elasticity of 6, a number much greater than 1. This clearly indicates that demand is elastic.
Elastic demand is typically associated with goods that have many substitutes, are not necessities, or are considered luxury items. When price rises even a little, consumers easily switch to alternatives, causing a significant drop in quantity demanded.
Understanding elasticity helps businesses and policymakers make informed decisions. For instance, if a company knows that its product has elastic demand, it may avoid raising prices because doing so could significantly reduce sales and total revenue. Conversely, for inelastic goods, firms may increase prices to boost revenue, knowing demand won’t drop much.
In conclusion, since the quantity demanded fell by 30% due to a 5% price increase, the price elasticity of demand is 6, and the demand is elastic.