If demand is inelastic and the price falls, the total revenue
A) rises.
B) falls.
C) remains constant.
D) might rise, fall, or remain constant.
E) becomes negative.
The correct answer and explanation is :
Correct Answer: B) falls.
Explanation (300 words):
In economics, price elasticity of demand measures how sensitive the quantity demanded of a good is to a change in its price. When demand is inelastic, the percentage change in quantity demanded is less than the percentage change in price. This means consumers do not significantly change the quantity they buy when the price changes.
Inelastic demand occurs for goods that are necessities or have few substitutes—examples include insulin for diabetics, gasoline in the short term, or basic utilities like water.
Let’s explore what happens when the price of a good falls and demand is inelastic:
- Price falls: The seller receives less money per unit sold.
- Quantity demanded increases, but not enough to offset the drop in price due to the inelastic nature of demand.
Total revenue (TR) is calculated as:
$$
\text{Total Revenue} = \text{Price} \times \text{Quantity}
$$
Since the increase in quantity demanded is proportionally smaller than the decrease in price, total revenue decreases. Here’s a numerical example to illustrate:
- Original price = \$10; Quantity sold = 100 units; TR = \$1,000
- Price drops to \$9 (10% decrease); Quantity increases to 105 units (5% increase); TR = \$945
In this case, even though more units are sold, the revenue drops from \$1,000 to \$945. This illustrates the key characteristic of inelastic demand: price and total revenue move in the same direction.
Therefore, when demand is inelastic and the price falls, total revenue falls as well. Conversely, if price rises under inelastic demand, total revenue would increase, since the loss in quantity sold is proportionally smaller than the gain in price per unit.
This principle is crucial for businesses and policymakers when setting prices or taxes on goods with inelastic demand.