If demand is price inelastic, then when price rises, total revenue
a. will fall.
b. will rise.
c. will remain unchanged.
d. may rise, fall, or remain unchanged. More information is needed to determine the change in total revenue with certainty.
The correct answer and explanation is :
The correct answer is b. will rise.
Explanation:
When the demand for a product is price inelastic, it means that the quantity demanded does not respond strongly to price changes. In other words, consumers’ willingness to purchase the good or service is not very sensitive to price increases or decreases. Price elasticity of demand is a measure of how much the quantity demanded of a good responds to a change in price. If the demand is inelastic, the elasticity coefficient (Ed) is less than 1, indicating that the percentage change in quantity demanded is smaller than the percentage change in price.
Why Total Revenue Will Rise:
Total revenue (TR) is calculated as the price of the good multiplied by the quantity sold:
$$
TR = P \times Q
$$
When demand is inelastic, an increase in price will lead to a smaller reduction in quantity demanded. This is because consumers are not very responsive to price increases. Therefore, while the quantity demanded decreases slightly, the increase in price more than compensates for this decrease, leading to an overall increase in total revenue.
For example, if the price of a product rises by 10% but the quantity demanded decreases by only 2%, the total revenue will increase because the price increase has a greater effect on revenue than the small decrease in quantity demanded. This effect can be illustrated mathematically as follows:
$$
\text{Percentage change in total revenue} = \text{Percentage change in price} + \text{Percentage change in quantity demanded}
$$
In the case of inelastic demand, the percentage change in price is larger than the percentage change in quantity demanded (in absolute value), meaning that total revenue rises.
Example:
Consider a product like gasoline, which is often considered price inelastic. When gasoline prices rise, people may still need to buy a similar amount of gasoline because there are limited alternatives in the short term. As a result, even though fewer people may purchase the gasoline (due to the higher price), the increase in price leads to higher total revenue.
Therefore, when demand is inelastic, a price increase results in an increase in total revenue, which is why the correct answer is b. will rise.