If the demand for a good has unitary elasticity, or elasticity is −1, it is always true that an increase in its price will lead to more revenues for sellers taken as a whole.
To determine whether an increase in price will lead to more revenues for sellers when the demand for a good has unitary elasticity or elasticity is -1, we need to understand the concept of elasticity and how it relates to revenue.
Elasticity measures the responsiveness of quantity demanded to changes in price. It tells us how sensitive consumers are to price changes. In this case, when the demand for a good has unitary elasticity or elasticity is -1, it means that the percentage change in quantity demanded and the percentage change in price are equal in magnitude but opposite in direction. For example, if the price of the good increases by 10%, the quantity demanded will decrease by 10%.
Now, to determine the impact on revenue, we need to consider the relationship between price, quantity, and revenue:
Revenue = Price x Quantity
If the price increases but the quantity demanded decreases by the same percentage, the overall effect on revenue will depend on the elastic or inelastic nature of the demand:
1. Inelastic demand: When the demand is inelastic (elasticity < 1), the percentage change in quantity demanded is smaller than the percentage change in price. In this case, an increase in price will lead to an increase in revenue because the decrease in quantity demanded is relatively smaller compared to the increase in price.
2. Elastic demand: When the demand is elastic (elasticity > 1), the percentage change in quantity demanded is larger than the percentage change in price. In this case, an increase in price will lead to a decrease in revenue because the decrease in quantity demanded is relatively larger compared to the increase in price.
3. Unitary elastic demand: When the demand is unitary elastic (elasticity = -1), the percentage change in quantity demanded is equal to the percentage change in price. In this case, if the price increases, the decrease in quantity demanded will be exactly proportional to the increase in price. As a result, the change in revenue will be neutral. There will be no net increase or decrease in revenue for sellers as a whole.
Therefore, it is not always true that an increase in the price of a good with unitary elasticity (-1) will lead to more revenues for sellers as a whole. The effect on revenue will depend on the initial price and quantity, as well as the specific demands and preferences of consumers.
If the demand for a good has unitary elasticity or elasticity of -1, it means that a percentage change in price will result in an equal percentage change in quantity demanded. In this case, it is not always true that an increase in price will lead to more revenues for sellers as a whole.
When demand is unitary elastic, the increase in price would lead to a proportional decrease in quantity demanded. Although the price per unit may be higher, the decrease in quantity demanded may offset the increase in price, resulting in the same total revenue or possibly even lower revenue for sellers.
Therefore, it is not accurate to say that an increase in price will always lead to more revenues for sellers when the demand has unitary elasticity.