No, in order to increase revenue, the price should be increased is not a necessity. The change in total revenue due to a change in price depends only on the elasticity of demand.
If the demand of a good is inelastic then it means that consumers will demand the same irrespective of the price of the product. In this case, increasing the price of a product will lead to an increase in total revenue.
On the other hand, if the demand of a good is elastic then an increase in price will lead to a fall in quantity demanded. The percentage change in quantity demanded will be more than the percentage change in price. So, in this case, the total revenue will fall if there is an increase in the price of a good.
Therefore, the seller will increase price if the demand for the good is inelastic and decrease price if the demand for the good is elastic in order to increase the total revenue.
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