Final answer:
To determine the optimal unit price for maximizing revenue, one must consider the price elasticity of demand. A price reduction is advised when elasticity is above 1, whereas a price increase may be more profitable if elasticity is below 1. At an elasticity of 1, the unit price should be maintained to keep revenue maximized.
Step-by-step explanation:
The student's question pertains to the relationship between the unit price p dollars and the revenue r (in dollars) for a gas clothes dryer manufacturer. This scenario typically involves understanding concepts such as price elasticity of demand.
Price elasticity of demand measures how the quantity demanded of a good responds to a change in its price. If the elasticity is greater than 1 (elastic), it indicates that a price decrease will lead to a proportionally larger increase in the quantity sold, thereby potentially increasing revenue. Conversely, if the elasticity is less than 1 (inelastic), a price increase may lead to a proportionally smaller decrease in quantity sold, potentially increasing revenue as well.
To maximize revenue based on price elasticity, we follow these general rules:
- If elasticity is greater than 1, it is advisable to lower the price.
- If elasticity is less than 1, increasing the price may be beneficial.
- If elasticity is equal to 1, the total revenue is already maximized at the current price level.