Final answer:
The absolute value of the price elasticity of demand can be used to calculate the percentage change in price when the price is increased. In this case, when the airline increases the price to $500, the percentage change in price is approximately -0.498%.
Step-by-step explanation:
The price elasticity of demand measures the responsiveness of the quantity demanded to a change in price. To calculate the price elasticity of demand, we need to know the percentage change in quantity demanded and the percentage change in price. However, in this question, we are given the absolute value of the price elasticity of demand and asked to calculate the percentage change in price when the price is increased to $500.
Since the price elasticity of demand is a negative value, we can take the absolute value and use it as a positive value. Let's assume the absolute value of the price elasticity of demand for leisure travelers is 0.4. This means that for every 1% increase in price, the quantity demanded will decrease by 0.4%. Using this information, we can calculate the percentage change in price as follows:
- Change in price = ($500 - $x) / $x
- 0.4% = -0.004
- 0.004 = ($500 - $x) / $x
- $x = $500 / (1 + 0.004)
- $x = $500 / 1.004
- $x ≈ $497.01
- Percentage change in price = ($x - $500) / $500 * 100
- ≈ ($497.01 - $500) / $500 * 100
- ≈ -0.498%
Therefore, when the airline increases the price to $500, the percentage change in price is approximately -0.498%.