To calculate the price elasticity of demand (PEOD) for water bottles at Dodger Stadium when the price is reduced from [tex]$5.25 to $[/tex]4.25, follow these steps:
1. Calculate the initial and new quantities and prices:
- Initial price ([tex]$P_1$[/tex]) = \[tex]$5.25
- New price ($[/tex]P_2[tex]$) = \$[/tex]4.25
- Initial quantity demanded ([tex]$Q_1$[/tex]) = 200
- New quantity demanded ([tex]$Q_2$[/tex]) = 300
2. Calculate the percentage change in price:
- The formula for percentage change is [tex]\( \frac{(New Value - Initial Value)}{Initial Value} \times 100 \)[/tex]
- Applying the values:
[tex]\[
\text{Percentage change in price} = \frac{(4.25 - 5.25)}{5.25} \times 100 = \frac{-1}{5.25} \times 100 \approx -19.05\%
\][/tex]
3. Calculate the percentage change in quantity demanded:
- Again, using the percentage change formula:
[tex]\[
\text{Percentage change in quantity demanded} = \frac{(300 - 200)}{200} \times 100 = \frac{100}{200} \times 100 = 50\%
\][/tex]
4. Calculate the price elasticity of demand (PEOD):
- The formula for PEOD is:
[tex]\[
PEOD = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}}
\][/tex]
- Plugging in the values:
[tex]\[
PEOD = \frac{50\%}{-19.05\%} \approx -2.625
\][/tex]
Conclusion:
- The percentage change in price is approximately -19.05%.
- The percentage change in quantity demanded is 50%.
- The price elasticity of demand (PEOD) for water bottles at Dodger Stadium is approximately -2.625.
This indicates that the demand for water bottles at Dodger Stadium is elastic, as the absolute value of the PEOD is greater than 1. This means that the quantity demanded changes more than proportionately in response to a change in price.
