To calculate the price elasticity of demand (PEOD) for water bottles at Dodger Stadium after a price reduction from [tex]$5.25 to $[/tex]4.25, follow these steps:
1. Determine the initial and new prices:
- Initial Price: [tex]$5.25
- New Price: $[/tex]4.25
2. Determine the initial and new quantities demanded:
- Initial Quantity: 200 water bottles
- New Quantity: 300 water bottles
3. Calculate the percent change in quantity demanded:
- Percent change in quantity demanded = [tex]\(\left(\frac{\text{New Quantity} - \text{Initial Quantity}}{\text{Initial Quantity}}\right) \times 100\)[/tex]
- [tex]\(\left(\frac{300 - 200}{200}\right) \times 100 = 50.0\%\)[/tex]
4. Calculate the percent change in price:
- Percent change in price = [tex]\(\left(\frac{\text{New Price} - \text{Initial Price}}{\text{Initial Price}}\right) \times 100\)[/tex]
- [tex]\(\left(\frac{4.25 - 5.25}{5.25}\right) \times 100 = -19.047619047619047\%\)[/tex]
5. Calculate the price elasticity of demand (PEOD):
- PEOD = [tex]\(\frac{\text{Percent Change in Quantity Demanded}}{\text{Percent Change in Price}}\)[/tex]
- PEOD = [tex]\(\frac{50.0}{-19.047619047619047} = -2.625\)[/tex]
6. Interpret the PEOD value:
- If PEOD < 1, the demand is considered inelastic.
- If PEOD > 1, the demand is considered elastic.
Since the calculated PEOD is -2.625, which is less than 1 in absolute value, we can say the demand for water bottles is inelastic.
7. Conclusion:
- In this scenario, the PEOD of water bottles is -2.625, which means consumers are not highly responsive to price changes. The Dodgers might have reduced the price to increase profits by attracting more customers, even though the demand isn't very elastic.
