To calculate the price elasticity of demand (PEOD) for water bottles at Dodger Stadium, we need to follow a detailed step-by-step approach based on the given data.
1. Identify Initial and New Prices and Quantities:
- Initial price (P1): \[tex]$5.25
- New price (P2): \$[/tex]4.25
- Initial quantity demanded (Q1): 200 water bottles
- New quantity demanded (Q2): 300 water bottles
2. Calculate the Percent Change in Quantity Demanded:
- Change in quantity (ΔQ) = Q2 - Q1 = 300 - 200 = 100
- Percent change in quantity demanded = (ΔQ / Q1) 100 = (100 / 200) 100 = 50.0%
3. Calculate the Percent Change in Price:
- Change in price (ΔP) = P2 - P1 = 4.25 - 5.25 = -1.00
- Percent change in price = (ΔP / P1) 100 = (-1.00 / 5.25) 100 ≈ -19.05%
4. Calculate the Price Elasticity of Demand (PEOD):
- PEOD = Percent change in quantity demanded / Percent change in price
- PEOD = 50.0% / -19.05% ≈ -2.625
5. Determine Elasticity:
- The elasticity of demand is determined by the value of PEOD:
- If PEOD < 1, demand is inelastic.
- If PEOD > 1, demand is elastic.
- In this case, PEOD ≈ -2.625
6. Conclusion:
- Since the PEOD is approximately -2.625, which is less than -1, it indicates that the demand for water bottles at Dodger Stadium is considered inelastic. This means consumers are not very sensitive to price changes of water bottles.
Putting it all together in the given context:
The price of a water bottle was recently reduced from \[tex]$5.25 to \$[/tex]4.25. As a result, the quantity demanded increased from 200 to 300 bottles.
The formula for PEOD is:
[tex]\[ \text{PEOD} = \frac{\% \text{change in quantity demanded}}{\% \text{change in price}} \][/tex]
For this problem, we calculated the following:
- The percent change in quantity demanded is 50.0%
- The percent change in price is approximately -19.05%
- Thus, the PEOD is approximately -2.625
Given that PEOD is less than -1, it means the demand is considered inelastic. In this scenario, consumers are not highly sensitive to the price change. The Dodgers might have reduced the price to help increase their total revenue by compensating for the lower price with higher sales volume.
