Math Problem Statement
Answer number 4
Solution
The fourth question asks about volatility, referring to the likelihood that something will change rapidly and unpredictably. In the context of this table, volatility can be evaluated based on the fluctuations of the average gas prices and petroleum import prices over time.
To identify which commodity (gas or import petroleum) is more volatile, we need to assess the variability in their price changes year over year. Volatility can be measured by looking at the relative percentage changes and how large and unpredictable those changes are.
Calculating Volatility for Both Commodities:
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Gas Prices:
- Look at the annual prices in the table. Gas prices fluctuated between a high of $4.059 in 2022 and a low of $2.520 in 2016. Over the years, there have been steady decreases followed by increases. However, the fluctuations are relatively moderate, with price changes between consecutive years ranging from small to moderate percentages.
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Petroleum Import Prices:
- The index for petroleum import prices shows greater fluctuations, moving from 387.9 in 2014 to a low of 142.6 in 2020 and back up to 456.5 in 2022. The drop from 2014 to 2016 and then the steep rise from 2020 to 2022 are much more drastic compared to the changes in gas prices.
Conclusion:
The petroleum import prices are more volatile than the gas prices. This is evident from the larger swings in price, especially between 2014-2016 and 2020-2022. Gas prices, while also fluctuating, do not exhibit as extreme changes.
Justification:
Petroleum import prices reflect changes in the global oil market, which can be subject to geopolitical events, changes in production levels, and international demand, leading to more unpredictability. Gas prices are influenced by domestic factors such as taxes, regulations, and refining costs, which tend to be more stable.
Would you like further details on how to calculate specific percentage changes?
Here are five follow-up questions to deepen your understanding:
- How do you calculate percentage change between two values?
- What is the relationship between gas prices and petroleum import prices over time?
- Why might petroleum import prices be more volatile than gas prices?
- How does volatility affect consumer behavior and business decisions in the energy market?
- How can investors use volatility to make strategic decisions in commodities markets?
Tip: Volatility is often seen as risk in investments, but it also presents opportunities for profit when managed carefully.
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Math Problem Analysis
Mathematical Concepts
Volatility
Percentage Change
Comparative Analysis
Formulas
Percentage change formula: ((New Value - Old Value) / Old Value) * 100
Theorems
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Suitable Grade Level
Grades 9-12
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