Question

The index number representing the price level changes from 110 to 115 in one year, and then from 115 to 120 the next year. since the index number increases by five each year, is five the inflation rate each year? Is the inflation rate the same each year? Explain your answer.

Short answer

The inflation rate is not the same each year, and it does not equal five each year. Inflation rate is calculated using the formula: Inflation Rate = \(\frac{New \ Index\ Number - Old\ Index \ Number}{Old \ Index\ Number}\) × 100. For the first year, the inflation rate is approximately 4.55%, and for the second year, it is around 4.35%. Even though the index number increased by 5 points in each year, it resulted in differing inflation rates due to their respective different base index numbers.

Step-by-step solution

Inflation rate is the percentage change in the price level from one period to another. We can calculate this by using the following formula: Inflation Rate = \(\frac{New \ Index\ Number - Old\ Index \ Number}{Old \ Index\ Number}\) × 100 Applying this formula, we can find the inflation rate for each year. #Step 2: Calculate the Inflation rate for the first year#

For the first year, the index number changes from 110 to 115. Plugging these values into the formula, we get: Inflation Rate (Year 1) = \(\frac{115 - 110}{110}\) × 100 Inflation Rate (Year 1) = \(\frac{5}{110}\) × 100 Inflation Rate (Year 1) ≈ 4.55% #Step 3: Calculate the Inflation rate for the second-year#

For the second year, the index number changes from 115 to 120. Plugging these values into the formula, we get: Inflation Rate (Year 2) = \(\frac{120 - 115}{115}\) × 100 Inflation Rate (Year 2) = \(\frac{5}{115}\) × 100 Inflation Rate (Year 2) ≈ 4.35% #Step 4: Compare the Inflation rate and answer the questions#

Comparing the Inflation Rate calculated in steps 2 and 3: Inflation Rate (Year 1) ≈ 4.55% Inflation Rate (Year 2) ≈ 4.35% It's clear that the inflation rate is not the same each year, even if the index number has increased by the same amount (5 points) each year. The inflation rate has slightly decreased from 4.55% to 4.35%. Conclusion: 1. No, five is not the inflation rate each year. 2. No, the inflation rate is not the same each year.

Key concepts

Price Level

The price level is essentially a snapshot of the overall prices of goods and services in an economy at a particular time. Think of it as a giant basket filled with all the items that people buy, from groceries to gadgets.
The items' prices are averaged out to give us a number that represents the price level.
This number helps us compare how expensive or cheap things are over time or between different economies. When economists look at changes in the price level, they might use something called a price index.
This index gives us a way to measure inflation, which is the general increase in prices.

• The Consumer Price Index (CPI) and Producer Price Index (PPI) are two common examples.

These indices help illustrate how the purchasing power of money changes over time.

Index Number

An index number in economics is a tool to track changes in a variable or group of variables over time.
It gives us a way to simplify and summarize data by comparing different periods with a base level—usually set as a reference point.
For price levels, an index number might start at 100 in a base year. If the index number rises to 110, that signifies a 10% increase in prices since the base year. Index numbers are instrumental in situations like calculating inflation rates because they help quantify how much prices have changed from one period to the next.
They offer a clear, straightforward way to understand complex economic changes and trends.

Percentage Change

The percentage change is a way to express how much a quantity has increased or decreased in relation to its original value.
In economics, percentage change is crucial, specifically when calculating the inflation rate.
This can be easily done using the formula:\[\text{Percentage Change} = \left(\frac{\text{New Value} - \text{Old Value}}{\text{Old Value}}\right) \times 100\]This tells us the rate of increase or decrease in a value, expressed as a percentage. For inflation, you're often looking at how the price level has changed over time.

• A positive percentage change indicates an increase, which is seen as inflation.
• A negative percentage change indicates a decrease, known as deflation.

Understanding percentage change is fundamental in economics because it helps us make informed decisions based on data.

Macroeconomics

Macroeconomics is the branch of economics that looks at the big picture of an economy.
It considers issues like inflation, unemployment, economic growth, and how different sectors and markets interact at a large scale. An important aspect of macroeconomics is understanding inflation, which reflects how the average price level of a basket of goods and services increases over time.
Macroeconomists use tools like price indices and inflation rates to analyze how prices evolve, which helps them predict future economic trends and guide policy decisions. By studying macroeconomics, we can better understand the factors that affect the economy as a whole and thus make more informed personal and policy-related decisions.