The BLS reported the following CPI data: $$ \begin{array}{ll} \text { June } 2008 & 217.3 \\ \text { June } 2009 & 214.6 \\ \text { June } 2010 & 216.9 \end{array} $$ Calculate the inflation rates for the years ended June 2009 and June \(2010 .\) How did the inflation rate change in 2010 ?

The Consumer Price Index (CPI) is a critical metric that helps understand inflation and deflation in an economy. It measures the average change over time in the prices paid by urban consumers for a market basket of consumer goods and services. The Bureau of Labor Statistics (BLS) reports this index monthly.
A rising CPI indicates inflation, meaning the general level of prices is increasing. Conversely, a falling CPI indicates deflation, reflecting a decrease in the general price level.
Knowing the CPI values across different periods enables us to calculate the inflation rate and understand the economy's performance. In the given exercise, the CPIs were for June 2008 (217.3), June 2009 (214.6), and June 2010 (216.9), providing the basis for calculating the inflation rates.

Deflation occurs when the inflation rate falls below 0%, indicating a decline in the general price level of goods and services. In simpler terms, deflation means the value of money increases as the prices of goods and services drop. It can lead to reduced consumer spending as people might expect prices to fall further, potentially leading to an economic slowdown.
In the given exercise, from June 2008 to June 2009, the CPI decreased from 217.3 to 214.6. Applying the inflation formula, we get a negative inflation rate of -1.24%, indicating deflation during that period. To calculate this:
\[ \text{Inflation Rate} = \frac{214.6 - 217.3}{217.3} \times 100 = -1.24\text{\text{%}} \]
Understanding deflation is crucial in economic analysis, as persistent deflation can signal serious economic problems, such as a recession.

The formula for calculating the inflation rate is: \[ \text{Inflation Rate} = \frac{\text{CPI}_{\text{end}} - \text{CPI}_{\text{start}}}{\text{CPI}_{\text{start}}} \times 100 \]
This formula is straightforward. It measures the percentage change in the Consumer Price Index (CPI) from one period to another.
In the exercise, we use this formula to compute the inflation rates for two periods:
1. **June 2008 to June 2009**: Starting CPI is 217.3, and ending CPI is 214.6. Calculation:
\[ \text{Inflation Rate} = \frac{214.6 - 217.3}{217.3} \times 100 = -1.24\text{\text{%}} \]
2. **June 2009 to June 2010**: Starting CPI is 214.6, and ending CPI is 216.9. Calculation:
\[ \text{Inflation Rate} = \frac{216.9 - 214.6}{214.6} \times 100 = 1.07\text{\text{%}} \]
These calculations show that deflation occurred in the first period, followed by inflation in the second. Using these simple calculations, you can determine how prices have changed over time. Applying the formula is crucial in economics to monitor inflation trends and make informed decisions.