Use the following data to work Problems 8 and 9 The people on Coral Island buy only juice and cloth. The CPI basket contains the quantities bought in \(2013 .\) The average household spent \(\$ 60\) on juice and \(\$ 30\) on cloth in 2013 when juice was \(\$ 2\) a bottle and cloth was \(\$ 5\) a yard. In 2014 , juice is \(\$ 4\) a bottle and cloth is \(\$ 6\) a yard. Calculate the CPI and the inflation rate in 2014

The inflation rate is a crucial economic indicator that shows how much prices have increased over a specific period. It's calculated using the Consumer Price Index (CPI). In simple terms, it represents how much more expensive a set of goods and services has become compared to a previous time period. For instance, in the Coral Island example, we found that the CPI in 2013 was set at 100. By 2014, the CPI had increased to 173.33, indicating a significant rise in prices. To find the inflation rate, we calculate the percentage change in CPI. This informs us that the inflation rate from 2013 to 2014 was 73.33%. This large inflation rate means that the cost of living significantly increased, affecting purchasing power and overall economic stability.

The CPI basket is a fixed set of goods and services that a typical household is expected to purchase and is used to track price changes over time. It reflects the spending habits of the average consumer. In our Coral Island example, the CPI basket includes juice and cloth. In 2013, the average household spent a specific amount on these items, helping us determine the quantities for the CPI basket: 30 bottles of juice and 6 yards of cloth. These quantities remain constant when calculating the CPI from year to year, allowing for consistent comparison. The prices change, but the quantities do not, which helps to isolate the effect of price changes on the overall cost of living.

Price changes are the variations in the cost of goods and services over time. They are essential for calculating the CPI and the inflation rate. For Coral Island, the price of juice doubled from \(2 to \)4 per bottle, and the price of cloth increased from \(5 to \)6 per yard from 2013 to 2014. By examining the price changes, we can see how these adjustments impact the overall cost of the CPI basket: it increased from \(90 in 2013 to \)156 in 2014. Tracking such changes helps in understanding economic trends and in making informed decisions about budgeting, purchasing, and investments.

Economic measurement involves various statistics and indices to gauge the performance of an economy. The CPI and inflation rate are key indicators used to measure economic health. They provide insight into price stability, cost of living, and purchasing power. Using the details from our Coral Island example, we can see how the CPI offers a snapshot of how much more (or less) households need to spend on a fixed basket of goods and services over time. This kind of data is not only crucial for policymakers assessing inflation and economic policy but also for businesses and consumers planning their financial futures. Understanding these measurements empowers individuals and institutions to make more informed decisions.