A typical family on Sandy Island consumes only juice and cloth. Last year, which was the base year, the family spent \(\$ 40\) on juice and \(\$ 25\) on cloth. In the base year, juice was \(\$ 4\) a bottle and cloth was \(\$ 5\) a length. This year, juice is \(\$ 4\) a bottle and cloth is \(\$ 6\) a length. Calculate a. The CPI basket. b. The CPI in the current year. c. The inflation rate in the current year.

CPI, or Consumer Price Index, measures the average change over time in the prices paid by consumers for a market basket of goods and services. It reflects the cost of living and helps to understand how much prices have risen or fallen. The formula for calculating CPI is: \ \ \[ \text{CPI} = \frac{\text{Cost of basket in current year}}{\text{Cost of basket in base year}} \times 100 \] \ \ Essentially, CPI compares the cost of a predefined basket of goods and services in the current year to the cost in a base year. This basket includes items that are representative of typical consumer spending. By collecting prices and calculating CPI, we can assess inflation and make informed economic decisions.

The inflation rate indicates the percentage increase in the general price level of goods and services over a period, usually a year. Inflation erodes purchasing power, meaning consumers need to spend more to buy the same things. It is calculated using CPI values from different years with the formula: \ \ \[ \text{Inflation rate} = \frac{\text{CPI current year} - \text{CPI base year}}{\text{CPI base year}} \times 100 \] \ \ If CPI for the current year is higher than the CPI for the base year, it signifies that prices have increased. Understanding the inflation rate helps consumers, businesses, and policymakers track price stability and adjust their economic plans accordingly.

The base year is a reference point for comparing economic data over time. It is the year against which other years' economic performance is measured. For CPI, the base year is when the weighted average cost of the basket of goods and services is set to 100. Using a base year allows consistency in calculations and helps to track price changes over multiple years. When selecting a base year, it should be a typical and stable period so that comparisons are meaningful, thus providing accurate inflation and cost of living trends.

Current year pricing is about evaluating prices for the same goods and services in the present year to calculate CPI. This comparison highlights how much more or less consumers are paying now compared to the base year. For example: \ \ - Juice was both \(4 per bottle in both years. \ - Cloth increased from \)5 to $6 per length. \ With current year pricing, economists assess the cost changes to determine if inflation occurred and to what extent. Accurate pricing data collection is crucial for precise CPI calculation and understanding trends.

The cost of the basket involves summing the prices of goods and services in a fixed basket bought by typical consumers. Calculating the cost in both the base year and the current year involves: \ \ - Identifying the fixed quantities of items in the base year. \ - Multiplying these quantities by their respective prices in the current year. \ For Sandy Island: \ \ \[ \text{Base year cost} = 10 \times 4 + 5 \times 5 = 65 \] \ \[ \text{Current year cost} = 10 \times 4 + 5 \times 6 = 70 \] \ \ The total cost helps calculate CPI by showing the price shift from the base year to the current year. Changes in the cost of the basket indicate how inflation has impacted consumer expenses.