Which of the following measures the change in the cost of a fixed basket of goods and services purchased by families over a period of time?

The correct answer is the Consumer Price Index (CPI). The CPI is specifically designed to measure the changes in the cost of a predetermined set of goods and services that are typically purchased by households over time. By tracking how the prices for these items change, the CPI reflects inflation or deflation in the economy, which is critical for understanding cost of living adjustments, economic policy decisions, and wage negotiations.

The CPI captures price changes for various categories such as food, housing, clothing, transportation, and medical care, making it a vital indicator for economic analysis. It provides insight into how everyday expenses are affected by overall economic trends, thereby serving as an important tool for both consumers and policymakers.

Other indices, while they measure price changes in different aspects of the economy, do not focus specifically on the basket of goods consumed by families in the same way the CPI does. For example, the Gross Domestic Product (GDP) covers all economic output, the Producer Price Index (PPI) tracks price changes from the perspective of the seller, and the Retail Price Index (RPI) also includes housing costs but has a different methodology and scope compared to the CPI. Hence, the CPI is the most appropriate measure for this question.