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Index numbers are used to measure the changes in the value of a group of related items over a specific period of time. They help economists to study the changes in variables like prices, quantities, and values over time. Instead of focusing on the actual dollar value of goods, index numbers allow for an easier comparison of data across different periods and analyze the changes in trends.

Using the dollar value of goods as a measure for the price level has several limitations: 1. Inflation: The value of money changes over time due to inflation, making it difficult to compare dollar values across different time periods. A \(10 item in 1980 is not the same as a \)10 item today, because the purchasing power of money has changed. 2. Changes in the composition of goods: Over time, there might be changes in which goods are being produced and consumed, causing shifts in the average prices of different goods. 3. Difficulty in comparing changes: When using dollar values, it is difficult to make a transparent comparison of the changes in prices over time. For example, if the dollar value of a product doubles, it is not clear what percentage change this represents in terms of the price level.

Index numbers offer several advantages over using dollar values to measure the price level: 1. Ease of comparison: Index numbers allow for an easier comparison of changes in the price level across different time periods. They provide a benchmark for comparison by setting a base year, making it easy to understand the changes in prices over time. 2. Adjusted for inflation: Index numbers take into account inflation, ensuring that the changes in the price level are more accurately reflected in the measures. 3. Control for changes in the composition of goods: Index numbers often use a fixed basket of goods and services that represents the typical consumption of an economy. This allows them to adjust for changes in the composition of goods, providing a more accurate comparison of the price level over time.

In summary, economists use index numbers to measure the price level instead of the dollar value of goods because they offer a more accurate and easier-to-understand method of comparing changes in prices over time. Index numbers address limitations such as inflation and changes in the composition of goods while providing a standardized benchmark for comparisons.