The index of prices of a given basket of commodities which are bought by the representative consumer is known as:

The correct option is Consumer Price Index.

To understand why this is the correct answer, let's break down the definition and the role of the index:
1. Representative Consumer: This refers to an average household or individual consumer in the economy. The index focuses on the goods and services that typical households purchase for daily living.
2. Basket of Commodities: This is a representative sample of consumer goods and services, including food, clothing, housing, transportation, medical care, and education.
3. Index of Prices: This measures the weighted average of prices of these commodities over time relative to a base year.

The Consumer Price Index (CPI) is specifically designed to measure the changes in the price level of this basket of consumer goods and services purchased by households. Therefore, it directly reflects the cost of living for a representative consumer.

In contrast:
- Wholesale Price Index (WPI) measures the change in the price of goods in the stages before the retail level (at the wholesale or producer level).
- Capital Good Index tracks the prices of goods used in producing other goods (like machinery and equipment), rather than final consumer goods.
- Inflation is the broad rate at which the general level of prices for goods and services is rising, which is measured by indices like the CPI, rather than being the index itself.