To measure the relative change in purchasing a specific basket of goods and services between two periods of a certain locality with a group of people with fixed incomes, which of the below can be used :

The logic follows here is:

To determine the relative change in purchasing a specific basket of goods and services between two periods for a group of people with fixed incomes, it is important to consider indices that reflect both price changes and cost of living adjustments.

The Consumer Price Index (CPI) is a measure that examines the weighted average of prices of a basket of consumer goods and services, such as transportation, food, and medical care. It is widely used to assess price changes associated with the cost of living.

The Cost of Living Index (COLI) measures the changes in the cost to maintain a certain standard of living. It takes into account the prices of goods and services, as well as the quantities consumed, to reflect the cost of maintaining a specific lifestyle.

Therefore, both the Consumer Price Index (CPI) and the Cost of Living Index (COLI) can be used to measure the relative change in purchasing a specific basket of goods and services between two periods.

Hence, the correct answer is "Option 4".

Important Points

CPI focuses on price changes, while COLI considers both price changes and the quantities consumed to maintain a standard of living.