The index most widely used by the government and the private sector to measure changes in the cost of living is the (a) the GDP deflator, (b) Producer Price Index, (c) The interest rate, (d) Consumer Price Index

The index most widely used by the government and the private sector to measure changes in the cost of living is the Consumer Price Index (CPI), which is option (d).

To understand why the Consumer Price Index is used to measure changes in the cost of living, let's break it down:

1. Consumer Price Index (CPI): The CPI is a measure that tracks the average price level of a basket of goods and services commonly purchased by households over time. It covers a wide range of items, including food, housing, transportation, healthcare, education, and more.

2. Cost of Living: Cost of living refers to the amount of money needed to sustain a certain lifestyle, including expenses related to housing, utilities, food, transportation, healthcare, and other essential goods and services.

3. Measuring Changes: The CPI is used to measure changes in the cost of living because it compares the price of the same basket of goods and services over different periods. By calculating the percentage change in the CPI over time, it provides insights into inflation or deflation, enabling governments, businesses, and individuals to assess changes in the cost of living.

The other options mentioned are not specifically designed to measure changes in the cost of living:

(a) The GDP deflator is a broader indicator that measures the average price change for all final goods and services produced within a country's borders. It is used to measure inflation/deflation in the overall economy.

(b) The Producer Price Index (PPI) measures price changes at the wholesale level for goods and services produced by industries. It reflects inflationary pressures before they reach the consumer level.

(c) The interest rate is the cost of borrowing or the return on investment. While it can indirectly influence the cost of living, it is not a direct measure of changes in the cost of living.

Therefore, based on the given options, the Consumer Price Index (CPI) is the most appropriate index to measure changes in the cost of living.