Index Numbers

The Cost of Living Index Number (CLI) is calculated using the formula for the weighted aggregate method: Where represents the price index for each group and represents the weight.
Given:
CLI = 150
We first calculate and from the table.

Now, substitute these into the CLI formula: Multiply both sides by : Rearrange the terms to solve for : The value of x is 18.

A weighted aggregate quantity index number measures the change in the quantity of a group of items over time, with each item's quantity being weighted by its importance (usually its price). The general formula is , where is the current year quantity, is the base year quantity, and is the weight. The most common form is Laspeyres' Quantity Index, which uses base year prices ( ) as weights:

The question asks for the Dorbish-Bowley Price Index, , given Laspeyres' Price Index, , and Paasche's Price Index, . The formula for the Dorbish-Bowley index is the arithmetic mean of the Laspeyres and Paasche indices: Given:


Substitute the values into the formula: Therefore, the Dorbish-Bowley Price Index is 65.

The Cost of Living Index Number (also known as the Consumer Price Index or CPI) measures the change in the general price level of goods and services that a household consumes. The purchasing power of money is the value of a currency in terms of the goods it can buy. It is inversely proportional to the price level. The formula to calculate it is: Since the index is a direct component of the calculation, the statement is True.