Answer to Question #132505 in Macroeconomics for Rachel Alfonso

Question

Briefly explain how the CPI index summarizes all the prices in the economy by using a single number.

Answer 1

The consumer price index (CPI) is a measure of the aggregate price level in the economy. It is the weighted average price of all the prices of all goods and services produced in an economy. It, thus, summarizes all the prices in the economy by averaging all the prices into one figure to arrive at the general price level.

To arrive at this single price, few steps are involved in coming up with the CPI. Firstly, a fixed market basket of goods and services is defined. This basket becomes a representative market basket for the whole economy. Secondly, prices of the representative market basket are found and traced over time. Thirdly, the cost of the fixed market basket is calculated for each year by using the formulae:

Cost of market basket = Quantity × Price. However, in a more practical approach, weights are attached to each element of the market basket.

Finally, a base year is chosen and the consumer price index (CPI) is calculated using the formulae:

$CPI_{year\space t} = \dfrac {Cost \space of \space market \space basket \space in \space year_{t}}{Cost \space of \space market \space basket \space in \space base \space year}$

The value of CPI obtained then represents the general price level for all prices in the economy. For the sake of illustration, let us assume an economy where bananas and apples are the major components of the consumers' market basket. Assuming the data for years 2010 and 2015 are as given below.

For simplicity, only prices have changed between 2010 and 2015 whereas quantities remain unchanged.

Cost of market basket, 2010

= (150 units × $2) + (135 units × $4)

= $300 + $540

= $840

Cost of market basket, 2015

= (150 units × $2.50) + (135 units × $6)

= $375 + $810

= $1,185

Assuming, 2010 is the base year:

$CPI_{2010} = \dfrac {\$840}{\$840} × 100$

$= 100$

$CPI_{2015} = \dfrac {\$1,185}{\$840}×100$

$= 141.07142857$

$\approx 141.07$

Therefore, this implies that, all 2010 prices are represented by 100 whereas all 2015 prices are represented by 141.07. As a result, the CPI is a summary of all prices of goods and services in the economy. It is the weighted average, general price level.