Answer to Question #235667 in Macroeconomics for Ali Hashim

Question

Examine the price-change numbers shown in the example on page 403.
a. Use the formula to calculate the increase in the CPI from March 2007 to March 2008 to two decimal places. Verify that the number shown in the table is correct to a single decimal place.
b. The level of the CPI in March 2007 was 205.10.
Calculate the CPI for March 2008.

Answer 1

In economics, CPI refers to the proportion or percentage by which the price level in the nation has changed from the previous period. By price level, we mean the average price of a typical commodity or service prevailing in the economy. CPI is popularly used in determining inflation in the economy. In other words, the percentage change in CPI gives the rate of inflation in the economy.

a)The percentage change in CPI is the weighted average of the percentage change in price of all goods and services. The weights are determined by the relative importance of the commodity. Mathematically, the percentage change in CPI can be estimated by the following expression:

% Change i n CPI = ∑ (Weight_i × Percentage change of good_i )/Total weights

Using the information from the given table:

% Change in CPI = ∑ (Weight_i × Percentage change of good_i) / Total weights = (14.9 × 4.4 + 42.4 × 3 + 3.7 × (-1.4) + 17.7 × 8.2 + 6.2 × 4.6 + 5.6 × 1.3 + 6.1 × 3.0 + 3.3 × 3.2)/100 = 397.38/100 = 3.9738

So, the increase in CPI would be 3.97 % (in case of two decimals). However, if it is converted into 1 decimal , then it would be equal to 4.0 percent which is exactly equal to the number shown in the table.

b)

CPI in 2008 would be the CPI in 2007 plus the percentage change in CPI over the period. Using this:

CPI 2008 = CPI 2007 + (%Change in CPI ) × CPI 2007 = 205.10 + 3.97 100 × 205.10 = 213.24247

Hence, CPI in 2008 would amount to 213.24.