Answer to Question #230291 in Macroeconomics for aqlama

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

comple 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

solution

(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:

$\% Change\space in\space CPI = \frac{∑_iWeighti×Percentage\space change\space of \space good_i}{Total \space weights}$

Using the information from the given table:

$=\frac{14.9×4.4 +42.4×3 +3.7×(−1.4) +17.7×8.2 +6.2×4.6+5.6×1.3+6.1×3.0+3.3×3.2}{100}\\=\frac{397.38}{100}\\=3.9738$

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:

$CPI_{2008} = CPI_{2007} + (\% Change \space in\space CPI) ×CPI_{2007}\\=205.10 +\frac{3.97}{100}×205.10\\=213.24247$

Hence, CPI in 2008 would amount to 213.24.