The Bureau of Labor Statistics has found that the base-year expenditures of the typical consumer break down as follows:

Food and beverages 17.8%
Housing 42.8%
Apparel and upkeep 6.3%
Transportation 17.2%
Medical care 5.7%
Entertainment 4.4%
Other goods, and services 5.8%
Total 100.0%
Suppose that since the base year, the prices of food and beverages have increased by 10 percent, the price of housing has increased by 5 percent, and the price of medical care has increased by 10 percent. Other prices are unchanged.

Instructions: Enter your responses by rounding the CPI to three decimal places.

The CPI for the current year is .

The CPI for the current year is    104.49  

Explanation:

A) Expenditure breakdown of the base year:

You must check that they add 100%

Food and beverages:               17.8%Housing:                                   42.8%Apparel and upkeep:                 6.3%Transportation:                          17.2%Medical care:                               5.7%Entertainment:                              4.4%Other goods, and services:       5.8%Total                                          100.0%

Total: 17.8 + 42.8 + 6.3 + 17.2 + 5.7 + 4.4 + 5.8 = 100

Thus, the CPI of the base year is 100.

B. Expenditure breakdown of the current year.

Calculate the changes by adding the percent of increase to each item tha has changed.

1. The prices of food and beverages have increased by 10 percent:

17.8% × 1.10 = 19.58%

2. The price of housing has increased by 5 percent:

42.8% × 1.05 = 44.94%

3. The price of medical care has increased by 10 percent:

5.7% × 1.10 = 6.27%

The other prices are unchanged.

Then, the new breakdown is:

Food and beverages:               19.58%Housing:                                   44.94%Apparel and upkeep:                 6.3%Transportation:                          17.2%Medical care:                              6.27%Entertainment:                              4.4%Other goods, and services:        5.8%Total                                           104.49%

Of course the new total is not 100%.

19.58 + 44.94 + 6.3 + 17.2 + 6.27 + 4.4 + 5.8 = 104.49

That means that the price of the total basket of products has increased from 100 to 104.49.

Thus, the CPI of the current year is 104.49 ← answer