Question

Government survey takers determine that typical family expenditures each month in the year designated as the base year are as follows:
25 pizzas at $10 each
Rent of apartment, $600 per month
Gasoline and car maintenance, $100
Phone service (basic service plus 10 long-distance calls), $50

In the year following the base year, the survey takers determine that pizzas have risen to $11 each, apartment rent is $700, gasoline and maintenance have risen to $120, and phone service has dropped in price to $40.

a) Find the CPI in the subsequent year and the rate of inflation between the base year and the subsequent year

Answer 1

Answer:

• 1. CPI in the subsequent year: 1,135

• 2. Rate of inflation: 13.5%

Explanation:

1. Calculate the CPI

CPI is the consumer price index.

CPI is created using a basket of goods and services that are typically consumed.

In the given case the typical basket is:

• 25 pizzas

• Rent of apartment

• Gasoline and car maintenance

• Phone service (basic service plus 10 long-distance calls).

Then to find the CPI for a determined year you multiply each item by its price and then add up all the results.

For the base year, the expenditures per month were:

• 25 pizzas at $ 10: $10 × 25 = $250

• Rent of apartment:  $600

• Gasoline and car maintenance: $100

• Phone service (basic service plus 10 long-distance calls): $50

Then, the CPI for the base year is:

• CPI = $250 + $600 + $100 + $50 = $1,000

The year following the base year, the expenditures per month are:

• 25 pizzas at $ 11 : $11 × 25 = $275

• Rent of apartment:  $700

• Gasoline and car maintenance: $120

• Phone service (basic service plus 10 long-distance calls): $40

Then the CPI for the followng year is:

• CPI = $275 + $700 + $120 + $40 = $1,135

2. Calculate the rate of inflation

The rate of inflation is defined as the increase of the CPI of the given year with respect ot the base year:

The formula to calculate the rate of inflation is:

• Inflation = (CPI of the year - CPI of the base year) / (CPF of the base year) × 100

• Inflation = [ (1,135 - 1,000) / (1,000)]  × 100 = 13.5%

Hence, the rate of inflation for the subsequent year is 13.5%