Consider a simple basket of goods that assumes consumers buy only bread and milk. The basket consists of 3 loaves of bread and 1 gallon of milk. The prices are shown in the table.
| Year | Price of a Loaf of Bread | Price of a Gallon of Milk |
| :----- | :----------------------- | :------------------------ |
| Year 1 | $1.50 | $2.90 |
| Year 2 | $1.65 | $3.10 |
Calculate the CPI to complete the statement. Round your answers to two decimal places, if necessary.
The CPI for year 2 is $\square$ and the rate of inflation from year 1 to year 2 is $\square$ %.
Answer (1)
Calculate the cost of the basket in Year 1: Cost_{Year1} = (3 \times 1.50) + (1 \times 2.90) = $7.40
Calculate the cost of the basket in Year 2: Cost_{Year2} = (3 \times 1.65) + (1 \times 3.10) = $8.05
Calculate the CPI for Year 2: CP I Y e a r 2 = 7.40 8.05 × 100 = 108.78
Calculate the inflation rate from Year 1 to Year 2: I n f l a t i o n R a t e = 100 108.78 − 100 × 100 = 8.78%
The CPI for year 2 is 108.78 and the rate of inflation from year 1 to year 2 is 8.78% .
Explanation
Calculate the cost of the basket in Year 1 First, we need to calculate the cost of the basket of goods in Year 1. The basket contains 3 loaves of bread and 1 gallon of milk. The price of a loaf of bread in Year 1 is $1.50, and the price of a gallon of milk is 2.90. T h ere f ore , t h ecos t o f t h e ba s k e t inY e a r 1 i sc a l c u l a t e d a s f o ll o w s : C os t Y e a r 1 = ( 3 × P r i c e B re a d , Y e a r 1 ) + ( 1 × P r i c e M i l k , Y e a r 1 ) C os t Y e a r 1 = ( 3 × 1.50 ) + ( 1 × 2.90 ) C os t Y e a r 1 = 4.50 + 2.90 $Cost_{Year1} = 7.40 $
Calculate the cost of the basket in Year 2 Next, we calculate the cost of the basket of goods in Year 2. The basket still contains 3 loaves of bread and 1 gallon of milk. The price of a loaf of bread in Year 2 is $1.65, and the price of a gallon of milk is 3.10. T h ere f ore , t h ecos t o f t h e ba s k e t inY e a r 2 i sc a l c u l a t e d a s f o ll o w s : C os t Y e a r 2 = ( 3 × P r i c e B re a d , Y e a r 2 ) + ( 1 × P r i c e M i l k , Y e a r 2 ) C os t Y e a r 2 = ( 3 × 1.65 ) + ( 1 × 3.10 ) C os t Y e a r 2 = 4.95 + 3.10 $Cost_{Year2} = 8.05 $
Calculate the CPI for Year 2 Now, we calculate the Consumer Price Index (CPI) for Year 2, using Year 1 as the base year. The CPI is calculated as follows: CP I Y e a r 2 = C os t Y e a r 1 C os t Y e a r 2 × 100 CP I Y e a r 2 = 7.40 8.05 × 100 CP I Y e a r 2 = 1.0878378378 × 100 CP I Y e a r 2 = 108.78 (Rounded to two decimal places)
Calculate the inflation rate from Year 1 to Year 2 Finally, we calculate the inflation rate from Year 1 to Year 2. The inflation rate is calculated as the percentage change in the CPI: I n f l a t i o n R a t e = CP I Y e a r 1 CP I Y e a r 2 − CP I Y e a r 1 × 100 Since Year 1 is the base year, CP I Y e a r 1 = 100 . Therefore, I n f l a t i o n R a t e = 100 108.78 − 100 × 100 I n f l a t i o n R a t e = 100 8.78 × 100 I n f l a t i o n R a t e = 8.78% (Rounded to two decimal places)
Final Answer The CPI for year 2 is 108.78 and the rate of inflation from year 1 to year 2 is 8.78 %.
Examples
Understanding CPI and inflation rates is crucial in everyday financial planning. For instance, if you're saving for retirement or a major purchase, knowing the expected inflation rate helps you estimate future costs and adjust your savings goals accordingly. Similarly, businesses use CPI data to adjust prices and wages, ensuring they keep pace with the changing cost of living. This ensures fair pricing and helps maintain employees' purchasing power, contributing to economic stability.
