Question

Hanna, who is a 5-year-old girl, eats nothing but pasta, yogurt, and lemonade. Each month her parents buy 25 pounds of pasta, 65 packages of yogurt, and 15 bottles of lemonade. These three items make up a basket of goods and services similar to the much larger basket used by the Bureau of Labor Statistics (BLS) when computing the official Consumer Price Index (CPI). The table below lists the average price for each item in this basket for the past four years.Hanna's Meals

Year	Pasta (dollars per pound)	Yogurt (dollars per package)	Lemonade (dollars per bottle)
1	$1.90	$1.00	$2.10
2	2.10	1.10	2.20
3	2.25	1.10	1.95
4	2.20	1.20	2.00

Instructions: Round your answers to two decimal places.

a. For each year, calculate the CPI, using year 1 as the base year.

     In year 1, the CPI was 100.00 Correct

     In year 2, the CPI was 109.30 Incorrect

     In year 3, the CPI was 109.30 Incorrect

     In year 4, the CPI was 113.19 Correct

b. For each year, calculate the CPI, using year 3 as the base year.

     In year 1, the CPI was 91.72 Correct

     In year 2, the CPI was 100.00 Correct

Answer 1

Ans:

Consumer Price Index (CPI) = (cost of market basket in a given year / cost of market basket in a base year) * 100

a)

Consumer Price Index (CPI) in year-1 = ((25 * $1.90) + (65 * $1) + (15 * $2.1)) / ((25 * $1.90) + (65 * $1) + (15 * $2.1))

= (($47.5 + $65 + $31.5) / ($47.5 + $65 + $31.5)) * 100

= ($144 / $144) * 100

= 100

Consumer Price Index (CPI) in year-2 = ((25 * $2.10) + (65 * $1.10) + (15 * $2.20)) / ((25 * $1.90) + (65 * $1) + (15 * $2.1))

= (($52.5 + $71.5 + $33) / ($47.5 + $65 + $31.5)) * 100

= ($157 / $144) *100

= 109.03

Consumer Price Index (CPI) in year-3 = ((25 * $2.25) + (65 * $1.10) + (15 * $1.95)) / ((25 * $1.90) + (65 * $1) + (15 * $2.1))

= (($56.25 + $71.5 + $29.25) / ($47.5 + $65 + $31.5)) * 100

= ($157 / $144) * 100

= 109.03

Consumer Price Index (CPI) in year-4 = ((25 * $2.2) + (65 * $1.2) + (15 * $2)) / ((25 * $1.90) + (65 * $1) + (15 * $2.1))

= (($55 + $78 + $30) / ($47.5 + $65 + $31.5)) * 100

= ($163 / $144) * 100

= 113.19

b)

Consumer Price Index (CPI) in year-1 = ((25 * $1.90) + (65 * $1) + (15 * $2.10)) / ((25 * $2.25) + (65 * $1.10) + (15 * $1.95))

= (($47.5 + $65 + $31.5) / ($56.25 + $71.5 + $29.25)) * 100

= (144 / 157) * 100

= 91.72  

Consumer Price Index (CPI) in year-2 = ((25 * $2.10) + (65 * $1.10) + (15 * $2.20)) / ((25 * $2.25) + (65 * $1.10) + (15 * $1.95))

= (($52.5 + $71.5 + $33) / ($56.25 + $71.5 + $29.25)) * 100

= (157 / 157) * 100

= 100