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

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

In year 1, the CPI was  .

In year 2, the CPI was  .

In year 3, the CPI was  .

In year 4, the CPI was  .

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

In year 1, the CPI was  .

In year 2, the CPI was  .

In year 3, the CPI was  .

In year 4, the CPI was  .

Answer 1

Solution:-

First calculate the cost of basket in each year,

Year	Price of Pasta	Price of Yogurt	Price of Lemonade	Cost of basket
1	1.9	1	2.1	(25 *1.9 + 65 * 1 + 15 * 2.1) = 144
2	2.1	1.1	2.2	(25*2.1 + 65 * 1.1 + 15 * 2.2) = 157
3	2.25	1.1	1.95	(25 * 2.25 + 65 * 1.1 + 15 * 1.95) = 157
4	2.2	1.2	2	(25 * 2.2 + 65 * 1.2 + 15 * 2) = 163

Cost of Basket = (25 * Price of Pasta in year n) + (65 * Price of Yogurt in year n) + (15 * Price of Lemonade in year n)

Now calculate the CPI values using the following formula:-

CPI in Year n = Cost of the basket in year n / Cost of the basket in base year * 100

Cost Of Basket	CPI using year 1 as a base year	CPI using year 3 as a base year
144	(144 / 144 * 100) = 100	(144 / 157 * 100) = 91.72
157	(157 / 144 * 100) = 109.03	(157 / 157 * 100) = 100
157	(157 / 144 * 100) = 109.03	(157 / 157 * 100) = 100
163	(163 / 144 * 100) = 113.19	(163 / 157 * 100) = 103.82

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

In year 1, the CPI was = 100

In year 2, the CPI was = 109.3

In year 3, the CPI was = 109.3

In year 4, the CPI was = 113.19

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

In year 1, the CPI was = 91.72

In year 2, the CPI was = 100

In year 3, the CPI was = 100

In year 4, the CPI was = 103.82