Question

In this problem you will calculate the CPI for the average urban consumer and for Jane using the prices for year 1 and year 2. The basket numbers represent the percentage of each dollar that is devoted to each good (written in decimal form). Assume year 1 is the base year. Round to two decimal places.

	Average Basket	Jane’s Basket	Price 1	Price 2
Housing	0.40	0.38	$900	$945
Food	0.18	0.17	$200	$204
Transportation	0.18	0.10	$150	$160
Medical	0.08	0.02	$120	$160
Education	0.04	0.10	$150	$158
Clothing/Fun	0.12	0.23	$100	$100

For the average person, the cost of the basket in year 1 is $ __ and the cost of the basket in year 2 is $ __ .

For the average person, the CPI in year 1 is __ and the CPI in year 2 is __ .

For the Jane, the cost of the basket in year 1 is $ __ and the cost of the basket in year 2 is $ __ .

For the Jane, the CPI in year 1 is __ and the CPI in year 2 is __ .

Answer 1

Calculate the cost of basket in Year 1 for average person -

Cost of basket = [Housing * Price] + [Food * Price] + [Transportation * Price] + [Medical * Price] + [Education * Price] + [Clothing/fun * Price]

Cost of basket = [0.40 * 900] + [0.18 * 200] + [0.18 * 150] + [0.08 * 120] + [0.04 * 150] + [0.12 * 100]

Cost of basket = 360 + 36 + 27 + 9.6 + 6 + 12

Cost of basket = 450.6

The cost of basket in Year 1 for average person is $450.60

Calculate the cost of basket in Year 2 for average person -

Cost of basket = [Housing * Price] + [Food * Price] + [Transportation * Price] + [Medical * Price] + [Education * Price] + [Clothing/fun * Price]

Cost of basket = [0.40 * 945] + [0.18 * 204] + [0.18 * 160] + [0.08 * 160] + [0.04 * 158] + [0.12 * 100]

Cost of basket = 378 + 36.72 + 28.8 + 12.8 + 6.32 + 12

Cost of basket = 474.64

The cost of basket in Year 2 for average person is $474.64

Thus,

For the average person, the cost of the basket in Year 1 is $450.60 and the cost of the basket in Year 2 is $474.64.

The base year is Year 1. The value of CPI in base year is always 100.

So, the CPI in Year 1 is 100.

Calculate the value of CPI in Year 2 -

CPI = [Cost of basket in Year 2/Cost of basket in Year 1] * 100

CPI = [$474.64/$450.6] * 100

CPI = 105.33

The CPI in Year 2 is 105.33

Thus,

For the average person, the CPI in Year 1 is 100 and the CPI in Year 2 is 105.33.

Calculate the cost of basket in Year 1 for Jane -

Cost of basket = [Housing * Price] + [Food * Price] + [Transportation * Price] + [Medical * Price] + [Education * Price] + [Clothing/fun * Price]

Cost of basket = [0.38 * 900] + [0.17 * 200] + [0.10 * 150] + [0.02 * 120] + [0.10 * 150] + [0.23 * 100]

Cost of basket = 342 + 34 + 15 + 2.4 + 15 + 23

Cost of basket = 431.40

The cost of basket in Year 1 for Jane is $431.40

Calculate the cost of basket in Year 2 for Jane -

Cost of basket = [Housing * Price] + [Food * Price] + [Transportation * Price] + [Medical * Price] + [Education * Price] + [Clothing/fun * Price]

Cost of basket = [0.38 * 945] + [0.17 * 204] + [0.10 * 160] + [0.02 * 160] + [0.10 * 158] + [0.23 * 100]

Cost of basket = 359.1 + 34.68 + 16 + 3.2 + 15.8 + 23

Cost of basket = 451.78

The cost of basket in Year 2 for Jane is $451.78

Thus,

For the Jane, the cost of the basket in Year 1 is $431.40 and the cost of the basket in Year 2 is $451.78.

The base year is Year 1. The value of CPI in base year is always 100.

So, the CPI in Year 1 is 100.

Calculate the value of CPI in Year 2 -

CPI = [Cost of basket in Year 2/Cost of basket in Year 1] * 100

CPI = [$451.78/$431.40] * 100

CPI = 104.72

The CPI in Year 2 is 104.72

Thus,

For the Jane, the CPI in Year 1 is 100 and the CPI in Year 2 is 104.72.