3. You have been hired by the government as an economic statistician and given the job of calculating the CPI (the chili price index, not the consumer price index). According to the government's official recipe, the ingredients for a batch of chili are: 3 pounds of hamburger, 2 pounds of tomatoes, and 1/2 pound of onions.
The base year for calculating the CPI is 1996. The prices of the ingredients for chili are determined by an extensive nationwide survey. The current and 1996 prices for the ingredients are:
Hamburger: $1.20 per pound in 1996; $1.15 per pound currently
Tomatoes: $1.50 per pound in 1996; $1.75 per pound currently
Onions: $.20 per pound in 1996; $.30 per pound currently
Calculate the cost of a batch of chili in 1996 and currently, and express the current price as a price index with 1996 as the base year.
Take a shot. What do you get. Hint: calculating the cost of chili in 1996 and today is easy. Calculate the ratio cost today/1996. For an index, make 1996=100, today's index will have the same percentage increase as the cost to produce the chili.
take it from here
7.40/6.95=
(7.40)/(6.95)=100
1.06=100
To calculate the cost of a batch of chili in 1996 and currently, we need to multiply the price of each ingredient by the corresponding weight and then sum them up.
In 1996:
Hamburger: 3 pounds * $1.20 per pound = $3.60
Tomatoes: 2 pounds * $1.50 per pound = $3.00
Onions: 0.5 pounds * $0.20 per pound = $0.10
Total cost in 1996: $3.60 + $3.00 + $0.10 = $6.70
Currently:
Hamburger: 3 pounds * $1.15 per pound = $3.45
Tomatoes: 2 pounds * $1.75 per pound = $3.50
Onions: 0.5 pounds * $0.30 per pound = $0.15
Total current cost: $3.45 + $3.50 + $0.15 = $7.10
To express the current price as a price index with 1996 as the base year, we can calculate the percentage change in price for each ingredient and then multiply it by 100 to create an index:
Hamburger: (($1.15 - $1.20) / $1.20) * 100 = -4.17%
Tomatoes: (($1.75 - $1.50) / $1.50) * 100 = 16.67%
Onions: (($0.30 - $0.20) / $0.20) * 100 = 50%
Weighted average index:
((-4.17% * 3) + (16.67% * 2) + (50% * 0.5)) = (-12.51 + 33.34 + 25) = 45.83
Therefore, the current price expressed as a price index with 1996 as the base year is 45.83.