Question

​Jim's favorite breakfast is two​ eggs, 1/5 lb. of​ bacon, 1/7 lb. of white​ toast, 1/6 can​ (16 ounce​ can) of frozen concentrate orange​ juice, and 1 lb. of grapefruit. The following table contains 1991 and 2001 prices for these five items. Using 1991 as the base​ year, compute the price index for​ Jim's breakfast for 2001.
One dozen eggs
​1991=$1.08
​2001=$1.02
One pound bacon
1991=​$2.15
​2001=$2.75
One pound bread
​1991=$0.63
2001=​$0.98
One can orange juice
​1991=$1.98
2001=​$1.86
One pound grapefruit
​1991=$0.57

Answer 1

​2001=$0.73

To compute the price index for​ Jim's breakfast for 2001, we first need to calculate the total cost of his breakfast in both 1991 and 2001 using the given prices:

- 1991:
2 eggs = 2 x $0.33 (1/2 of $0.66, the price of a dozen eggs in 1991) = $0.66
1/5 lb. bacon = $0.43 (1/5 of $2.15)
1/7 lb. bread = $0.09 (1/7 of $0.63)
1/6 can orange juice = $0.33 (1/6 of $1.98)
1 lb. grapefruit = $0.57
Total cost in 1991 = $2.08

- 2001:
2 eggs = 2 x $0.085 (1/2 of $1.02, the price of a dozen eggs in 2001) = $0.17
1/5 lb. bacon = $0.55 (1/5 of $2.75)
1/7 lb. bread = $0.14 (1/7 of $0.98)
1/6 can orange juice = $0.31 (1/6 of $1.86)
1 lb. grapefruit = $0.73
Total cost in 2001 = $1.90

Now we can use the formula for calculating a price index:

Price index = (Total cost in current year / Total cost in base year) x 100

Price index = ($1.90 / $2.08) x 100 = 91.35

Therefore, the price index for​ Jim's breakfast for 2001, using 1991 as the base​ year, is 91.35. This means that the cost of his breakfast in 2001 was about 91% of what it would have been if prices had remained at 1991 levels.