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
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.
To compute the price index for Jim's breakfast in 2001, we need to calculate the average price change for each item from the 1991 to 2001.
First, we need to calculate the price change for each item:
- Eggs: Price change = (2001 price - 1991 price) / 1991 price = (1.02 - 1.08) / 1.08 = -0.0556
- Bacon: Price change = (2.75 - 2.15) / 2.15 = 0.2791
- Bread: Price change = (0.98 - 0.63) / 0.63 = 0.5556
- Orange juice: Price change = (1.86 - 1.98) / 1.98 = -0.0606
- Grapefruit: Price change = (0.57 - 0.57) / 0.57 = 0 (price remained the same)
Next, we need to calculate the average price change:
Average price change = (price change for eggs + price change for bacon + price change for bread + price change for orange juice + price change for grapefruit) / 5
= (-0.0556 + 0.2791 + 0.5556 - 0.0606 + 0) / 5
= 0.1439
Finally, we can calculate the price index for Jim's breakfast in 2001:
Price index = (average price change + 1) * 100
= (0.1439 + 1) * 100
= 114.39
Therefore, the price index for Jim's breakfast in 2001, using 1991 as the base year, is 114.39.