The following table shows the prices and quantities consumed by a family of four
ID: 3392505 • Letter: T
Question
The following table shows the prices and quantities consumed by a family of four for selected food commodities for 1990 and 2006. Use 1990 as the base period.
1990
2006
Commodity
Price
Quantity
Price
Quantity
Ground beef (per lb)
$1.39
80
$2.09
110
Milk (1 gallon)
1.69
100
2.75
120
Cookies (dozen)
1.29
95
2.59
100
Steak (per pound)
4.99
50
9.49
40
a. Determine the simple index for steak for 2006.
b. Determine the simple aggregate price index for 2006.
c. Determine the Laspeyres price index for 2006.
d. Determine the Paasche price index for 2006.
e. Determine a value index for 2006.
14. The table reports the net profit for Heban Tool and Die, Inc. for the years 1996 and 2006. Also reported is the tool and die index for the same years (1985 = 100).
Year
Net profit
Index
1996
$45,380
136.3
2006
65,035
150.2
a. What was the percent increase in the index from 1996 to 2006?
b. Convert the index to a 1996 base. What is the new index for 2006?
c. Determine the net profit for 2006 in terms of the 1996 base. Comment on the change.
1990
2006
Commodity
Price
Quantity
Price
Quantity
Ground beef (per lb)
$1.39
80
$2.09
110
Milk (1 gallon)
1.69
100
2.75
120
Cookies (dozen)
1.29
95
2.59
100
Steak (per pound)
4.99
50
9.49
40
Explanation / Answer
Determine the simple index for steak for 2006.
First we have to make the table for finding index numbers.
Formula for that is,
P01 = (p1/p0 / n) * 100
and quantity index number is,
Q01 = (q1/q0 / n) * 100
where n is the number of categories. = 4
P01 = (7.0404 / 4 ) * 100 = 176. 0093
Q01 = (4.4276 / 4) * 100 = 110.6908
Simple agreegate price index for steak for 2006.
P01 = sum of prices in current year / sum of prices in base year * 100
Q01 = sum of quantities in current year / sum of quantities in base year * 100
current year = 2006
base year = 1990
P01 = ( 16.92 / 9.36 ) * 100 = 180.7692
Q01 = (370 / 325) * 100 = 113.8462
Determine the Laspeyres price index for 2006.
The formula for Laspeyres price index is,
P01L = ( p1q0 / p0q0 ) * 100
= (1162.75 / 652.25) * 100 = 178.2675
Q01L = ( q1p0 / p0q0 ) * 100
= 104.9138
Determine the Paasche price index for 2006.
P01P = (p1q1 / p0q1) * 100
= 175.1425
Q01P = (q1p1 / q0p1) * 100
= 103.0746
1990 2006 p0 q0 p1 q1 p1/p0 q1/q0 p1q0 p0q0 q1p0 p1q1 p0q1 q0p1 gb 1.39 80 2.09 110 1.503597 1.375 167.2 111.2 152.9 229.9 152.9 167.2 milk 1.69 100 2.75 120 1.627219 1.2 275 169 202.8 330 202.8 275 cookies 1.29 95 2.59 100 2.007752 1.052632 246.05 122.55 129 259 129 246.05 steak 4.99 50 9.49 40 1.901804 0.8 474.5 249.5 199.6 379.6 199.6 474.5 total 9.36 325 16.92 370 7.040372 4.427632 1162.75 652.25 684.3 1198.5 684.3 1162.75Related Questions
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