The following table shows the prices and quantities consumed

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

Solution

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,

P01^L = ( p1q0 / p0q0 ) * 100

= (1162.75 / 652.25) * 100 = 178.2675

Q01^L = ( q1p0 / p0q0 ) * 100

=   104.9138

Determine the Paasche price index for 2006.

P01^P = (p1q1 / p0q1) * 100

= 175.1425

Q01^P = (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	1162.75