Statistical Techniques in Business and Economics
Statistical Techniques in Business and Economics
16th Edition
ISBN: 9780077639723
Author: Lind
Publisher: Mcgraw-Hill Course Content Delivery
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Chapter 17, Problem 7E

a.

To determine

Develop a simple price index using 2000 as the base period.

a.

Expert Solution
Check Mark

Answer to Problem 7E

The simple price index using 2000 as the base period is given below:

ItemPrice ($) (2000)Price ($) (2014)Simple Price Index
Washer0.070.10142.9
Cotter pin0.040.0375
Stove bolt0.150.15100
Hex nut0.080.10125

Explanation of Solution

Calculation:

The simple price index using 2000 as the base period is obtained as follows:

ItemPrice ($) (2000)Price ($) (2014)Simple Price Index(P)=ptp0×100
Washer0.070.100.100.07×100=142.9
Cotter pin0.040.030.030.04×100=75
Stove bolt0.150.150.150.15×100=100
Hex nut0.080.100.100.08×100=125

b.

To determine

Develop a simple aggregate price index using 2000 as the base period.

b.

Expert Solution
Check Mark

Answer to Problem 7E

The simple aggregate price index using 2000 as the base period is 111.76.

Explanation of Solution

Calculation:

The simple aggregate price index using 2000 as the base period is obtained as follows:

Simple aggregate price index(P)=ptp0×100=0.10+0.03+0.15+0.100.07+0.04+0.15+0.08×100=0.380.34×100=111.76

Thus, the simple aggregate price index using 2000 as the base period is 111.76.

c.

To determine

Find Laspeyres’ price index using 2000 as the base period.

c.

Expert Solution
Check Mark

Answer to Problem 7E

Laspeyres’ price index using 2000 as the base period is 102.92.

Explanation of Solution

Calculation:

Laspeyres’ price index using 2000 as the base period is obtained as follows:

P=ptq0p0q0×100=0.10(17,000)+0.03(125,000)+0.15(40,000)+0.10(62,000)0.07(17,000)+0.04(125,000)+0.15(40,000)+0.08(62,000)×100=102.92

Thus, Laspeyres’ price index using 2000 as the base period is 102.92.

d.

To determine

Find Paasche’s index using 2000 as the base period.

d.

Expert Solution
Check Mark

Answer to Problem 7E

Paasche’s index using 2000 as the base period is 103.32.

Explanation of Solution

Calculation:

Paasche’s index using 2000 as the base period is obtained as follows:

P=ptqtp0qt×100=0.10(20,000)+0.03(130,000)+0.15(42,000)+0.10(65,000)0.07(20,000)+0.04(130,000)+0.15(42,000)+0.08(65,000)×100=103.32

Thus, Paasche’s index using 2000 as the base period is 103.32.

e.

To determine

Find Fisher’s ideal index.

e.

Expert Solution
Check Mark

Answer to Problem 7E

Fisher’s ideal index is 103.12.

Explanation of Solution

Calculation:

Fisher’s ideal index is obtained as follows:

Fishers ideal index=Laspeyres price index×Paasches index =102.92×103.32=103.12

Thus, Fisher’s ideal index is 103.12.

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