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 6E

a.

To determine

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

a.

Expert Solution
Check Mark

Answer to Problem 6E

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

FruitPrice ($) (2000)Price ($) (2014)Simple Price Index
Bananas (pound)0.230.69300
Grapefruit (each)0.291344.83
Apples (pound)0.351.89540
Strawberries (basket)1.023.79371.57
Oranges (bag)0.892.99335.96

Explanation of Solution

Calculation:

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

FruitPrice ($) (2000)Price ($) (2014)Simple Price Index(P)=ptp0×100
Bananas (pound)0.230.690.690.23×100=300
Grapefruit (each)0.29110.29×100=344.83
Apples (pound)0.351.891.890.35×100=540
Strawberries (basket)1.023.793.791.02×100=371.57
Oranges (bag)0.892.992.990.89×100=335.96

b.

To determine

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

b.

Expert Solution
Check Mark

Answer to Problem 6E

The simple aggregate price index using 2000 as the base period is 372.66.

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=0.69+1+1.89+3.79+2.990.23+0.29+0.35+1.02+0.89×100=10.362.78×100=372.66

Thus, the simple aggregate price index using 2000 as the base period is 372.66.

c.

To determine

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

c.

Expert Solution
Check Mark

Answer to Problem 6E

The Laspeyres’ price index using 2000 as the base period is 406.08.

Explanation of Solution

Calculation:

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

P=ptq0p0q0×100=0.69(100)+1(50)+1.89(85)+3.79(8)+2.99(6)0.23(100)+0.29(50)+0.35(85)+1.02(8)+0.89(6)×100=406.08

Thus, the Laspeyres’ price index using 2000 as the base period is 406.08.

d.

To determine

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

d.

Expert Solution
Check Mark

Answer to Problem 6E

The Paasche’s index using 2000 as the base period is 397.56.

Explanation of Solution

Calculation:

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

P=ptqtp0qt×100=0.69(120)+1(55)+1.89(85)+3.79(10)+2.99(8)0.23(120)+0.29(55)+0.35(85)+1.02(10)+0.89(8)×100=397.56

Thus, the Paasche’s index using 2000 as the base period is 397.56.

e.

To determine

Find the Fisher’s ideal index.

e.

Expert Solution
Check Mark

Answer to Problem 6E

The Fisher’s ideal index is 401.80.

Explanation of Solution

Calculation:

The Fisher’s ideal index is obtained as follows:

Fishers ideal index=Laspeyres price index×Paasches index =406.08×397.56=401.80

Thus, the Fisher’s ideal index is 401.80.

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