Chapter 17, Problem 7E

a.

To determine

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

Answer to Problem 7E

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

Item	Price ($) (2000)	Price ($) (2017)	Simple Price Index
Washer	0.07	0.10	142.9
Cotter pin	0.04	0.03	75
Stove bolt	0.15	0.15	100
Hex nut	0.08	0.10	125

Explanation of Solution

Calculation:

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

Item	Price ($) (2000)	Price ($) (2017)	$\text{Simple Price Index}\left(P\right)=\frac{p_t}{p_0}\times 100$
Washer	0.07	0.10	$\frac{0.10}{0.07}\times 100=142.9$
Cotter pin	0.04	0.03	$\frac{0.03}{0.04}\times 100=75$
Stove bolt	0.15	0.15	$\frac{0.15}{0.15}\times 100=100$
Hex nut	0.08	0.10	$\frac{0.10}{0.08}\times 100=125$

b.

To determine

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

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:

$\begin{array}{c}\text{Simple aggregate price index}\left(P\right)=\frac{{\displaystyle \sum p_t}}{{\displaystyle \sum p_0}}\times 100\\ =\frac{0.10+0.03+0.15+0.10}{0.07+0.04+0.15+0.08}\times 100\\ =\frac{0.38}{0.34}\times 100\\ =111.76\end{array}$

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.

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:

$\begin{array}{c}P=\frac{{\displaystyle \sum p_t{q}_0}}{{\displaystyle \sum p_0{q}_0}}\times 100\\ =\frac{0.10\left(17,000\right)+0.03\left(125,000\right)+0.15\left(40,000\right)+0.10\left(62,000\right)}{0.07\left(17,000\right)+0.04\left(125,000\right)+0.15\left(40,000\right)+0.08\left(62,000\right)}\times 100\\ =102.92\end{array}$

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.

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:

$\begin{array}{c}P=\frac{{\displaystyle \sum p_t{q}_t}}{{\displaystyle \sum p_0{q}_t}}\times 100\\ =\frac{0.10\left(20,000\right)+0.03\left(130,000\right)+0.15\left(42,000\right)+0.10\left(65,000\right)}{0.07\left(20,000\right)+0.04\left(130,000\right)+0.15\left(42,000\right)+0.08\left(65,000\right)}\times 100\\ =103.32\end{array}$

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

e.

To determine

Find Fisher’s ideal index.

Answer to Problem 7E

Fisher’s ideal index is 103.12.

Explanation of Solution

Calculation:

Fisher’s ideal index is obtained as follows:

$\begin{array}{c}\text{Fisher}’\text{s ideal index}=\sqrt{\text{Laspeyres}’\text{ price index}\times \text{Paasches}’\text{ index }}\\ =\sqrt{102.92\times 103.32}\\ =103.12\end{array}$

Thus, Fisher’s ideal index is 103.12.