Chapter 17, Problem 8E

a.

To determine

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

Answer to Problem 8E

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

Item	Price ($) (2000)	Price ($) (2014)	Simple Price Index
Syringes (dozen)	6.10	6.83	111.97
Thermometers	8.10	9.35	115.43
Advil (bottle)	4	4.62	115.5
Patient record forms (box)	6	6.85	114.17
Computer paper (box)	12	13.65	113.75

Explanation of Solution

Calculation:

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

Item	Price ($) (2000)	Price ($) (2014)	$\text{Simple Price Index}\left(P\right)=\frac{p_t}{p_0}\times 100$
Syringes (dozen)	6.10	6.83	$\frac{6.83}{6.10}\times 100=111.97$
Thermometers	8.10	9.35	$\frac{9.35}{8.10}\times 100=115.43$
Advil (bottle)	4	4.62	$\frac{4.62}{4}\times 100=115.5$
Patient record forms (box)	6	6.85	$\frac{6.85}{6}\times 100=114.17$
Computer paper (box)	12	13.65	$\frac{13.65}{12}\times 100=113.75$

b.

To determine

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

Answer to Problem 8E

The simple aggregate price index using 2000 as the base period is 114.09.

Explanation of Solution

Calculation:

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

$\begin{array}{c}\text{Simple aggregate price index}\left(P\right)=\frac{{\displaystyle \sum p_t}}{{\displaystyle \sum p_0}}\times 100\\ =\frac{6.83+9.35+4.62+6.85+13.65}{6.10+8.10+4+6+12}\times 100\\ =\frac{41.30}{36.20}\times 100\\ =114.09\end{array}$

Thus, the simple aggregate price index using 2000 as the base period is 114.09.

c.

To determine

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

Answer to Problem 8E

Laspeyres’ price index using 2000 as the base period is 113.03.

Explanation of Solution

Calculation:

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

$\begin{array}{c}P=\frac{{\displaystyle \sum p_t{q}_0}}{{\displaystyle \sum p_0{q}_0}}\times 100\\ =\frac{6.83\left(1,500\right)+9.35\left(10\right)+4.62\left(250\right)+6.85\left(1,000\right)+13.65\left(30\right)}{6.10\left(1,500\right)+8.10\left(10\right)+4\left(250\right)+6\left(1,000\right)+12\left(30\right)}\times 100\\ =113.03\end{array}$

Thus, Laspeyres’ price index using 2000 as the base period is 113.02.

d.

To determine

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

Answer to Problem 8E

Paasche’s index using 2000 as the base period is 112.83.

Explanation of Solution

Calculation:

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

$\begin{array}{c}P=\frac{{\displaystyle \sum p_t{q}_t}}{{\displaystyle \sum p_0{q}_t}}\times 100\\ =\frac{6.83\left(2,000\right)+9.35\left(12\right)+4.62\left(250\right)+6.85\left(900\right)+13.65\left(40\right)}{6.10\left(2,000\right)+8.10\left(12\right)+4\left(250\right)+6\left(900\right)+12\left(40\right)}\times 100\\ =112.83\end{array}$

Thus, Paasche’s index using 2000 as the base period is 112.83.

e.

To determine

Find Fisher’s ideal index.

Answer to Problem 8E

Fisher’s ideal index is 112.93.

Explanation of Solution

Calculation:

Fisher’s ideal index is obtained as follows:

$\begin{array}{c}\text{Fisher}’\text{s ideal index}=\sqrt{\text{Laspeyres}’\text{ price index}\times \text{Paasches}’\text{ index }}\\ =\sqrt{113.03\times 112.83}\\ =112.93\end{array}$

Thus, Fisher’s ideal index is 112.93.