Chapter 17, Problem 6E

a.

To determine

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

Answer to Problem 6E

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

Fruit	Price ($) (2000)	Price ($) (2017)	Simple Price Index
Bananas (pound)	0.23	0.69	300
Grapefruit (each)	0.29	1	344.83
Apples (pound)	0.35	1.89	540
Strawberries (basket)	1.02	3.79	371.57
Oranges (bag)	0.89	2.99	335.96

Explanation of Solution

Calculation:

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

Fruit	Price ($) (2000)	Price ($) (2017)	$\text{Simple Price Index}\left(P\right)=\frac{p_t}{p_0}\times 100$
Bananas (pound)	0.23	0.69	$\frac{0.69}{0.23}\times 100=300$
Grapefruit (each)	0.29	1	$\frac{1}{0.29}\times 100=344.83$
Apples (pound)	0.35	1.89	$\frac{1.89}{0.35}\times 100=540$
Strawberries (basket)	1.02	3.79	$\frac{3.79}{1.02}\times 100=371.57$
Oranges (bag)	0.89	2.99	$\frac{2.99}{0.89}\times 100=335.96$

b.

To determine

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

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:

$\begin{array}{c}\text{Simple aggregate price index}\left(P\right)=\frac{{\displaystyle \sum p_t}}{{\displaystyle \sum p_0}}\times 100\\ =\frac{0.69+1+1.89+3.79+2.99}{0.23+0.29+0.35+1.02+0.89}\times 100\\ =\frac{10.36}{2.78}\times 100\\ =372.66\end{array}$

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.

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:

$\begin{array}{c}P=\frac{{\displaystyle \sum p_t{q}_0}}{{\displaystyle \sum p_0{q}_0}}\times 100\\ =\frac{0.69\left(100\right)+1\left(50\right)+1.89\left(85\right)+3.79\left(8\right)+2.99\left(6\right)}{0.23\left(100\right)+0.29\left(50\right)+0.35\left(85\right)+1.02\left(8\right)+0.89\left(6\right)}\times 100\\ =406.08\end{array}$

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.

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:

$\begin{array}{c}P=\frac{{\displaystyle \sum p_t{q}_t}}{{\displaystyle \sum p_0{q}_t}}\times 100\\ =\frac{0.69\left(120\right)+1\left(55\right)+1.89\left(85\right)+3.79\left(10\right)+2.99\left(8\right)}{0.23\left(120\right)+0.29\left(55\right)+0.35\left(85\right)+1.02\left(10\right)+0.89\left(8\right)}\times 100\\ =397.56\end{array}$

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

e.

To determine

Find the Fisher’s ideal index.

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:

$\begin{array}{c}\text{Fisher}’\text{s ideal index}=\sqrt{\text{Laspeyres}’\text{ price index}\times \text{Paasches}’\text{ index }}\\ =\sqrt{406.08\times 397.56}\\ =401.80\end{array}$

Thus, the Fisher’s ideal index is 401.80.