In the following table, we present prices for three commonly used products—bread, fruits, and beverages—for the years 2008 through 2012.
$\begin{array}{|l|l|l|l|}\hline &\text { Bread } & \text { Fruits } & \text { Beverages } \
\hline \text { Year } & (\$ \text { per loaf) } & (\$ \text { per } \mathrm{kg}) & (\$ \text { per } \mathrm{L}) \
\hline 2008 & \$ 1.21 & \$ 2.18 & \$ 0.75 \
\hline 2009 & \$ 1.23 & \$ 2.35 & \$ 0.75 \
\hline 2010 & \$ 1.29 & \$ 2.41 & \$ 0.77 \
\hline 2011 & \$ 1.35 & \$ 2.54 & \$ 0.77 \
\hline 2012 & \$ 1.42 & \$ 2.87 & \$ 0.78 \
\hline
\end{array}$
Consider a family with the following yearly consumption for these products for the years 2008 through 2012.
$$\begin{array} { | l | l | l | l | } \hline &\text { Bread } & \text { Fruits } & \text { Beverages } \
\hline \text { Year } &\text { (loaves) } & (\mathrm{kg}) & (\mathrm{L}) \
\hline \mathbf { 2 0 0 8 } & 2,200 & 250 & 2,400 \
\hline \mathbf { 2 0 0 9 } & 2,200 & 235 & 2,450 \
\hline \mathbf { 2 0 1 0 } & 2,200 & 210 & 2,580 \
\hline \mathbf { 2 0 1 1 } & 2,200 & 180 & 2,690 \
\hline \mathbf { 2 0 1 2 } & 2,200 & 140 & 2,810 \
\hline
\end{array}$$
Answer the following questions using 2008 as the base year.

-Compute the Paasche index for 2011.
A)101.68
B)112.67
C)105.46
D)108.41
E)100

Question

In the following table, we present prices for three commonly used products—bread, fruits, and beverages—for the years 2008 through 2012.
$\begin{array}{|l|l|l|l|}\hline &\text { Bread } & \text { Fruits } & \text { Beverages } \
\hline \text { Year } & (\$ \text { per loaf) } & (\$ \text { per } \mathrm{kg}) & (\$ \text { per } \mathrm{L}) \
\hline 2008 & \$ 1.21 & \$ 2.18 & \$ 0.75 \
\hline 2009 & \$ 1.23 & \$ 2.35 & \$ 0.75 \
\hline 2010 & \$ 1.29 & \$ 2.41 & \$ 0.77 \
\hline 2011 & \$ 1.35 & \$ 2.54 & \$ 0.77 \
\hline 2012 & \$ 1.42 & \$ 2.87 & \$ 0.78 \
\hline
\end{array}$
Consider a family with the following yearly consumption for these products for the years 2008 through 2012.
$$\begin{array} { | l | l | l | l | } \hline &\text { Bread } & \text { Fruits } & \text { Beverages } \
\hline \text { Year } &\text { (loaves) } & (\mathrm{kg}) & (\mathrm{L}) \
\hline \mathbf { 2 0 0 8 } & 2,200 & 250 & 2,400 \
\hline \mathbf { 2 0 0 9 } & 2,200 & 235 & 2,450 \
\hline \mathbf { 2 0 1 0 } & 2,200 & 210 & 2,580 \
\hline \mathbf { 2 0 1 1 } & 2,200 & 180 & 2,690 \
\hline \mathbf { 2 0 1 2 } & 2,200 & 140 & 2,810 \
\hline
\end{array}$$
Answer the following questions using 2008 as the base year.

-Compute the Paasche index for 2011.
A)101.68
B)112.67
C)105.46
D)108.41
E)100

Quizplus · Accepted Answer

The Paasche index for 2011 is calculated by comparing the cost of the basket of goods in 2011 to the cost in the base year (2008), using the quantities from 2011. The formula for the Paasche index is:$$ \text{Paasche Index} = \left( \frac{\text{Cost of basket in current year}}{\text{Cost of basket in base year}} \right) \times 100 $$For 2011, the cost of the basket is:- Bread: $2,200 \text{ loaves} \times \$1.35/\text{loaf} = \$2,970$- Fruits: $180 \text{ kg} \times \$2.54/\text{kg} = \$457.2$- Beverages: $2,690 \text{ L} \times \$0.77/\text{L} = \$2,071.3$Total cost in 2011: $ \$2,970 + \$457.2 + \$2,071.3 = \$5,498.5$For 2008, using 2011 quantities:- Bread: $2,200 \text{ loaves} \times \$1.21/\text{loaf} = \$2,662$- Fruits: $180 \text{ kg} \times \$2.18/\text{kg} = \$392.4$- Beverages: $2,690 \text{ L} \times \$0.75/\text{L} = \$2,017.5$Total cost in 2008: $ \$2,662 + \$392.4 + \$2,017.5 = \$5,071.9$Paasche Index for 2011: $\left( \frac{\$5,498.5}{\$5,071.9} \right) \times 100 = 108.41$Therefore, the correct answer is D) 108.41.

In the Following Table, We Present Prices for Three Commonly