The country of Old Jersey produces milk and butter,and it has published the following macroeconomic data,where quantities are in gallons and prices are dollars per gallon:
$$\begin{array} { l c r c c }
& 2000 &&{ 2001 } \
\hline \text { Good } & \text { Quantity } & \text { Price } & \text { Quantity } & \text { Price } \
\hline \text { Milk } & 500 & \$ 2 & 900 & \$ 3 \
\text { Butter } & 2000 & \$ 1 & 3000 & \$ 2 \
\hline
\end{array}$$
Between 2000 and 2001,the percent change in the price level as measured by a variable-weight price index was

Question

The country of Old Jersey produces milk and butter,and it has published the following macroeconomic data,where quantities are in gallons and prices are dollars per gallon:
$$\begin{array} { l c r c c } 
& 2000 &&{ 2001 } \
\hline \text { Good } & \text { Quantity } & \text { Price } & \text { Quantity } & \text { Price } \
\hline \text { Milk } & 500 & \$ 2 & 900 & \$ 3 \
\text { Butter } & 2000 & \$ 1 & 3000 & \$ 2 \
\hline
\end{array}$$
Between 2000 and 2001,the percent change in the price level as measured by a variable-weight price index was

Quizplus · Accepted Answer

To calculate the percent change in the price level, we need to use a variable-weight price index. This index takes into account both the change in quantity and the change in price for each good. We can calculate the percent change in the price level using the following formula:
$\frac{	ext{Value in} \ 2001}{	ext{Value in} \ 2000} 	imes 100\%$
To calculate the value in each year, we multiply the quantity by the price:
\begin{align*}
	ext{Value of milk in 2000} &= 500 	imes \$2 = \$1000 \
	ext{Value of butter in 2000} &= 2000 	imes \$1 = \$2000 \
	ext{Value of milk in 2001} &= 900 	imes \$3 = \$2700 \
	ext{Value of butter in 2001} &= 3000 	imes \$2 = \$6000 \
\end{align*}
Next, we calculate the variable-weight price index by summing the values in each year and dividing by the total quantity for each year:
\begin{align*}
	ext{Price index in 2000} &= \frac{\$1000 + \$2000}{500 + 2000} = \frac{\$3000}{2500} = 1.2 \
	ext{Price index in 2001} &= \frac{\$2700 + \$6000}{900 + 3000} = \frac{\$8700}{3900} = 2.23 \
\end{align*}
Finally, we can calculate the percent change in the price level:
$\frac{2.23}{1.2} 	imes 100\% \approx 81.25\%$
Therefore, the best choice is B.

The Country of Old Jersey Produces Milk and Butter,and It