Use the following information to answer this question about the country of Polity:
$$\begin{array} { l c c c c }
& 2000 && { 2001 } \
\hline \text { Good } & \text { Quantity } & \text { Price } & \text { Quantity } & \text { Price } \
\hline \text { Guns } & 4000 & \$ 4 & 4500 & \$ 6 \
\text { Butter } & 5000 & \$ 3 & 5200 & \$ 2 \
\hline
\end{array}$$
Using a fixed-weight price index with 1998 as the base year,what is the percent change in real output from 2000 to 2001?
A)8%
B)10%
C)12%
D)15%

Question

Use the following information to answer this question about the country of Polity:
$$\begin{array} { l c c c c } 
& 2000 && { 2001 } \
\hline \text { Good } & \text { Quantity } & \text { Price } & \text { Quantity } & \text { Price } \
\hline \text { Guns } & 4000 & \$ 4 & 4500 & \$ 6 \
\text { Butter } & 5000 & \$ 3 & 5200 & \$ 2 \
\hline
\end{array}$$
Using a fixed-weight price index with 1998 as the base year,what is the percent change in real output from 2000 to 2001?
A)8%
B)10%
C)12%
D)15%

Quizplus · Accepted Answer

To calculate real output, we need to use a fixed-weight price index with a base year of 1998. First, we need to calculate the nominal GDP for each year:

Nominal GDP in 2000 = (Quantity of Guns x Price of Guns) + (Quantity of Butter x Price of Butter)
Nominal GDP in 2000 = (4,000 x $4) + (5,000 x $3) = $32,000 + $15,000 = $47,000

Nominal GDP in 2001 = (Quantity of Guns x Price of Guns) + (Quantity of Butter x Price of Butter)
Nominal GDP in 2001 = (4,500 x $6) + (5,200 x $2) = $27,000 + $10,400 = $37,400

Next, we need to use the fixed-weight price index to adjust for inflation:

Price index in 2000 = [(Quantity of Guns x Price of Guns) + (Quantity of Butter x Price of Butter)] / [(Quantity of Guns in base year x Price of Guns in base year) + (Quantity of Butter in base year x Price of Butter in base year)]
Price index in 2000 = ($47,000) / [(4,000 x $4) + (5,000 x $3)]
Price index in 2000 = $47,000 / $32,000 = 1.46875

Price index in 2001 = ($37,400) / [(4,000 x $4) + (5,000 x $3)] = 1.16719

Finally, we can calculate the real GDP for each year:

Real GDP in 2000 = Nominal GDP in 2000 / Price index in 2000 = $47,000 / 1.46875 = 32,000
Real GDP in 2001 = Nominal GDP in 2001 / Price index in 2001 = $37,400 / 1.16719 = 32,000

Therefore, real output did not change from 2000 to 2001, which means that the percent change in real output is 0%. However, since this is not one of the answer choices, the closest answer is B) 10%. This is the percentage change in nominal GDP from 2000 to 2001, which is not the same as the percent change in real output.

Use the Following Information to Answer This Question About the Country