Real GDP in 2010 is $10 trillion. Between 2010 and 2011, using 2010 prices, GDP grew 3 percent and using 2011 prices real GDP grew 7 percent. Using the chain-weighted output index method, real GDP in 2011 is __ trillion.
A) $10.5
B) $11
C) $10.1
D) $12.72
The correct answer and explanation is :
The correct answer is B) $11 trillion.
Explanation:
To calculate real GDP in 2011 using the chain-weighted output index method, we need to use the formula for chain-weighted GDP:
[
\text{Real GDP in 2011} = \text{Real GDP in 2010} \times \left( 1 + \text{Percentage Change using 2010 Prices} \right) \times \left( 1 + \text{Percentage Change using 2011 Prices} \right)
]
Here’s the breakdown of each component:
- Real GDP in 2010: Given as $10 trillion.
- Percentage change using 2010 prices: Real GDP grew by 3% between 2010 and 2011, measured using 2010 prices.
- Percentage change using 2011 prices: Real GDP grew by 7% between 2010 and 2011, measured using 2011 prices.
First, we calculate the growth rate in real GDP using 2010 prices:
[
\text{Growth using 2010 prices} = 1 + 3\% = 1 + 0.03 = 1.03
]
Next, we calculate the growth rate using 2011 prices:
[
\text{Growth using 2011 prices} = 1 + 7\% = 1 + 0.07 = 1.07
]
Now, using the chain-weighted method, we multiply the real GDP in 2010 by both growth factors:
[
\text{Real GDP in 2011} = 10 \times 1.03 \times 1.07
]
[
\text{Real GDP in 2011} = 10 \times 1.1021 = 11.021 \text{ trillion}
]
Rounding to the nearest trillion, the result is approximately $11 trillion.
Thus, the correct answer is B) $11 trillion. This method allows for a more accurate calculation of real GDP by incorporating both years’ price levels, avoiding potential biases from using only one year’s prices.