To calculate the Real GDP for Year 2, we will use the prices of Year 1 and the quantities of Year 2 for each of the products. This approach allows us to measure the real output change without being affected by the price changes between the years.
Here's a step-by-step explanation of how to calculate the Real GDP in Year 2:
1. Identify the prices of Year 1 and the quantities of Year 2 for each product:
- Product [tex]\(X\)[/tex]:
- Year 1 Price: \[tex]$5.00
- Year 2 Quantity: 6
- Product \(Y\):
- Year 1 Price: \$[/tex]4.00
- Year 2 Quantity: 7
- Product [tex]\(Z\)[/tex]:
- Year 1 Price: \[tex]$8.00
- Year 2 Quantity: 15
2. Calculate the Real GDP contribution for each product:
- For Product \(X\):
\[
\text{Year 1 Price} \times \text{Year 2 Quantity} = \$[/tex]5.00 \times 6 = \[tex]$30.00
\]
- For Product \(Y\):
\[
\text{Year 1 Price} \times \text{Year 2 Quantity} = \$[/tex]4.00 \times 7 = \[tex]$28.00
\]
- For Product \(Z\):
\[
\text{Year 1 Price} \times \text{Year 2 Quantity} = \$[/tex]8.00 \times 15 = \[tex]$120.00
\]
3. Sum up the Real GDP contributions from all products to get the Real GDP for Year 2:
\[
\text{Real GDP for Year 2} = \$[/tex]30.00 + \[tex]$28.00 + \$[/tex]120.00 = \[tex]$178.00
\]
Hence, the Real GDP in Year 2, using the prices from Year 1, is \$[/tex]178.00.
