Answer :
To solve this problem, we need to find the missing values in the table using the relationship between Nominal GDP, Real GDP, and the Price Index. The formula we use is:
[tex]\[ \text{Real GDP} = \frac{\text{Nominal GDP}}{\text{Price Index}} \times 100 \][/tex]
This formula helps us to convert Nominal GDP to Real GDP, ensuring the GDP is adjusted for inflation by using the Price Index.
Step-by-Step Solution:
1. Year 1: Find Real GDP
- Given: Nominal GDP = 14,964.4 billion, Price Index = 101.2
- Use the formula:
[tex]\[
\text{Real GDP} = \frac{14964.4}{101.2} \times 100 = 14782.0 \, \text{billion (rounded to 1 decimal place)}
\][/tex]
2. Year 3: Find Price Index
- Given: Nominal GDP = 16,155.3 billion, Real GDP = 15,354.7 billion
- Rearrange the formula to solve for the Price Index:
[tex]\[
\text{Price Index} = \frac{16155.3}{15354.7} \times 100 = 105.2 \, (\text{rounded to 1 decimal place})
\][/tex]
3. Year 4: Find Nominal GDP
- Given: Real GDP = 15,612.2 billion, Price Index = 106.9
- Use the rearranged formula:
[tex]\[
\text{Nominal GDP} = \frac{15612.2 \times 106.9}{100} = 16685.5 \, \text{billion (rounded to 1 decimal place)}
\][/tex]
4. Year 6: Find Real GDP
- Given: Nominal GDP = 18,036.6 billion, Price Index = 110
- Use the formula:
[tex]\[
\text{Real GDP} = \frac{18036.6}{110} \times 100 = 16306.0 \, \text{billion (rounded to 1 decimal place)}
\][/tex]
Now, we have calculated all the missing values in the table. Here is the completed information:
- Year 1: Real GDP = 14,782.0 billion
- Year 3: Price Index = 105.2
- Year 4: Nominal GDP = 16,685.5 billion
- Year 6: Real GDP = 16,306.0 billion
[tex]\[ \text{Real GDP} = \frac{\text{Nominal GDP}}{\text{Price Index}} \times 100 \][/tex]
This formula helps us to convert Nominal GDP to Real GDP, ensuring the GDP is adjusted for inflation by using the Price Index.
Step-by-Step Solution:
1. Year 1: Find Real GDP
- Given: Nominal GDP = 14,964.4 billion, Price Index = 101.2
- Use the formula:
[tex]\[
\text{Real GDP} = \frac{14964.4}{101.2} \times 100 = 14782.0 \, \text{billion (rounded to 1 decimal place)}
\][/tex]
2. Year 3: Find Price Index
- Given: Nominal GDP = 16,155.3 billion, Real GDP = 15,354.7 billion
- Rearrange the formula to solve for the Price Index:
[tex]\[
\text{Price Index} = \frac{16155.3}{15354.7} \times 100 = 105.2 \, (\text{rounded to 1 decimal place})
\][/tex]
3. Year 4: Find Nominal GDP
- Given: Real GDP = 15,612.2 billion, Price Index = 106.9
- Use the rearranged formula:
[tex]\[
\text{Nominal GDP} = \frac{15612.2 \times 106.9}{100} = 16685.5 \, \text{billion (rounded to 1 decimal place)}
\][/tex]
4. Year 6: Find Real GDP
- Given: Nominal GDP = 18,036.6 billion, Price Index = 110
- Use the formula:
[tex]\[
\text{Real GDP} = \frac{18036.6}{110} \times 100 = 16306.0 \, \text{billion (rounded to 1 decimal place)}
\][/tex]
Now, we have calculated all the missing values in the table. Here is the completed information:
- Year 1: Real GDP = 14,782.0 billion
- Year 3: Price Index = 105.2
- Year 4: Nominal GDP = 16,685.5 billion
- Year 6: Real GDP = 16,306.0 billion
