Question

using the table below, calculate real gdp per capita for both years. show your work:
year | 2019 | 2020
population | 10,000 | 10,000
gdp deflator | 100 | 110
nominal gdp | $500,000 | $580,000
2019:
2020:

Explanation:

Step 1: Recall the formula for Real GDP

The formula for real GDP is \( \text{Real GDP} = \frac{\text{Nominal GDP}}{\text{GDP Deflator}} \times 100 \) (since GDP deflator is an index with base year deflator = 100). Then, real GDP per capita is \( \text{Real GDP per capita} = \frac{\text{Real GDP}}{\text{Population}} \).

Step 2: Calculate Real GDP for 2019

For 2019:

• Nominal GDP = $500,000
• GDP Deflator = 100

Using the real GDP formula: \( \text{Real GDP}_{2019} = \frac{500000}{100} \times 100 = 500000 \)
Then, real GDP per capita for 2019: Population = 10,000
\( \text{Real GDP per capita}_{2019} = \frac{500000}{10000} = 50 \)

Step 3: Calculate Real GDP for 2020

For 2020:

• Nominal GDP = $580,000
• GDP Deflator = 110

First, calculate real GDP: \( \text{Real GDP}_{2020} = \frac{580000}{110} \times 100 \approx \frac{58000000}{110} \approx 527272.73 \) (rounded to two decimal places)
Then, real GDP per capita for 2020: Population = 10,000
\( \text{Real GDP per capita}_{2020} = \frac{527272.73}{10000} \approx 52.73 \) (rounded to two decimal places)

Answer:

• 2019 Real GDP per capita: $50
• 2020 Real GDP per capita: Approximately $52.73