Question

Brazil's real GDP was 1,180 trillion reais in 2013 and 1,202 trillion reais in \(2014 .\) Brazil's population was 198 million in 2013 and 200 million in \(2014 .\) Calculate a. The growth rate of real GDP. b. The growth rate of real GDP per person. c. The approximate number of years it takes for real GDP per person in Brazil to double if the 2014 growth rate of real GDP and the population growth rate are maintained.

Short answer

a. 1.86% b. 0.85% c. 82.35 years

Step-by-step solution

Calculate the growth rate of real GDP

To find the growth rate of real GDP between 2013 and 2014, use the formula: \[ \text{Growth Rate} = \frac{\text{Real GDP in 2014} - \text{Real GDP in 2013}}{\text{Real GDP in 2013}} \times 100 \text{\text{%}} \] Plug in the values from the problem: \[ \text{Growth Rate} = \frac{1,202 - 1,180}{1,180} \times 100 \text{\text{%}} \] This gives: \[ \text{Growth Rate} = \frac{22}{1,180} \times 100 \text{\text{%}} \ = 1.86\text{\text{%}} \]

Calculate the per person variable for each year

First, find the real GDP per person for each year: In 2013: \[ \text{Real GDP per Person} = \frac{\text{Real GDP}}{\text{Population}} \] \[ \text{Real GDP per Person in 2013} = \frac{1,180 \text{ trillion}}{198 \text{ million}} \] Divide the numbers (convert trillion to billion to make the division simpler): \[ \text{Real GDP per Person in 2013} = \frac{1,180,000 \text{ billion}}{198} \] This gives: \[ \text{Real GDP per Person in 2013} = 5,959.6 \text{ billion/billion} \] In 2014: \[ \text{Real GDP per Person in 2014} = \frac{1,202 \text{ trillion}}{200 \text{ million}} \] \[ \text{Real GDP per Person in 2014} = \frac{1,202,000 \text{ billion}}{200} \] This gives: \[ \text{Real GDP per Person in 2014} = 6,010 \text{ billion/billion} \]

Calculate the growth rate of real GDP per person

Use the growth rate formula again for real GDP per person: \[ \text{Growth Rate per Person} = \frac{\text{Real GDP per Person in 2014} - \text{Real GDP per Person in 2013}}{\text{Real GDP per Person in 2013}} \times 100 \text{\text{%}} \] Plug in the values: \[ \text{Growth Rate per Person} = \frac{6,010 - 5,959.6}{5,959.6} \times 100 \text{\text{%}} \] This gives: \[ \text{Growth Rate per Person} = \frac{50.4}{5,959.6} \times 100 \text{\text{%}} \ = 0.85\text{\text{%}} \]

Calculate the number of years for GDP per person to double

Use the Rule of 70 to estimate the doubling time: \[ \text{Doubling Time} = \frac{70}{\text{Growth Rate per Person}} \] Plug in the growth rate calculated: \[ \text{Doubling Time} = \frac{70}{0.85} \] This gives: \[ \text{Doubling Time} = 82.35 \text{ years} \]

Key concepts

real_GDP_growth

Real GDP growth measures the increase in the value of all goods and services produced by an economy over a specific period, adjusted for inflation. This allows for a more accurate comparison of economic performance across different time frames. Calculating real GDP growth involves the formula: \(\text{Growth Rate} = \frac{\text{Real GDP in Current Year} - \text{Real GDP in Previous Year}}{\text{Real GDP in Previous Year}} \times 100\% \). Plugging in the figures from Brazil, where the GDP grew from 1,180 trillion to 1,202 trillion reais between 2013 and 2014: \(\frac{1,202 - 1,180}{1,180} \times 100\% = 1.86\% \). This 1.86% is the real GDP growth, representing how much the economy expanded in real terms.

GDP_per_capita

GDP per capita is a metric that breaks down a country’s economic output per person and is calculated by dividing the total GDP by the population. It provides insight into the average economic well-being of the citizens. In 2013, Brazil’s real GDP per person was calculated as follows: \(\frac{1,180 \text{ trillion}}{198 \text{ million}} = 5,959.6 \text{ reais per person} \). For 2014, the calculation was: \(\frac{1,202 \text{ trillion}}{200 \text{ million}} = 6,010 \text{ reais per person} \). The increase in GDP per capita indicates that the economic growth outpaced the population growth, suggesting improved average economic well-being.

rule_of_70

The Rule of 70 is a simple way to estimate how long it takes for a quantity to double, assuming consistent growth. The formula is: \(\text{Doubling Time} = \frac{70}{\text{Growth Rate}} \) where the growth rate is expressed as a percentage. From the example, with Brazil's GDP per capita growth rate being 0.85%: \(\text{Doubling Time} = \frac{70}{0.85} = 82.35 \text{ years} \). This means that if Brazil's GDP per capita continues to grow at 0.85% annually, it will take approximately 82.35 years for it to double.

population_growth

Population growth affects the distribution of GDP among individuals. To understand its effect, we compare initial and subsequent population figures. Brazil's population grew from 198 million in 2013 to 200 million in 2014—an increase of about 1.01%. Population growth can dilute the effects of GDP growth, as more people share the economic output. Therefore, evaluating GDP per capita alongside population growth gives a clearer view of economic progress and living standards. If population grows too rapidly without corresponding GDP growth, per capita well-being might stagnate or decline.