Question

Suppose an economy’s real GDP is \(30,000 in year 1 and \)31,200 in year 2. What is the growth rate of its real GDP? Assume that the population is 100 in year 1 and 102 in year 2. What is the growth rate of real GDP per capita?

Short answer

• The growth rate of the country’s real GDP is 4 percent.
• The growth rate of real GDP per capita is 1.96 percent.

Step-by-step solution

Step 1. Calculation of country’s growth rate of real GDP

The country’s growth rate of real GDP is calculated by dividing the difference between the real GDP’s of the current year and base year with the real GDP of the base year and multiplying it by 100. The formula for calculating a country’s real GDP is shown below:

$Growthrate=\frac{\left(RealGDPofcurrentyear-RealGDPofbaseyear\right)}{RealGDPofbaseyear}\times 100$

For the given economy, the first year is the base year, and the second year is the current year. The country’s growth rate is calculated by using the above formula.

$$\begin{gathered} Growthrate=\frac{\left(31200-30000\right)}{30000}\times 100 \\ =\frac{1200}{30000}\times 100 \\ =4percent \end{gathered}$$

The growth rate of the country’s real GDP is 4 percent.

Step 2. Calculation of country’s growth rate of real GDP per capita

The country’s first-year and second-year real GDP per capita are calculated by dividing the GDPs of the respective years by their population.

$$\begin{gathered} Country\text{'}ssecondyearrealGDPpercapita=\frac{31200}{102} \\ =305.88 \end{gathered}$$

$$\begin{gathered} Country\text{'}sfirstyearrealGDPpercapita=\frac{30000}{100} \\ =300 \end{gathered}$$

The country’s growth rate of real GDP per capita is calculated by dividing the difference between the per capita real GDP in the current year and base year with the base year per capita GDP and multiplying it by 100. The formula for calculating a country’s real GDP per capita is shown below:

$Growthrate=\frac{\left(PercapitarealGDPincurrentyear-PercapitarealGDPinbaseyear\right)}{PercapitarealGDPinbaseyear}100$

By using the above formula, the country’s growth rate of real GDP per capita is calculated below:

$$\begin{gathered} Growthrate=\frac{\left(305.88-300\right)}{300}\times 100 \\ =\frac{5.88}{300}\times 100 \\ =1.96percent \end{gathered}$$

Therefore, the growth rate of the real GDP per capita of the country is 1.96 percent.