Question

In \(2013,\) Turkey's real GDP was growing at 4.1 percent a year and its population was growing at 1.26 percent a year. If these growth rates continued, in what year would Turkey's real GDP per person be twice what it is in 2013 ?

Short answer

The real GDP per person in Turkey would be twice its 2013 value around the year 2038.

Step-by-step solution

Understand the Problem

We need to find out in what year Turkey's real GDP per person will be twice its 2013 value given the annual growth rates of GDP and the population.

Define the Growth Rates

Let the real GDP growth rate be 4.1 percent, i.e., 0.041, and the population growth rate be 1.26 percent, i.e., 0.0126.

Calculate the Growth Rate of GDP per Person

The growth rate of real GDP per person (g) can be approximated by subtracting the population growth rate from the real GDP growth rate: g = 0.041 - 0.0126 = 0.0284 or 2.84% per year.

Use the Doubling Formula

To find the time (T) it takes for an amount to double at a given growth rate, we use the Rule of 70: T = 70 / g, where g is the growth rate in percentage.

Apply the Rule of 70

Substitute the growth rate into the formula: T = 70 / 2.84 T ≈ 24.65 years.

Find the Target Year

Add the calculated duration to the base year: 2013 + 25 (approximately 24.65) = 2038.

Key concepts

real GDP growth rate

The real GDP growth rate indicates how much a country’s economy is growing over time, adjusted for inflation.
It is expressed as a percentage and represents the annual increase in the value of all goods and services produced within a nation’s borders.
For example, if Turkey’s real GDP growth rate is 4.1 percent, it means that the economy grew by this percentage over the past year.
This rate helps us understand the economic health of a country, showing how effectively it is growing over a certain period.
Regular growth in real GDP is vital for improving living standards and creating new job opportunities.
Understanding the real GDP growth rate is essential for economic planning and forecasting future prosperity.

population growth rate

The population growth rate is the percentage by which a population increases in a given time period, typically one year.
It takes into account births, deaths, and net migration.
For instance, Turkey's population growth rate of 1.26 percent means that the population increases by this percentage annually.
This rate is important to consider as it affects the per capita distribution of the real GDP.
If the population grows faster than the GDP, the GDP per capita (income per person) may decrease, potentially lowering living standards.
Conversely, if the population grows slower than the GDP, the GDP per capita increases, which is a sign of improving economic health.

Rule of 70

The Rule of 70 is a simple formula used to estimate the number of years it will take for a quantity to double, given a fixed annual growth rate.
The formula is:
\( T = \frac{70}{g} \)
where \( T \) is the doubling time and \( g \) is the annual growth rate in percentage.
For instance, in Turkey's case, to find out when the real GDP per person will double, if the annual growth rate is 2.84%, we use the Rule of 70:
\( T = \frac{70}{2.84} ≈ 24.65 \) years.
So in approximately 25 years, the real GDP per person will be double what it is today.
This rule provides a quick way to understand the long-term impact of different growth rates on economic factors.

economic growth calculations

Economic growth calculations involve the processes by which the growth rates of GDP and population are factored together.
To determine the real GDP per person, one subtracts the population growth rate from the real GDP growth rate:
\( g = 4.1\text{%} - 1.26\text{%} = 2.84\text{%} \).
This resulting growth rate indicates how much the real GDP per capita is increasing each year.
Next, using the Rule of 70, we calculate the doubling time for this growth rate to find out how long it will take for the real GDP per person to double.
These calculations help in understanding long-term economic trends and setting realistic economic goals.
They offer insights into whether growth is sufficient to improve living standards over time.