Question

Turkey's real GDP (in U.S. dollars) was \(\$ 788.9\) billion in 2012 and \(\$ 822.1\) billion in 2013 Turkey's population was 74 million in 2012 and 74.93 million in \(2013 .\) Calculate a. The growth rate of GDP. b. The growth rate of real GDP per person. c. The approximate number of years it takes for GDP per person in Turkey to double if the 2013 growth rate of GDP and the population growth rate are maintained.

Short answer

\(GDP\) growth rate: 4.21\%. Growth rate of \(real GDP\) per person: 2.97\%. Time to double \(GDP\) per person: 23.57 years.

Step-by-step solution

- Calculate GDP Growth Rate

The GDP growth rate can be found using the formula: \[ \text{Growth Rate} = \frac{\text{GDP in 2013} - \text{GDP in 2012}}{\text{GDP in 2012}} \times 100 \] Substituting the provided values: \[ \text{Growth Rate} = \frac{822.1 - 788.9}{788.9} \times 100 \] Simplifying: \[ \text{Growth Rate} = \frac{33.2}{788.9} \times 100 \ \text{Growth Rate} \ \text{Growth Rate} \approx 4.21\text{%} \]

- Calculate Real GDP per Person for 2012 and 2013

First, find the real GDP per person for each year: \[ \text{Real GDP per Person (2012)} = \frac{\text{GDP in 2012}}{\text{Population in 2012}} = \frac{788.9 \times 10^9}{74 \times 10^6} \approx 10655.41 \] \[ \text{Real GDP per Person (2013)} = \frac{\text{GDP in 2013}}{\text{Population in 2013}} = \frac{822.1 \times 10^9}{74.93 \times 10^6} \approx 10972.00 \]

- Calculate Growth Rate of Real GDP per Person

Use the formula for growth rate to find the growth rate of real GDP per person: \[ \text{Growth Rate of Real GDP per Person} = \frac{\text{Real GDP per Person (2013)} - \text{Real GDP per Person (2012)} }{\text{Real GDP per Person (2012)}} \times 100 \] Substituting the values: \[ \text{Growth Rate} = \frac{10972.00 - 10655.41}{10655.41} \times 100 \] Simplifying: \[ \text{Growth Rate} = \frac{316.59}{10655.41} \times 100 \] \[ \text{Growth Rate} \approx 2.97\text{%} \]

- Calculate the Number of Years for GDP per Person to Double

To estimate the number of years required for the GDP per person to double, use the Rule of 70: \[ \text{Number of Years} = \frac{70}{\text{Growth Rate of Real GDP per Person}} \] Given the growth rate of 2.97\text{%}: \[ \text{Number of Years} = \frac{70}{2.97} \] Simplifying: \[ \text{Number of Years} \approx 23.57 \]

Key concepts

real GDP growth rate

The **real GDP growth rate** measures the percentage increase in the value of real GDP from one period to another. This growth rate provides a snapshot of how fast an economy is expanding. You can calculate it easily with a simple formula. First, subtract the GDP of the starting year from the GDP of the ending year. Then, divide the result by the GDP of the starting year and multiply by 100 to convert it to a percentage.

Using our example:
- Real GDP in 2012 = \(788.9 billion
- Real GDP in 2013 = \)822.1 billion

Formula:
\[ \text{Growth Rate} = \frac{\text{GDP in 2013} - \text{GDP in 2012}}{\text{GDP in 2012}} \times 100 \]

Substitute the values:
\[ \text{Growth Rate} = \frac{822.1 - 788.9}{788.9} \times 100 \]
Simplify:
\[ \text{Growth Rate} = \frac{33.2}{788.9} \times 100 \approx 4.21\% \]
This means Turkey's real GDP grew by approximately 4.21% from 2012 to 2013.

real GDP per capita

The **real GDP per capita** is a measure of the average economic output per person, providing a more accurate depiction of an individual's standard of living within a country. To find this, divide the real GDP by the population.

Here's how you do it:
1. Calculate the real GDP per capita for both years.

For 2012:
\[ \text{Real GDP per Person (2012)} = \frac{\text{GDP in 2012}}{\text{Population in 2012}} = \frac{788.9 \times 10^9}{74 \times 10^6} \approx 10655.41 \]

For 2013:
\[ \text{Real GDP per Person (2013)} = \frac{\text{GDP in 2013}}{\text{Population in 2013}} = \frac{822.1 \times 10^9}{74.93 \times 10^6} \approx 10972.00 \]

In summary, the average amount of real GDP per person increased from approximately \(10,655.41 in 2012 to \)10,972.00 in 2013.

Rule of 70

The **Rule of 70** is a straightforward way to estimate how long it will take for a quantity to double, given a consistent growth rate. This rule can be particularly useful in economics to project the doubling time of GDP per capita.

The formula is:
\[ \text{Number of Years} = \frac{70}{\text{Growth Rate}} \]

Using the real GDP per capita growth rate from our example, which is 2.97%:
\[ \text{Number of Years} = \frac{70}{2.97} \approx 23.57 \]

Therefore, if Turkey's real GDP per capita continues to grow at this rate, it will take approximately 23.57 years for the GDP per capita to double.

population growth rate

The **population growth rate** indicates how quickly the population of a country is increasing or decreasing over time. This rate is crucial for understanding the larger context of economic growth. Changes in population size directly impact real GDP per capita calculations.

To calculate the population growth rate, use a similar formula to that for GDP growth rate:
\[ \text{Population Growth Rate} = \frac{\text{Population in 2013} - \text{Population in 2012}}{\text{Population in 2012}} \times 100 \]

Given:
- Population in 2012 = 74 million
- Population in 2013 = 74.93 million

Substitute the values:
\[ \text{Population Growth Rate} = \frac{74.93 - 74}{74} \times 100 \approx 1.26\% \]

Thus, Turkey's population grew by approximately 1.26% from 2012 to 2013.