Question

The Central African Republic has a GDP of 1,107,689 million CFA francs and a population of 4.862 million. The exchange rate is 284.681 CFA francs per dollar. Calculate the GDP per capita of Central African Republic.

Short answer

The GDP per capita of the Central African Republic is approximately 800.262 United States dollars.

Step-by-step solution

Convert GDP to USD

To determine the GDP in US dollars, we will use the exchange rate provided, which is 284.681 CFA francs per 1 dollar. The formula to convert GDP in CFA francs to USD is: GDP in USD = (GDP in CFA francs) / (Exchange rate) GDP in USD = (1,107,689 million CFA) / (284.681 CFA/USD)

Calculate GDP per capita in USD

To calculate the GDP per capita, we will divide the GDP in USD by the population of Central African Republic: GDP per capita = (GDP in USD) / (Population) GDP per capita = \( (\frac{1,107,689 million CFA}{284.681 CFA/USD}) / (4.862 million people) \)

Simplify the expression

To obtain the GDP per capita, we must now simplify the expression: GDP per capita = \( \frac{1,107,689/284.681}{4.862} \) GDP per capita = \( \frac{3,891.44 million USD}{4.862 million people} \)

Divide and calculate the GDP per capita

Divide the numerator by the denominator to get the GDP per capita in USD: GDP per capita = \( \frac{3,891.44 million USD}{4.862 million people} \) = 800.262 USD The GDP per capita of the Central African Republic is approximately 800.262 United States dollars.

Key concepts

Exchange Rate Conversion

Understanding how to convert currency using an exchange rate is crucial in macroeconomics. In its simplest form, the exchange rate indicates how much of one currency can be exchanged for another currency. For instance, if the exchange rate from CFA francs to US dollars is 284.681 CFA francs per 1 dollar, it means that for every US dollar, you could get 284.681 CFA francs.

When performing this conversion, a common approach is to take the amount of money you have in the original currency and divide it by the exchange rate. The formula looks like this:
GDP in USD = (GDP in local currency) / (Exchange rate).

This step is pivotal because it allows comparison between different economies, regardless of their local currency values. For students working on such exercises, it is essential to ensure accuracy in conversion as errors can significantly affect the final results.

GDP Conversion to USD

The Gross Domestic Product (GDP) measures a country's economic output. To make an 'apples to apples' comparison between countries, we often convert GDP into a common currency, typically US dollars. The process involves using the exchange rate, which fluctuates regularly based on market conditions.

For example, when we convert the GDP of the Central African Republic from CFA francs to US dollars, we divide the total GDP by the exchange rate:
GDP in USD = (1,107,689 million CFA) / (284.681 CFA/USD).

This step simplifies comparison across nations and provides a clearer understanding of each country's economic size and health in a global context. For students, mastering this conversion not only helps with homework but also enhances their understanding of global economics.

Macroeconomic Indicators

Macroeconomic indicators are statistics that reflect the current economic status of a country. GDP per capita is one such indicator, representing the average economic output per person and is calculated by dividing the GDP by the country's population. It's a critical measure because it can give insight into the standard of living and productivity of a nation's residents.

Other major indicators include inflation rate, unemployment rate, and balance of trade. Understanding these indicators helps grasp the broader economic picture, which can inform government policy, investment decisions, and academic research. For a student learning economics, gaining a clear understanding of these indicators, their computation, and their implications is essential to interpreting real-world economic scenarios.