Question

If real GDP grows at 7 percent per year, then real GDP will double in approximately______years. a. 70 b. 14 c. 10 d. 7

Short answer

Real GDP will double in approximately 10 years. The correct answer is (c) 10.

Step-by-step solution

Understanding the Growth Formula

We are going to use the Rule of 70, which is a way to estimate the number of years it takes for a value to double at a constant annual growth rate. The formula is given by \( \text{Years to double} = \frac{70}{\text{Growth Rate}} \).

Applying the Formula

Given that the real GDP grows at a rate of 7 percent per year, we can substitute the growth rate into the formula. Thus, \( \text{Years to double} = \frac{70}{7} \).

Calculating the Years to Double

Perform the division from the formula: \( \frac{70}{7} = 10 \). This means that it will take approximately 10 years for the real GDP to double.

Key concepts

Growth Rate

A growth rate is a measure of how quickly a quantity, such as an economic variable, increases over time. In economic terms, it often refers to how much the GDP (Gross Domestic Product) grows per year. The growth rate is usually expressed as a percentage.

To calculate the growth rate, you need two key figures: the value today and the value at a previous time. The growth rate formula is:\[ \text{Growth Rate} = \left(\frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}}\right) \times 100 \% \]This formula helps us understand economic health. A positive growth rate indicates expansion, while a negative one shows contraction. For example, a 7% growth rate indicates real GDP is growing quite rapidly, which is why it can double in a relatively short time.

The growth rate is used in various analyses and forecasts, shaping economic policies and business strategies. It is important to monitor as it impacts employment, inflation, and overall economic well-being.

Real GDP

Real GDP stands for Real Gross Domestic Product. It measures the value of economic output adjusted for price changes, i.e., inflation or deflation. This adjustment provides a more accurate reflection of an economy’s size and how it’s growing over time.

The GDP can be thought of as the sum of all goods and services produced within a country’s borders and is given at constant prices to factor out the effects of inflation. This is done using a base year’s prices so that the economy's growth can be observed without price distortion.

Why use Real GDP?

• It accounts for inflation, giving a clearer picture of the economy's growth.
• It compares economic output from different years without inflation bias.
• It helps in making year-to-year comparisons.

If, for example, the real GDP grows at 7%, as in our exercise, this is a strong indicator of economic growth. However, looking at real GDP growth also means that improvements are not due to rising prices but true increases in production and services output.

Doubling Time

Doubling time is a concept that tells us how long it takes for a quantity growing at a consistent rate to double. It’s a simple yet powerful way to understand exponential growth, and it's widely used in finance and economics.

The 'Rule of 70' is commonly used for calculating doubling time. With this rule, the doubling time can be approximated by dividing 70 by the annual growth rate percentage. \[ \text{Doubling Time} = \frac{70}{\text{Growth Rate}} \]This rule provides a quick estimation without complex math. In our exercise, the growth rate is 7%, so:\[\frac{70}{7} = 10 \text{ years}\]This means if an economy grows at 7% annually, its real GDP will double in about 10 years.

Uses of Doubling Time:

• Quick assessment of economic growth impact over time.
• Understanding the long-term implications of growth rates.
• Practical tool for comparing different growth scenarios.

By learning to estimate doubling time, students and professionals can effectively evaluate and communicate growth dynamics in various contexts.