Question

As discussed in this chapter, real GDP per capita in the United States grew from about \(\$ 6,000\) in 1900 to about \(\$ 51,500\) in \(2016,\) which represents an average annual growth rate of 1.9 percent. If the U.S. economy continues to grow at this rate, how many years will it take for real GDP per capita to double? If government economic policies meant to stimulate economic growth result in the annual growth rate increasing to 2.2 percent, how many years will it take for real GDP per capita to double?

Short answer

If the U.S. economy continues to grow at an annual rate of 1.9%, it will take approximately 37 years for the real GDP per capita to double. If government economic policies increase the annual growth rate to 2.2%, it will take approximately 32 years for the real GDP per capita to double.

Step-by-step solution

Understanding the rule of 70

The rule of 70 is a way to estimate the time it takes for the amount of something growing exponentially to double. The rule states that, for a given percentage rate, the time it takes for a value to double is approximately 70 divided by that rate. The rate is expressed in percentage terms for this formula.

Calculate Time for GDP to double with 1.9% growth rate

First, let's plug in the annual growth rate of 1.9% into the rule of 70 formula. Therefore, \( Time \approx \frac{70}{1.9} = 36.84\) years. The GDP per capita for the US economy will double in approximately 37 years, if the growth continues at this rate.

Calculate Time for GDP to double with 2.2% growth rate

In this step, let's calculate the time for GDP to double, but this time with a growth rate of 2.2%. So, \(Time \approx \frac{70}{2.2} = 31.82 \) years. Therefore, if the Government policies result in the annual growth rate of 2.2%, the GDP per capita for the US economy will double in approximately 32 years.

Key concepts

Understanding Real GDP Per Capita

Real GDP per capita is a metric that represents the average economic output per person in a country adjusted for inflation. This measure is crucial because it accounts for population growth and changes in the price level, providing a more accurate reflection of an individual's economic well-being than just looking at total GDP.

For example, if a country's GDP is increasing, but its population is growing at a faster rate, then the GDP per capita could actually be decreasing, implying that, on average, individuals might not be getting wealthier. Therefore, tracking changes in real GDP per capita can give us insight into the average living standards and economic health of a country over time.

In our exercise, the real GDP per capita in the United States grew from about \(6,000 in 1900 to about \)51,500 in 2016. This growth is significant because it suggests an increase in the standard of living and prosperity of the average American over the mentioned period.

The Rule of 70 Explained

The rule of 70 is a simple way to estimate the time it will take for a quantity experiencing exponential growth to double. To utilize this rule, you divide the number 70 by the annual percentage growth rate. Remarkably, it can be applied to various contexts, like population growth, investment returns, or, as in our exercise, the growth rate of the real GDP per capita.

In the exercise, we apply the rule of 70 to estimate how long it would take for the real GDP per capita to double given growth rates of 1.9% and 2.2%. Using the figures provided,

• At a 1.9% growth rate, it would take about \( \approx \frac{70}{1.9} = 36.84 \) years for real GDP per capita to double.
• At a 2.2% growth rate, it would take about \( \approx \frac{70}{2.2} = 31.82 \) years for it to double.

It's worth noting that this rule is an approximation and assumes a constant growth rate, which in real-world scenarios can fluctuate due to various economic factors.

Exponential Growth in Economics

Exponential growth refers to a situation where a quantity grows at a rate proportional to its current value. In economics, this concept is particularly important when discussing things like population growth, interest rates, and economic development.

Unlike linear growth, which adds a constant amount over time, exponential growth becomes more dramatic as time goes on because the increase is based on the multiplying effect. For instance, if a country's economy is growing at a steady exponential rate, it means that as the economy gets larger, the actual amount of growth each year gets larger too, even if the percentage growth rate stays the same.

This concept explains why relatively small differences in growth rates can lead to substantial differences in economic outcomes over time. As seen in the exercise, an increase in the growth rate from 1.9% to 2.2% can reduce the time it takes for the GDP per capita to double by several years. This showcases the power of exponential growth and the significant impact of sustained economic policies aimed at improving growth rates.