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Chapter 21: Problem 2

What is the rule of \(70 ?\) If real GDP per capita grows at a rate of 5 percent per year, how many years will it take to double?

Short Answer

Expert verified
It will take 1,400 years for real GDP per capita to double if it grows at a rate of 5% per year according to the rule of 70.

Step by step solution

01

Understand the Rule of 70

The 'Rule of 70' is used to estimate the number of years it takes for a variable to double, by dividing 70 by the rate of growth. Given the growth rate here is 5% per year, it is important to note that in the formula, the growth rate should be expressed in its decimal format i.e.5% = 0.05.
02

Apply the Rule of 70

Apply the Rule of 70 formula to calculate the number of years it will take for the real GDP per capita to double at a growth rate of 5% per year. So, it will be: \[ Years = \frac{70}{Growth\ Rate} = \frac{70}{0.05} \]
03

Perform the Calculation

Calculate the right side of the equation \[ Years = \frac{70}{0.05} = 1400 \]. Therefore, it will take 1,400 years for the real GDP per capita to double if it grows at a rate of 5% per year according to the rule of 70.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Real GDP Per Capita
Real GDP per capita is an important term in economics. It measures the average income of each person in a country. This figure is adjusted to account for inflation, making it "real".
Real GDP per capita is calculated by dividing a country's GDP (Gross Domestic Product) by the total population.
It provides a more precise representation of economic prosperity than just GDP alone because it considers population size. Here are key points to remember:
  • Reflects the average economic output per person.
  • Helps compare the standard of living between countries.
  • Adjusted for price level changes, so it removes the effects of inflation.
This indicator is essential in assessing the true wealth and economic health of nations over time.
Deciphering Economic Growth Rate
The economic growth rate is a measure of how much a country's economy has grown over a specific period. It is generally expressed as a percentage that shows the increase in real GDP. This indicates how fast an economy is expanding.
There are several ways to assess and understand the significance of the economic growth rate.
  • A high growth rate signals a booming economy, while a low rate might indicate stagnation.
  • It's important for setting policy and guiding economic decisions.
  • Regular monitoring helps in predicting future economic performance.
Understanding the economic growth rate helps countries plan effectively, manage inflation, and ensure sustainable development for the future.
Grasping Doubling Time
Doubling time is a concept that refers to the period it takes for a certain variable, like real GDP per capita, to double in size. This is crucial for predicting economic growth and planning for future development.
To calculate the doubling time, economists commonly use the Rule of 70. This simple formula provides a quick estimation method without complex calculations. Simply divide 70 by the annual growth rate:
  • For example, with a 5% growth rate, doubling time is calculated as follows: \( \frac{70}{5} = 14 \). So, it will take approximately 14 years for an economy to double at this rate.
Keep in mind, though, actual time might vary due to fluctuations in growth rate.
Understanding doubling time can help governments and businesses align their strategies with expected economic trends and changes.

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Most popular questions from this chapter

What two key factors cause labor productivity to increase over time?

The federal government in the United States has been running large budget deficits. Suppose that Congress and the president take actions that turn the budget deficits into budget surpluses. a. Use a market for loanable funds graph to illustrate the effect of the federal budget surpluses. What happens to the equilibrium real interest rate and the quantity of loanable funds? What happens to the level of saving and investment? b. Now suppose that households believe that surpluses will result in Congress and the president cutting taxes in the near future in order to move from budget surpluses to balanced budgets. As a result, households increase their consumption spending in anticipation of paying lower taxes. Briefly explain how your analysis in part (a) will be affected.

Consider the following data for a closed economy: $$ \begin{aligned} Y &=\$ 12 \text { trillion } \\ C &=\$ 8 \text { trillion } \\ G &=\$ 2 \text { trillion } \\ S_{\text {Public }} &=-\$ 0.5 \text { trillion } \\ T &=\$ 2 \text { trillion } \end{aligned} $$ Use these data to calculate the following: a. Private saving b. Investment spending c. Transfer payments d. The government budget deficit or budget surplus

Firms care about their after-tax rate of return on investment projects. In the market for loanable funds, draw a graph and explain the effect of an increase in taxes on business profits. (For simplicity, assume no change in the federal budget deficit or budget surplus.) What happens to the equilibrium real interest rate and the quantity of loanable funds? What will be the effect on the level of investment by firms and the economy's capital stock in the future?

An article in the Wall Street Journal on the use of artificial intelligence (AI) in the financial system stated that "similar to index-tracking funds, funds managed in part by artificial intelligence require less human intervention and therefore can often cost less to run." The article also noted that banks are using AI to decrease the costs and increase the accuracy of compliance with government regulations. a. What financial intermediary do "index-tracking funds" or "funds" refer to? b. How does the use of AI affect labor productivity in the financial system? Briefly explain. c. How would the financial system's use of AI affect the rate of long-run economic growth? Briefly explain using the loanable funds model.
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