5 - Economic Growth

Economic Growth

  • Definition: Economic growth refers to an increase in real GDP per capita over time.

  • Importance: This relationship ties economic growth to the quality of life, which is significant for understanding overall well-being.

  • Measurement: Economic growth is measured as real GDP divided by population.

    • Emphasizes the need to ensure that population growth does not outpace economic output, which could lead to decreased average well-being.

    • A scenario where population grows by 20% while output grows by only 1% results in worse outcomes for individuals due to diminished per capita resources.

Challenges of Real GDP Measurement

  • Quality Changes: Evaluations of GDP don’t account for improvements in product quality alongside price increases.

    • The difficulty lies in distinguishing whether rising prices reflect increased quality or merely inflation.

  • Leisure Time: Real GDP measures output but fails to capture benefits from leisure activities that enhance personal well-being.

    • If individuals choose more leisure (family time or vacations) at the expense of production, this does not show up in GDP figures despite its inherent value to quality of life.

Measuring Economic Growth Mathematically

  • Basic Notation:

    • GDP0: GDP today

    • GDPT: GDP at a future time (T years from now)

    • G: constant growth rate

  • Formula: To predict future GDP:

    • GDPT = GDP0 * (1 + G) ^ T

    • Assumes a constant growth rate over the specified period, with averages smoothing out variability in actual output changes.

Rule of 72

  • A useful heuristic to estimate how long it takes for an investment or GDP to double based on a fixed rate of growth.

  • Estimation Process:

    • If G = growth rate, then to find the time to double, use:

      • Years to Double = 72 / G

  • Example: If G is 10%,

    • 72 / 10 = 7.2 years to double GDP.

  • Comparison with Logs: More precise calculations using logarithms yield a time to double of around 7.27 years for the same growth rate, demonstrating the rule’s utility despite slight differences.

    GDPT = 2

    GDP0 = 1

    2 = GDP0*(1+G)^T

    T=ln(2)/ln(1.1)

Implications of Growth Rates

  • For a 3% growth rate, using the formula indicates a doubling time of approximately 24 years.

    • This method allows quick assessments of potential investment returns based on known growth rates.