Understanding the Solow Growth Model

Aug 28, 2024

Lecture Notes: Solow Model

Introduction to the Solow Model

  • The Solow Model is a fundamental model in economics used to understand:
    • Economic growth
    • Business cycles
  • Developed by Robert Solow, Nobel Prize winner in 1987.
  • Follow along with the textbook "Modern Principles" by Tyler and Solow.

Production Function

  • Output (Y) is a function of:
    • Physical Capital (K)
    • Human Capital (eL): education times the number of laborers
    • Ideas (A): later interpreted as productivity
  • Initially, assume:
    • A, e, and L are constant (no growth in population, ideas, or education)
  • Output is thus a function of capital alone.

Properties of the Production Function

  • Positive Relationship: More capital leads to more output.
  • Diminishing Returns: Each additional unit of capital generates less additional output.
  • Example: Square root function for output:
    • If K = 16, then Y = 4.
    • If K = 100, then Y = 10.

Visualizing the Production Function

  • Graph with capital (K) on the horizontal axis and output (Y) on the vertical.
  • Example outputs:
    • K = 100 -> Y = 10
    • K = 400 -> Y = 20
  • Diminishing returns illustrated through example with tractors:
    • First tractor: 10 units output
    • Second tractor: ~4 units output
    • Third tractor: ~3 units output

Implications of Diminishing Returns

  • Countries with low capital stocks can experience rapid growth due to high productivity of new capital.
  • Example: China adopting new capital leading to high growth rates.
  • As capital accumulates, growth rates will slow down.
  • Not all poor countries grow rapidly; institutional improvements are crucial.

Conditional Convergence

  • Countries grow towards their natural GDP per capita based on:
    • Institutional quality
    • Savings rates
  • Example of post-WWII Germany and Japan:
    • High growth rates due to low capital stocks and rebuilding after destruction.

Investment and Consumption

  • Output can be either:
    • Invested to increase future output
    • Consumed
  • Assumption: constant fraction (e.g., 30%) of output is saved/invested.
  • Investment function: 0.3Y.

Capital Depreciation

  • Capital depreciates over time (e.g., wear and tear on tractors, cars, factories).
  • Depreciation rate example: 2% of capital stock.

Key Relationships in the Model

  • Investment vs. Depreciation:
    • If investment > depreciation, capital stock grows.
    • If investment < depreciation, capital stock shrinks.
    • Steady state occurs when investment equals depreciation: capital stock remains constant.

Steady State and Growth Rates

  • Steady state example:
    • Capital stock = 225, steady-state output = 15.
  • Growth occurs when below steady state, slows as approaching it.
  • Long-term growth cannot rely solely on capital accumulation; need to explore ideas.

Conclusion

  • The Solow Model outlines that:
    • Capital deepening cannot sustain long-run growth on its own.
    • Future lectures will explore the role of ideas in long-term growth.