Aug 28, 2024

- 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.

**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.

**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.

- 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

- 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.

- 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.

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

- 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 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.

- 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.