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Understanding the Solow Growth Model
Aug 28, 2024
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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.
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