Solow Growth Model

Overview:

The Solow-Swan model (also known as the Solow growth model) is a long-run model of economic growth that explains how capital accumulation, labor force growth, and technological progress contribute to economic output. Unlike the Harrod-Domar model, it considers technological progress as an important driver of growth.

Key Assumptions:

• • Capital and labor are the primary factors of production.
  • There is diminishing returns to capital.
  • Technological progress is an exogenous factor that enhances productivity.
  • The model assumes a closed economy with no trade.

Key Equations

1. Capital Accumulation:
   ΔK=s⋅Y−δ⋅K 
   • ΔK: Change in capital stock
   • s: Savings rate
   • δ: Depreciation rate of capital
2. Steady-State Capital:
   • At the steady state: s⋅f(k)=(δ+n)⋅k 
     • k: Capital per worker
     • n: Population growth rate
3. Output Per Worker in Steady State:
   • Output per worker depends on the capital per worker and the level of technology.

Key Insights

1. Steady-State Growth:
   • In the long run, growth in output per worker is driven solely by technological progress.
2. Convergence:
   • Poorer countries with lower capital per worker will grow faster than richer countries, provided they have similar savings rates, population growth rates, and access to technology.
3. Golden Rule of Savings:
   • The optimal savings rate maximizes consumption per worker in the steady state.
4. Impact of Population Growth:
   • Higher population growth reduces steady-state capital and output per worker, as resources must be spread more thinly.

Strengths

1. Realistic Dynamics:
   • Incorporates diminishing returns and technological progress.
2. Policy Implications:
   • Highlights the importance of investment in technology and human capital.
3. Convergence Hypothesis:
   • Explains why developing economies can catch up to developed ones under similar conditions.

Limitations

• Exogenous Technological Progress:
  • The model does not explain how or why technological progress occurs.
• Simplified Assumptions:
  • Assumes constant returns to scale and no market imperfections.
• Neglect of Human Capital:
  • Does not initially account for the role of education and skills.

Implications:

The model suggests that, in the long run, economic growth is driven primarily by technological progress, as capital accumulation alone cannot sustain continuous growth due to diminishing returns to capital.