Economic Growth and Business Cycle Lecture Notes

Course Overview

• Focus on Solow Growth Model, Romer Model, and Business Cycles.
• Playlist created for:
  • Full Solow Growth Model
  • Romer Model (including technology aspects)
• Key readings are uniform across various academic backgrounds.

Solow Growth Model

Recording Structure

1. Assumptions
   • Countries consume a single homogeneous good (no international trade).
   • Technology is exogenous (not affected by firm's actions).
2. Key Equations
   • Production Function:
     • Y = f(K, L) = K^α L^(1-α)
       • α: constant between 0 and 1.
   • Capital Accumulation Equation:
     • K̇ = sY - δK
3. Diagram and Concepts
   • Steady states dependent on population growth and savings rates.
   • Transition dynamics interpretation.

Technological Progress Section

• Move from traditional to technological progress models in Solow.
• Derivation of key equations with technology included.
• Discussion on convergence hypothesis: do poorer countries catch up to richer ones?

Capital Deepening vs. Capital Widening

• Capital Deepening:
  • More machines per worker leads to increased output per worker.
• Capital Widening:
  • Increase in machines at the same rate as labor increases, keeping output per labor constant.

Comparative Statics in the Solow Model

Changes in Savings Rate

• Increase in savings rate leads to:
  • Higher growth rate temporarily until new steady state is reached.
• Long-term growth effects remain unchanged.

Changes in Population Growth Rate

• Increase in population growth rate results in:
  • Slower capital per worker growth and lower output per worker over time.

Romer Model of Endogenous Growth

Key Differences from Solow

• Technology is endogenous.
• Technological progress is driven by R&D (Research and Development).

Structure of the Romer Model

1. Final Goods Sector
   • Produces output using labor and capital.
2. Intermediate Goods Sector
   • Produces capital goods using new ideas/technology.
3. Research Sector
   • Engages in R&D to produce new ideas, affecting technological progress.

Key Equations

• Production functions with capital and labor inputs.
• Derivative equations for marginal returns.

Growth Rate Analysis

• Growth of technology equations derived:
  • g = λn / (1-η)
  • Implications of higher R&D share on growth rates.

Convergence Hypothesis

Definitions

• Convergence: Backward countries growing faster than richer ones to close the gap.
• Conditional Convergence: Identical countries converging due to similar parameters; richer countries have lower growth rates.

Key Points

• Empirical Evidence: Not all countries converge; access to technology differs.
• Government interventions can impede access to technology.

Summary

• Overall understanding of economic growth through Solow and Romer models.
• Comparative statics, policy implications, and convergence dynamics explored extensively.