# Lecture 06 - Growth and the Solow-Swan Model II.pdf -...

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Economics 100B: Macroeconomics Growth and the Solow-Swan Model: Part 2 September 16, 2020 Reading: The Solow-Swan and Romer Models, R.J. Hawkins Mishkin - Chapter 6 Lecture 6 – Solow–Swan Model II: R. J. Hawkins Econ 100B: Macroeconomics 1/ 16
The Capital Accumulation Equation Solution overview. The solution κ ( t ) of the capital accumulation equation d κ dt = s κ α - ( g E + g L + δ ) κ is important because it is directly related to per-capita income by Y ( t ) L ( t ) = κ α ( t ) E ( t ) . Lecture 6 – Solow–Swan Model II: R. J. Hawkins Econ 100B: Macroeconomics 2/ 16
The Capital Accumulation Equation Solution overview. The capital accumulation equation d κ dt = s κ α - ( g E + g L + δ ) κ has two solutions of interest: 1 The steady-state solution corresponding to d κ dt = 0 2 The general solution κ ( t ). Lecture 6 – Solow–Swan Model II: R. J. Hawkins Econ 100B: Macroeconomics 3/ 16
The Capital Accumulation Equation The steady-state solution. The steady-state solution to the capital accumulation equation follows from d κ dt = s κ α - ( g E + g L + δ ) κ = 0 so s κ α = ( g E + g L + δ ) κ κ 1 - α = s g E + g L + δ and κ * = s g E + g L + δ 1 1 - α where the star (*) indicates the steady-state. Lecture 6 – Solow–Swan Model II: R. J. Hawkins Econ 100B: Macroeconomics 4/ 16
The Capital Accumulation Equation The steady-state solution. In the steady state κ ( t ) = κ * so per-capita income Y ( t ) L ( t ) = ( κ ( t )) α E ( t ) is given by Y ( t ) L ( t ) = ( κ * ) α E ( t ) or Y ( t ) L ( t ) = s g E + g L + δ α 1 - α E ( t ) , and from which it follows that g Y / L = g E .