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It illustrates dynamic systems using Mathematica, Maple and spreadsheets. It provides a thorough introduction to phase diagrams and their economic appli-cation and explains the nature of saddle path solutions.
Phase diagrams are a popular technique that allow us to see the joint dynamics of two variables. Many models in economics can be boiled down to two variables so this method is widely used. Let’s start with a very general example x_ = g (x;y) @g @x <0 @g @y <0 y_ = f (x;y) @f @x <0 @f @y >0 where g and f are continuous di erentiable functions.
Phase diagrams are a nifty but different type of graph. They require you to mentally plot out the movement of a variable over time. They take a little getting used to, but once you understand how they work, phase diagrams are a powerful way to quickly analyze an equilibration process. C15Lab.pdf 4
We study an endogenous growth model with transitional dynamics. The model is asymptotically AK. As an example of a phase diagram with endogenous growth. where F(K,L) = Lf (k) satisfies Inada conditions and has constant returns to scale in K and L jointly. For simplicity, assume f (k) = kα with α < 1. ̇k =
It focuses on the most popular educational instance of a phase diagram in economics, the representative-household and the overlapping-generations deterministic, continuous time, saddle-path stable models of growth. 1. Constructing the phase diagram.
Phase Diagrams • How analyze (ODE)? In one-dimensional case (scalar x): use phase-diagram • Two possible phase-diagrams: (i) in (λ,k)-space: more general strategy. (ii) in (c,k)-space: nicer in terms of the economics. • For (i), use U′(c) = λ or c = (U′)−1(λ) to write (ODE) as λ˙ = λ(ρ+δ −F′(k)) k˙ = F(k)−δk −(U ...
It provides detailed coverage of dynamics and phase diagrams including: quantitative and qualitative dynamic systems, continuous and discrete dynamics, linear and nonlinear systems. It illustrates dynamic systems using Mathematica, Maple and spreadsheets.
