How to Plot Ramsey Phase Plane

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econogist
econogist 2022-5-18
评论： econogist 2022-5-18
I am trying to plot the phase plane from the famous Ramsey macroeconomic model with Matlab's quiver. The system of equations are and . Most plots of the function look like the attachment. But what I want is to plot a bunch of arrows as is typically seen when you just google images of phase planes. This seems like it should be simple enough, but I'm stuck. How do I do this? What am I missing? Below is what I've done so far.
clc
clear all
alpha=0.5;
rho=0.8;
delta=0.3;
n=1;
g=1;
theta=1;
[k, c] = meshgrid(0:1:30, 0:1:30);
kdot = k.^alpha-c-(n+g+delta).*k;
cdot = (1/theta).*(alpha.*(k^(alpha-1))-delta-rho-theta.*g).*c;
quiver(k,c, kdot, cdot, 1), axis tight
xlabel 'x', ylabel 'y'
title 'Ramsey Model'
  2 个评论
Mathieu NOE
Mathieu NOE 2022-5-18
see what you get with
quiver(k,c,kdot,cdot,0)
does it makes sense ?
econogist
econogist 2022-5-18
Attached is what it spits out. It doesn't make sense. Just a blank plot.

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采纳的回答

David Goodmanson
David Goodmanson 2022-5-18
HI ec,
There are a couple of issues here. First, the cdot expression lacks a dot, should be
k.^(alpha-1).
Second, the grid for k begins at zero, so
0^(alpha-1) = inf
which you don't want. Then you have to adjust the grid to find the fixed point for the given parameters. In the code below, quiver also multiplies the arrows by 3 to make them more visible.
clc
clear all
alpha=0.5;
rho=0.8;
delta=0.3;
n=1;
g=1;
theta=1;
[k, c] = meshgrid(.01:.01:.15, .01:.01:.25);
kdot = k.^alpha-c-(n+g+delta)*k;
cdot = (1/theta)*(alpha*(k.^(alpha-1))-delta-rho-theta*g).*c;
quiver(k,c, kdot, cdot,3), axis tight
xlabel 'x', ylabel 'y'
title 'Ramsey Model'

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