Copyright (c) Christopher Makler / econgraphs.org

Ramsey-Cass-Koopmans Model

The solid green line shows the dynamic path of the economy starting at point O. Try dragging point O to see how the dynamic path changes; you can also change the parameters using the sliders to the right.

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Parameters

\alpha :
{{ params.alpha | number:2 }}
\delta :
{{ params.delta | number:3 }}
n :
{{ params.n | number:3 }}
g :
{{ params.g | number:3 }}
\rho :
{{ params.rho | number:3 }}
\gamma :
{{ params.theta | number:2 }}
\text{Steady-state capital } (\dot k = 0)
c = k^\alpha - (\delta + n + g) k
c = k^{ {{ params.alpha | number:2 }} } - ({{ params.delta | number:3 }} + {{ params.n | number:3 }} + {{ params.g | number:3 }}) k
c = k^{ {{ params.alpha | number:2 }} } - {{ params.delta + params.g + params.n | number:3 }}k
\text{Steady-state consumption } (\dot c = 0)
\alpha k^{\alpha - 1} = \rho + \delta + \gamma g
{{ params.alpha | number:2 }} k^{ {{ params.alpha | number:2 }} - 1} = {{ params.rho | number:3 }} + {{params.delta | number:3}} + {{params.theta | number:2}} \times {{params.g | number:3}}
k = {{ model.steadyStateK | number:2 }}