Goodwin Model (1967)

A few words about the model. Consider that the production function has complementary factors according to the following equation:MATHwe know that such an assumption is useful to engender fluctuations. The effective labor at the period $t$ is denoted $L_{t}$ but the working population is $N_{t}=N_{0}e^{nt}$ so that the labor rate is $x_{t}=L_{t}/N_{t}$. The wage depends on the labor rate according to an assumption of the Philips curve type. The profits are entirely reinvested, they are equal to the savings $S=r\cdot K$ and the part of profits in the global income is the complement of the part of wages $z$ so that $1-z=r\cdot K/Y$. The labor depends on the capital according to $L=u\cdot K/v$. Then we have the systemMATHThere is stationary state if MATH , i.e., MATH and MATH


[1] ref. to Alain Goergen. "Dynamique Economique. Solutions de problèmes avec Maple et Matlab". Economica. 2006.

[2] ref. to Gilbert Abraham-Frois.