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The Official Journal of the Pan-Pacific Association of Input-Output Studies (PAPAIOS)

Table 14 New intensive feedback loops involving level s at unstable Xb undergoing AHB in L-2

From: Increasing returns and business cycles in a family of Goodwinian models with Leontiev technology

Loop

First order

Second order

Third order

Number 1—positive

\(s\mathop{\longrightarrow}\limits^{{}}\dot{s}\)

Number 2—positive

\(s\mathop{\longrightarrow}\limits^{ - }\dot{z}\mathop{\longrightarrow}\limits^{{}}z\mathop{\longrightarrow}\limits^{ - }\dot{s}\)

Number 4—positive

\(s\mathop{\longrightarrow}\limits^{ - }\dot{z}\mathop{\longrightarrow}\limits^{{}}z\mathop{\longrightarrow}\limits^{ - }\dot{u}\mathop{\longrightarrow}\limits^{{}}u\mathop{\longrightarrow}\limits^{{}}\dot{s}\)

Number 3—positive

\(s\mathop{\longrightarrow}\limits^{{}}\dot{u}\mathop{\longrightarrow}\limits^{{}}u\mathop{\longrightarrow}\limits^{{}}\dot{s}\)

Number 5—positive

\(s\mathop{\longrightarrow}\limits^{{}}\dot{u}\mathop{\longrightarrow}\limits^{{}}u\mathop{\longrightarrow}\limits^{ - }\dot{z}\mathop{\longrightarrow}\limits^{{}}z\mathop{\longrightarrow}\limits^{ - }\dot{s}\)

Number 6—negative

\(s\mathop{\longrightarrow}\limits^{ - }\dot{v}\mathop{\longrightarrow}\limits^{{}}v\mathop{\longrightarrow}\limits^{ - }\dot{z}\mathop{\longrightarrow}\limits^{{}}z\mathop{\longrightarrow}\limits^{ - }\dot{s}\)

Number 7—negative

\(s\mathop{\longrightarrow}\limits^{ - }\dot{v}\mathop{\longrightarrow}\limits^{{}}v\mathop{\longrightarrow}\limits^{{}}\dot{u}\mathop{\longrightarrow}\limits^{{}}u\mathop{\longrightarrow}\limits^{{}}\dot{s}\)

Fourth order

 Number 8—negative \(s\mathop{\longrightarrow}\limits^{ - }\dot{v}\mathop{\longrightarrow}\limits^{{}}v\mathop{\longrightarrow}\limits^{ - }\dot{z}\mathop{\longrightarrow}\limits^{{}}z\mathop{\longrightarrow}\limits^{ - }\dot{u}\mathop{\longrightarrow}\limits^{{}}u\mathop{\longrightarrow}\limits^{{}}\dot{s}\)

 Number 9—negative \(s\mathop{\longrightarrow}\limits^{{}}\dot{u}\mathop{\longrightarrow}\limits^{{}}u\mathop{\longrightarrow}\limits^{ - }\dot{v}\mathop{\longrightarrow}\limits^{{}}v\mathop{\longrightarrow}\limits^{ - }\dot{z}\mathop{\longrightarrow}\limits^{{}}z\mathop{\longrightarrow}\limits^{ - }\dot{s}\)

 Number 10—negative \(s\mathop{\longrightarrow}\limits^{ - }\dot{z}\mathop{\longrightarrow}\limits^{{}}z\mathop{\longrightarrow}\limits^{{}}\dot{v}\mathop{\longrightarrow}\limits^{{}}v\mathop{\longrightarrow}\limits^{{}}\dot{u}\mathop{\longrightarrow}\limits^{{}}u\mathop{\longrightarrow}\limits^{{}}\dot{s}\)

 Number 11—negative \(s\mathop{\longrightarrow}\limits^{ - }\dot{v}\mathop{\longrightarrow}\limits^{{}}v\mathop{\longrightarrow}\limits^{{}}\dot{u}\mathop{\longrightarrow}\limits^{{}}u\mathop{\longrightarrow}\limits^{ - }\dot{z}\mathop{\longrightarrow}\limits^{{}}z\mathop{\longrightarrow}\limits^{ - }\dot{s}\)

  1. The strongest greed feedback loop R2 in L-1 is present in L-2 too