The Official Journal of the Pan-Pacific Association of Input-Output Studies (PAPAIOS)
Table 2 Intensive feedback loops in M-1 and B-1
From: Increasing returns and business cycles in a family of Goodwinian models with Leontiev technology
No. | Order, sign | Loop | Shift in loop polarity | |
|---|---|---|---|---|
M-1 | B-1 | |||
1 | 1, − | B1 \(u\mathop{\longrightarrow}\limits^{{}}\dot{u}_{{{\text{out}}}}\) | \(u\mathop{\longrightarrow}\limits^{ - }\dot{u}\) when \(\hat{u}\) < 0 for v < vG and \(u\mathop{\longrightarrow}\limits^{{}}\dot{u}\) when \(\hat{u}\) > 0 for v > vG | \(u\mathop{\longrightarrow}\limits^{ - }\dot{u}\) when \(\hat{u}\) < 0 for \(\hat{w} < \hat{a}\) and \(u\mathop{\longrightarrow}\limits^{{}}\dot{u}\) when \(\hat{u}\) > 0 for \(\hat{w} > \hat{a}\) |
2 | 1, + | R1 \(u\mathop{\longrightarrow}\limits^{{}}\dot{u}_{{{\text{in}}}}\) | ||
3 | 1, − | B2 \(v\mathop{\longrightarrow}\limits^{{}}\dot{v}_{{{\text{out}}}}\) | \(v\mathop{\longrightarrow}\limits^{ - }\dot{v}\) when \(\hat{v}\) < 0 for u > uG and \(v\mathop{\longrightarrow}\limits^{{}}\dot{v}\) when \(\hat{v}\) > 0 for u < uG | \(v\mathop{\longrightarrow}\limits^{ - }\dot{v}\) when \(\hat{v}\) < 0 for u > up and \(v\mathop{\longrightarrow}\limits^{{}}\dot{v}\) when \(\hat{v}\) > 0 for u < up |
4 | 1, + | R2 \(v\mathop{\longrightarrow}\limits^{{}}\dot{v}_{{{\text{in}}}}\) | ||
5 | 2, − | B3 \(v\mathop{\longrightarrow}\limits^{{}}\dot{u}_{{{\text{in}}}} \mathop{\longrightarrow}\limits^{{}}u\mathop{\longrightarrow}\limits^{ - }\dot{v}_{{{\text{in}}}}\) | No shift (negative) \(v\mathop{\longrightarrow}\limits^{{}}\dot{u}\mathop{\longrightarrow}\limits^{{}}u\mathop{\longrightarrow}\limits^{ - }\dot{v}\) | No shift (negative) \(v\mathop{\longrightarrow}\limits^{{}}\dot{u}\mathop{\longrightarrow}\limits^{{}}u\mathop{\longrightarrow}\limits^{ - }\dot{v}\) |