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(a–c) are examples of nonlinear production functions extracted from the economics literature [2].

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posted on 01.04.2014, 02:46 by Calistus N. Ngonghala, Mateusz M. Pluciński, Megan B. Murray, Paul E. Farmer, Christopher B. Barrett, Donald C. Keenan, Matthew H. Bonds

The x-axis is the stock of capital. The blue line represents the rate of capital accumulation (i.e., savings) and the red line represents that rate of capital depreciation. Income (generated from capital) will necessarily fall when the red line is above the blue line, and will rise when the reverse is true. (c) is the canonical depiction of a poverty trap, but (a–c) all have stable equilibria in the basin of attraction of a poverty trap, and unstable equilibria that represent a critical threshold of capital necessary for growth. These models are speculative, based on hypothetical scenarios, but are useful for demonstrating a range of theoretical possibilities. The scientific community should contribute to our understanding of how such nonlinearities might emerge from, or be nested within, real world biophysical systems.