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Concatenated Disruptions with Resilience

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Advances in Spatial and Economic Modeling of Disaster Impacts

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Abstract

This chapter presents a method for modelling resilience in economic systems confronted by multiple irregular shocks. For this, investment portfolio theory is reformulated as a protected production function. This function determines the share of output that is dedicated to protection as economic agents attempt to maintain their preferred level of consumption and safety in the face of exogenous hazards. With this, resilience becomes the ability of production to withstand and recover from the repeated shocks. This mechanism is illustrated via model comprising aggregated domestic sector and a single export sector trading with a larger regional system. Solving the model, first as a comparative static system gives multiple stable and unstable equilibrium solutions for the level of economic activity. Equating these solutions gives the level of protection that offers greatest well-being. This production–protection relationship is then incorporated into a time-step simulation showing how the economy evolves in response to random shocks and concatenated disturbances, including irregular collapses beyond the desired resilience regime. Within this dynamic model, solutions to the static model appear as weak attractors. Thus, a further contribution of the paper is that it bridges between equilibrium and evolutionary economics, and comparable challenges in other disciplines. The method is advanced as a closure for a social accounting-event matrix based approach.

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Notes

  1. 1.

    The cost of protecting utility O(1 − e) is Oe, so the ratio Cost of Protection/Utility Protected = 1/(1 − 1/e) is constant for all magnitude of shocks for a given level of protection. This is consistent with the assertion that the function represents an optimal protection portfolio. Again, the imperfections of this approximation are recognized.

  2. 2.

    The solution to the quadratic equation may be obtained by substitution of (11.7) into (11.6) and obtain the standard solutions x = {−B ± √(A2 + 4AC)}/2A to the quadratic Ax2 + Bx + C = 0. These expressions are, however, less easy to decipher.

  3. 3.

    Goldenfeld and Kadanoff (1999) say that many biological, physical, and social, and economic systems are dominated by big events and “intermediacy.” Empirically, the probability Ω of a jump j is found to be Ω(j) = exp(−|j|/δ|) where δ is the standard deviation, rather than the usual Gaussian form Ω = exp(|j2|/2δ2)/(2δ2). Thus, such events are far more likely than suggested by Gaussian statistics; see also Mandelbrot (1999).

  4. 4.

    Definitions of “complexity” vary: the most concise is from Goldenfeld and Kadanoff (1999) is “structure with variations”. They distinguish this from “chaos”, which they describe as sensitivity to initial conditions with outcomes difficult to predict and growing exponentially with time; see also Gardener and Ashby (1970), Prigogine (1976), Feigenbaum (1978), Anderson et al. (1988) and Ledesdorf and van der Besselaar (1994).

  5. 5.

    This term was introduced by Lorentz (1963). Attempting to understand turbulence in weather systems, but unable to solve the seemingly-simple 3-dimensional equations, Lorentz simulated trajectories similar to the 2 dimensional equations and trajectories shown here. Similar behavior is observed in the extended Lotka-Volterra (1920) predator-prey model (see Chen and Cohen 2001; Neubert and Caswell 1997) observe that, despite local stability, a perturbation may be temporarily amplified and DeAngelis and Waterhouse (1987) showed that frequent perturbations might maintain ecological systems far from equilibrium.

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  1. University at Buffalo, The State University of New York, Buffalo, NY, USA

    Sam Cole

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  1. University of Kitakyushu, Kitakyushu, Japan

    Yasuhide Okuyama

  2. Sol Price School of Public Policy, University of Southern California, Los Angeles, CA, USA

    Adam Rose

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Cole, S. (2019). Concatenated Disruptions with Resilience. In: Okuyama, Y., Rose, A. (eds) Advances in Spatial and Economic Modeling of Disaster Impacts. Advances in Spatial Science. Springer, Cham. https://doi.org/10.1007/978-3-030-16237-5_11

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