Toward sustainable consumption of a renewable resource by a network

Introduction

In this work, we consider the social planner's problem, linked to ensuring sustainable consumption, of how a network of consumers influences the consumption of a renewable resource. We propose that by understanding the factors driving the dynamics of individual consumer behavior, we can identify policies  that are favorable to sustainability. The scope of this research is twofold. The first part consists of construction and evaluation of a dynamic model of individual consumer behaviors, coupled with the resource dynamics. The second part consists of posing the problem as an optimal control one, in order to maximize consumption utility. We look for the conditions under which a stable optimal path exists, and analyze the solutions. These conditions can be used as guidelines for policymaking.

Methodology

Although the problem of resource consumption has been studied extensively in the past, a mathematical model describing the evolution of individual consumption rates and the quantity of the resource has not yet been developed (at least to our knowledge). To do this, we review previous studies regarding consumer psychology and identify the factors that prompt individuals to alter their consumption behaviors. We find that consumers consider both ecological and social factors before altering these behaviors.  Ecological factors are represented by the perceived resource quantity and social factors by the consumption behaviors of other individuals present in the consumer network. The extent to which each individual affects the consumption of another individual depends upon the strength of the tie between the two individuals. Based on this, we are able to develop a system of ordinary differential equations describing the process. We then formulate the optimal control problem, with the objective of maximizing the consumption utility, over an infinite horizon. After an equilibrium analysis of the Hamiltonian system, we are able to identify conditions under which sustainable consumption is possible.

Results

Assuming a homogeneous consumer network, we were able to obtain a simplified and easy-to-analyze version of the model. This simplified model fulfills the verification criteria we set for the equilibrium points and the flow of the trajectories, hence validating it. There are two equilibria, an unstable one representing depletion of the resource, and a stable one representing sustainable consumption. From a similar analysis of the Hamiltonian system, we observe that sustainable consumption is possible only when the discount rate is lower than the intrinsic growth rate of the resource. This essentially means that when the discount rate is high, the future is so unimportant that it is more efficient to consume as much as possible today. Thus, in order to ensure sustainability, the government must either increase the intrinsic growth rate of the resource (if possible), or decrease the discount rate of the objective functional.

Conclusions

Our results adhere to what intuition suggests. For sustainability, governments must either increase resource production, or plan long term. The problem has much room for expansion. We hope to obtain more interesting results as complexities are added to the model.

Please note these Proceedings have received limited or no review from supervisors and IIASA program directors, and the views and results expressed therein do not necessarily represent IIASA, its National Member Organizations, or other organizations supporting the work.

Last edited: 19 August 2015