Bulletin of Mathematical Biology

, Volume 77, Issue 2, pp 348–367 | Cite as

Sustainability and Substitutability

  • Eli P. Fenichel
  • Jinhua Zhao
Original Article


Developing a quantitative science of sustainability requires bridging mathematical concepts from fields contributing to sustainability science. The concept of substitutability is central to sustainability but is defined differently by different fields. Specifically, economics tends to define substitutability as a marginal concept while fields such as ecology tend to focus on limiting behaviors. We explain how to reconcile these different views. We develop a model where investments can be made in knowledge to increase the elasticity of substitution. We explore the set of sustainable and optimal trajectories for natural capital extraction and built and knowledge capital accumulation. Investments in substitutability through knowledge stock accumulation affect the value of natural capital. Results suggest that investing in the knowledge stock, which can enhance substitutability, is critical to desirable sustainable outcomes. This result is robust even when natural capital is not managed optimally. This leads us to conclude that investments in the knowledge stock are of first order importance for sustainability.


Economics Knowledge Constant elasticity of substitution (CES) Optimal control 


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Copyright information

© Society for Mathematical Biology 2014

Authors and Affiliations

  1. 1.Yale UniversityNew HavenUSA
  2. 2.Department of EconomicsMichigan State UniversityEast LansingUSA

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