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The word “convexity” is ubiquitous in economics, but absent from economics. In this paper we explain why, and show what difference it makes to economic analysis if ecosystem non-convexities are taken seriously. A simple proof is provided of the connection between “self-similarity” and “power laws”. We also provide an introduction to each of the papers in the Symposium and draw out the way in which...
We review various aspects of the notion of scale applied to natural systems, in particular complex adaptive systems. We argue that scaling issues are not only crucial from the standpoint of basic science, but also in many applied issues, and discuss tools for detecting and dealing with multiple scales, both spatial and temporal. We also suggest that the techniques of statistical mechanics, which have...
The relationship between grass production and the quantity of trees in mixed tree-grass ecosystems (savannas) is convex for all or most of its range. In other words, the grass production declines more steeply per unit increase in tree quantity at low tree cover than at high tree cover. Since much of the economic value in savannas is ultimately derived from grass, and the main mechanism controlling...
We study here optimal management of dynamic ecological systems that exhibit a destabilizing positive feedback. The prototype example is that of a shallow lake in which phosphorous loading placed by anthropogenic activities (fertilizers for farming and gardening) is stored in sediments until a critical level is reached after which there is a destabilizing return to the water - the tradeoff between...
Ecological systems such as shallow lakes are usually non-linear and display discontinuities and hysteresis in their behaviour. These systems often also provide conflicting services as a resource and a waste sink. This implies that the economic analysis of these systems requires to solve a non-standard optimal control problem or, in case of a common property resource, a non-standard differential game...
Recent research in natural sciences shows that the dynamics in boreal forests are much more complex than what many models traditionally used in forestry economics reflect. This essay analyzes some challenges of accounting for such complexity. It shows that the optimal harvesting strategy for forest owners is history dependent and for some states of the forest, more than one strategy may be optimal...
We are interested in three related questions: (1) How should accounting prices be estimated? (2) How should we evaluate policy change in an imperfect economy? (3) How can we check whether intergenerational well-being will be sustained along a projected economic programme? We do not presume that the economy is convex, nor do we assume that the government optimizes on behalf of its citizens. We show...
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