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Economics & Social Sciences Research Program

Optimal Growth with Population Dynamics

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Maximum Economic Yield (MEY) is used in fisheries economics to evaluate efficiency of outcomes. The definition of MEY is based on a bioeconomic model. Rosenman (1986) presented conditions for MEY under uncertainty that compared outcomes to a bioeconomic competitive equilibrium. In this project, these conditions were generalized to incorporate population dynamics and were then applied using dynamic game theory to analyze outcomes of a rationalized fishery that includes a quota market. Multi-stage population dynamics are a crucial feature of this bioeconomic model because these provide an internal representation of MSY which is used as a reference point and assumed steady-state of a dynamic game.  Rosenman’s MEY applies to yields with an incomplete (i.e., partially optimizing) feedback between abundance and costs which is not the same as optimal growth of a fish stock. However the biggest disadvantage of Rosenman’s bioeconomic model is that it requires stringent restrictions on population dynamics. In particular, it rules out Beverton-Holt type population dynamics which is not a tenable assumption for this project; recent work in this project analyzed conditions for optimal growth in a family of bioeconomic models with population dynamics that include competition for resources by juveniles and adults, and Beverton-Holt population dynamics arise with juvenile predation. Many models in this family have degenerate, or unnecessarily complex, dynamics and were excluded from consideration as an optimal growth model for a fish stock. One class of models met the conditions for optimal growth and these dynamics are equivalent to Lucas and Prescott’s (1971) model of investment under uncertainty, and interestingly, to von Bertalanffy growth.


By Michael Dalton

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