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Autor : Sudipto Sakar Prof : Fabbri Paolo Makamte dorcas Prophete Nemours

University of Parma INTERNATIONAL BUISINESS AND DEVELOPMENT Optimal Harvesting of a Renewable Resource: A Mathematical Model. Autor : Sudipto Sakar Prof : Fabbri Paolo Makamte dorcas Prophete Nemours. Introduction.

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Autor : Sudipto Sakar Prof : Fabbri Paolo Makamte dorcas Prophete Nemours

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  1. University of ParmaINTERNATIONAL BUISINESS AND DEVELOPMENTOptimal Harvesting of a Renewable Resource: A Mathematical Model Autor : Sudipto Sakar Prof : Fabbri Paolo Makamte dorcas Prophete Nemours

  2. Introduction • Our work entitle optimal Harvesting of a Renewable resource: a mathematical model will be illustrated using the well known "optimal rotation" problem from forest economics. The optimal trigger depends on those points that you will see in the following slides

  3. Many renewable natural resources are under serious theat. But if properly managed, renewable resources such as fish and forest stocks should not be really at risk of extinction. So this work will propose a general economic model of renewable resource harvesting that takes into account the features that will be mentioned :

  4. growth rate is higher • harvesting is done when the stock level is higher • Size of the replacement seedlings • Government role in the environment • Perspectives futures now let us see the model and its specification

  5. As you can see we use a real-option model : • Dx=µ(x)dt +σ(x)dzwhich explains the change in the value of the Tree. The first component “µ(x)dtrepresents a determinant part of the Tree Growth , so the value is expected to increase at a rate of µ(x).The second component σ(x)dzcaptures the uncertainties that exist in all Natural Resources because theforecast of natural resources isstudied by probability ,for this reason it is very difficult to have the exact certitude about future event that can be happened to natural resources.

  6. Let’s take into account this variable “ x” that represents a Tree when it rises at such a level U the tree has to be replaced by seedlings

  7. the matured trees generate a cash flow of (U-C) ,we also have to consider the future life of these new seedlings represented by “L” and “ V” the value of the tree before being cutting . From there we found the payoff at harvest depicted by this formula: V(U)=U-C+V(L)

  8. Consequences of cutting trees first after

  9. Conclusion In a simple way it means that the value of a natural resource precisely a tree has to be valuated by its managing costs and the benefits that it could be given and also the costs of seedlings to replace the oldest one . Sometime it happens that fire turn on into the forest, the question is ,does fire do any good to a forest ? Of course the response is no, it’s true that it can be an eventual possibility to create job in the economy but in the other hand seedlings take too much time to grow meanwhile animals which lived within that area die of starving or go far away . The government’s on the invironment problem : Create restrictive policy able to shrink the negative human actions

  10. Perspective futures: Preservation of the invironment by planting trees that would be able to replace the oldests after their maturity because

  11. THANK YOU FOR YOURATTENTION

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