zel In the text, we looked at the simplest bioeconomic model for renewable resource growth, the...

  

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zel In the text, we looked at the simplest bioeconomic model for renewable resource growth, the logistic growth function. That function, S = S, + gS 1- , defines the stock of the renewable resource at time 1+1, S., as a function of the stock of the renewable resource at time t, S,, the intrinsic growth rate of the renewable resource, g, and the natural carrying capacity, K. For this question, let the renewable resource be the number of lobsters off the shore of Corduroy Island. a. (2 marks) Briefly explain the relationship between S, and S, that indicates a "sustainable" lobster population. b. (2 marks) If the lobster population is sustainable, determine how many, if any, can be sustainably "harvested" (ie, caught) in any given year. Use the variable H to represent this amount and describe it in terms of g, S and K. Assume that the harvest, H, is a function of the fisher's effort, e, and how easy it is to catch lobsters, (this is known as the "catchability coefficient"). In other words, assume that H = 0eS. c. (2 marks) Use this information, along with your result in part (b) to calculate the sustainable stock of lobsters, S, as a function of g, K, e and 0. d. (2 marks) Briefly explain how the sustainable stock depends on g, K, e and 8. (No math is required here nor is getting the correct answer in part (c), just common sense.) zel In the text, we looked at the simplest bioeconomic model for renewable resource growth, the logistic growth function. That function, S = S, + gS 1- , defines the stock of the renewable resource at time 1+1, S., as a function of the stock of the renewable resource at time t, S,, the intrinsic growth rate of the renewable resource, g, and the natural carrying capacity, K. For this question, let the renewable resource be the number of lobsters off the shore of Corduroy Island. a. (2 marks) Briefly explain the relationship between S, and S, that indicates a "sustainable" lobster population. b. (2 marks) If the lobster population is sustainable, determine how many, if any, can be sustainably "harvested" (ie, caught) in any given year. Use the variable H to represent this amount and describe it in terms of g, S and K. Assume that the harvest, H, is a function of the fisher's effort, e, and how easy it is to catch lobsters, (this is known as the "catchability coefficient"). In other words, assume that H = 0eS. c. (2 marks) Use this information, along with your result in part (b) to calculate the sustainable stock of lobsters, S, as a function of g, K, e and 0. d. (2 marks) Briefly explain how the sustainable stock depends on g, K, e and 8. (No math is required here nor is getting the correct answer in part (c), just common sense.)

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