Name: ________________________________SOS 325Homework #5: Renewable Resources, Common Property and Open AccessAnswer all questions on this sheet of paper and turn it in in-class or submit itelectronically via Blackboard by 4:30 pm December 3rd (the last day of class). Do NOTemail it to me or the TA. Make your answers clear, legible and to the point.1. (100 pts.) Consider a resource whose net growth in biomass (X) each year F(X) isgiven by a logistic growth function where r=.1 and K=10. (You can think of theunits of the biomass as being millions of animals so that the carrying capacity ofthe environment is ten million animals.)F ( X ) rX ( 1 X / K ) . 1 X ( 1X)10Suppose that harvest occurs according to the following relationship: Yield =Y=qEX, where E is â€œeffortâ€ pursuing the resource (number of boats for a fisheryor number of hunters for big game hunting) and q = .001.a. (10 pts.) Graph the growth function of the biomass F(X), being clear tolabel maximum sustainable yield (MSY) harvest, biomass levels at MSYand carrying capacity on your graph. What is the maximum amount ofharvest that can be sustainably achieved in this system? What level ofbiomass generates this amount of harvest?b. (15 pts.) Now, using the equation derived in class and in Keohane andOlmstead, graph the curve showing the sustainable harvest for any givenamount of effort (the â€œharvest/effortâ€ or â€œyield/effortâ€ curve). Whatlevel of effort exhausts the resource? What amount of effort isconsistent with the maximum sustainable harvest of the resource?c. (15 pts.) Suppose ecologists discover that r=.05 rather than .1 so that thegrowth rate for any level of biomass is now much lower than thought.Graph the new yield/effort curve. How does this change your answers tothe previous question? If managers set effort to the level that wouldmaximize sustainable yields in question b), what would happen to thebiomass over time?d. (20 pts.) Sticking to the parameter values given in a) and b), suppose thatthe price of a single unit of harvest is 1000 (so that the sustainablerevenue/effort curve is 1000 times the harvest/effort curve youâ€™vealready found in question b) and the cost of a unit of effort is constantand =1. Find the level of effort that maximizes sustainable profits.(NOTE: It is ok to find this number graphically or by trial and errorsubstitution into the equation.)e. (20 pts.) Find the level of effort that you would expect to occur underopen access conditions. How does this compare to the level found inquestion d)? Can you tell if the stock will be biologically overexploited(i.e. at a level of biomass below the level consistent with the productionof maximum sustainable yield)?f. (10 pts.) Suppose that the resource stock is privatized to a singleindividual or corporation. How much effort would you expect them toutilize assuming that they have as their goal the maximization ofsustainable profits? Would they have an incentive to defend theresource against encroachment by other users? Why?g. (10 pts.) Resource managers, faced with the open access conditionsdescribed in e), subsidize fuel costs and supply low-interest loans toharvesters, lowering the marginal cost of a unit of effort. The objective ofthis program is to improve the livelihoods of resource-dependentcommunities. Graphically demonstrate how this affects the amount oflong-run effort in the industry. What happens to sustainable profits?Resource stocks?
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