pesticide_practice_problem

# pesticide_practice_problem - Practice Problems Week 14...

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Unformatted text preview: Practice Problems Week 14 Economic Threshold Suppose that you have decided to grow some spinach in your backyard, to earn extra cash by selling it at the local farmer's market. An insect called aphids is threatening your spinach patch. You can make \$4 per bunch of spinach, and your garden can produce 100 bunches. Your friend from the entomology department has determined that you currently have a population of 1600 √ aphids in your backyard. The damage function for aphids is D(a) = 0.01 a . You can purchase some organic pesticide to decrease the aphid population by 50%, but it will cost \$60. Would you pay for the pesticide? What is the economic threshold? Question. Your prots with pesticide is py [1 − D(a)] − w, where p is the perbunch spinach price, y is the yield, D(a) is the damage function, and w is the cost of organic pesticide application. You want to maximize prots, so in this case compare prots with and without pesticide application. Prots with the pesticide application are 4 × 100 × 1 − 0.01 0.5(1600) − 60 ≈ 227. Prots √ without the pesticide application are 4 × 100 × 1 − 0.01 1600 = 240. You will not pay for the pesticide in this case. Economic threshold is the pest population level at which it becomes prot-maximizing to apply the pesticide. We solve for this by setting the cost of applying pesticide equal to the change in losses (damage) from applying pesticides: py [D0 (a ) − D1 (a )] = w, and solve for a . Answer. √ √ √ √ 4 × 100 × 0.01 a − 0.01 0.5a = 60 → a − 0.5a = 15 √ a 1− √ 0.5 = 15 → √ a ≈ 51 → a ≈ 2623 The economic threshold is 2,623 pests. We interpret this as the number of pests that would justify a pesticide application that cost \$60. 1 ...
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