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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 prots 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 prots, so in this
case compare prots with and without pesticide application. Prots with the
pesticide application are 4 × 100 × 1 − 0.01 0.5(1600) − 60 ≈ 227. Prots
√
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 protmaximizing 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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This note was uploaded on 09/24/2011 for the course ECON C125 taught by Professor Zelberman during the Spring '09 term at Berkeley.
 Spring '09
 ZELBERMAN

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