Suppose you want to remove seventy sh of an exotic species that have been illega

Question

Suppose you want to remove seventy sh of an exotic species that have been illegally
introduced to a lake (e.g., piranha). You have three possible removal methods. Assume
that Q1, Q2, and Q3 are, respectively, the amount of sh removed by each method that
you choose to use so that the goal will be accomplished by any combination of methods
such that Q1 + Q2 + Q3 = 70.

(a) If the marginal costs of each removal method are, respectively, 10Q1,
5Q2, and 2.5Q3, how much of each method should you use to achieve the removal
cost-eectively?

(b) Why isn’t an exclusive use of method 3 cost eective?

(c) Suppose that the three marginal costs were constant (not increasing as
in case 5a) such that MC1 = 10, MC2 = 5, and MC3 = 3.5. What is the most
eective outcome in that case?

Explanation / Answer

a. One should chose such that MC in each case are equal

MC1 = MC2 = MC3

10Q1 = 5Q2 = 2.5Q3

Q1/Q2 = 1/2 , Q2/Q3 = 1/2 and Q1/Q3 = 1/4

So the ratio for outcome

1:2:4

So, Q1 = 10

Q2 = 20

Q3 = 40

b. an exclusive use of method 3 isn't cost eective because the marginal cost in method is variable and is increasing as Q increases and thus becomes greater than MC1 and MC2 as Q increases vary high.

c.  the most eective outcome in this case would be MC3 as all three MCs are constant and MC3 is the lowest one.

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