b. Can the total abatement cost be lowered by requiring unequal pollution reductions from the Firms, while still maintaining a total pollution reduction of 107 Show the total cost for reductions of 6 ond 4 units, 7 and 3 units, etc., for Firms 1 and 2 respectively

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b. Can the total abatement cost be lowered by requiring unequal pollution reductions from the
Firms, while still maintaining a total pollution reduction of 10? Show the total cost for reductions
of 6 and 4 units, 7 and 3 units, etc., for Firms 1 and 2 respectively.
Transcribed Image Text:b. Can the total abatement cost be lowered by requiring unequal pollution reductions from the Firms, while still maintaining a total pollution reduction of 10? Show the total cost for reductions of 6 and 4 units, 7 and 3 units, etc., for Firms 1 and 2 respectively.
An important question in economics is how to minimize the total cost of pollution reduction (called
the abatement cost, which is considered a "cost to society"). Two companies, Fim 1 and Firm 2,
each emit 10 units of pollution per year. The table below shows the total cost for each company to
reduce its pollution to a given value x. Due to technology differences, is more expensive for Fim
2 to reduce pollution than for Firm 1. When x = 10, no abatement has occurred (it is "business as
usual"); when x = 0, no pollution is emitted.
The table also shows an algebraic formula for each abatement cost. (BTW, it is a common
economic approximation that abatement cost goes up quadratically.)
Below, we solve this for two firms, but the method is applicable to a situation with multiple firms.
Per-firm pollution emissions x
Firm 1 total abatement cost = (10-x)
where x is the amount of pollution
Firm 2 total abatement cost = (20-2x)
where x is the amount of pollution
1.
3.
4.
9.
7.
8.
6.
10
100
81
64
49
36
25
16
9.
4.
400
324
256
196
144
100
64
36
16
4.
Transcribed Image Text:An important question in economics is how to minimize the total cost of pollution reduction (called the abatement cost, which is considered a "cost to society"). Two companies, Fim 1 and Firm 2, each emit 10 units of pollution per year. The table below shows the total cost for each company to reduce its pollution to a given value x. Due to technology differences, is more expensive for Fim 2 to reduce pollution than for Firm 1. When x = 10, no abatement has occurred (it is "business as usual"); when x = 0, no pollution is emitted. The table also shows an algebraic formula for each abatement cost. (BTW, it is a common economic approximation that abatement cost goes up quadratically.) Below, we solve this for two firms, but the method is applicable to a situation with multiple firms. Per-firm pollution emissions x Firm 1 total abatement cost = (10-x) where x is the amount of pollution Firm 2 total abatement cost = (20-2x) where x is the amount of pollution 1. 3. 4. 9. 7. 8. 6. 10 100 81 64 49 36 25 16 9. 4. 400 324 256 196 144 100 64 36 16 4.
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