There are two beef packing plants, A and B, in the city of Rybinsk, Russia. Both plants put partially treated liquid waste into the Volga river. The two plants together dump over 33 000 kilograms of BOD5 per day. (BOD5 is the amount of oxygen used by microorganisms over five days to decompose the waste.) This is more than half the total BOD5 dumped into the river at this location. The city wants to reduce the BOD5 dumped by the two plants by 10 000 kilograms per day.
The following data are available concerning the two plants:
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Output of the two plants
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Steers/Day
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BODS/Steer (Kg)
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Plant A
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20,000
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1.0
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Plant B
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9,000
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1.5
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The costs of making reductions in BOD5 per steer in Russian rubles (RL T B) are shown below:
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Incremental cost of reducing BOD(rubles/ kg/ steer)
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Reduction (kg/steer)
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0.1
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0.2
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0.3
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0.4
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0.5
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0.6
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0.7
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Plant A
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1.5
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2.4
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3.6
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7.5
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13.5
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19.5
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28.5
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Plant B
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4.5
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4.5
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4.5
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4.5
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4.5
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10.5
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13.5
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For example, to reduce the BOD5 of plant A by 0.25 kilograms per steer, the cost is calculated as
(0.1 X 1.5) + (0.1 X 2.4) + (0.05 X 3.6) = RUB 0.57/steer
The council is considering three methods of inducing the plants to reduce their BOD5 dumping: (1) a regulation that limits BOD5 dumping to 0.81 kilograms/steer, (2) a tax of RUB 4.8/kilogram of BOD5 dumped, and (3) a subsidy paid bv the town to the plants of RUB 4.8/kilogram reduction from their current levels in BOD5 dumped.
(a) Verify that, if both plants reduce their BOD5 dumping to 0.81 kilograms/steer, there will be a 10 000 kilograms/day reduction in BOD5 dumped. What will this cost?
(b) Under a tax of RUB 4.8/kilogram, how much BOD5 will plant A dump? How much will plant B dump? (Assume that outputs of steers would not be affected by the tax.)
Verify that this will lead to more than a 10 000 kilograms/day reduction in BOD5. What will this cost?
(c) Under a subsidy of RUB 4.8/kilogram reduction in BODS, how much will plant A dump? How much will plant B dump? Verify that this will lead to more than a 10 000 kilograms/day reduction in BODS. What will this cost?
(d) Explain why the tax and subsidy schemes lead to the same behaviour by the meat packing plants.
(e) Explain why the tax and subsidy schemes have lower costs for the company than the regulation.