There are two factories in a small town. Both of them emit carbon dioxide into the air. Factory 1 currently emits 120 tons per month, whereas factory 2 currently emits 160 tons per month. The technology of each factory is different, so their costs of reducing emissions are different as well. The tables below show the costs of reducing emissions in increments of 20 tons per month for each factory:
Total cost of reducing emissions by 20 tons/month | $50 |
Total cost of reducing emissions by 40 tons/month | $150 |
Total cost of reducing emissions by 60 tons/month | $270 |
Total cost of reducing emissions by 80 tons/month | $410 |
Total cost of reducing emissions by 100 tons/month | $570 |
Total cost of reducing emissions by 20 tons/month | $20 |
Total cost of reducing emissions by 40 tons/month | $60 |
Total cost of reducing emissions by 60 tons/month | $110 |
Total cost of reducing emissions by 80 tons/month | $200 |
Total cost of reducing emissions by 100 tons/month | $300 |
The existing technology does not allow for reductions in emissions
beyond 100 tons/month. That is, the most each factory could reduce
its emissions by is 100 tons/month.
Suppose the government in this town would like to cut monthly emissions to half of the current level. To do that, the government has decided to impose a tax for every 20 tons of pollution per month emitted by a factory. To achieve its desired goal (but not exceed the goal), the tax would have to be set between $______ and $______ for every 20 tons/month. (The first number should be the lower end of the tax, and the second number should be the higher end of the tax.)
Here,
Factory 1 emissions per month = 120 tons
Factory 2 emissions per month = 160 tons
Total Emissions = 280 tons
Emission that government wants to reduce is 50%
So emission level Government is looking for = 50% of 280 = 140 tons
Now ,
Tons reduced per month | Factory 1 Cost | Marginal Cost factory 1 | Factory 2 Cost | Marginal Cost factory 1 |
20 tons | 50 | 50 | 20 | 20 |
40 tons | 150 | 100 | 60 | 40 |
60 tons | 270 | 120 | 110 | 50 |
80 tons | 410 | 140 | 200 | 90 |
100 tons | 570 | 160 | 300 | 100 |
So,
IF the tax is $100 than 140 tons can be saved wit factory 1 saving 40 tons and factory 2 saving entire 100 tons
Now if the tax is increased till it reaches $120 there wont be incremental savings byong 120n factory 1 will save another 20 tons
So Range $100-$120 fr every 20 tons
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