Question

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:

Factory 1

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

Factory 2

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.)

Answer 1

Current Emissions

Factory 1 = 120 tons

Factory 2 = 160 tons

Total Emissions = 120 + 160 = 280 tons

Now Government want to reduce emission to 50%

i.e = 50% of 280 tons = 140 tons

Now For both,

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 MArginal Cost of 100 will reduce it by 140 tons - 40 from Factory1 and 100 from factory 2

i.e Tax of 100 pe 20 tons can reduce it by 140 tons

so minimum is 100

If we go beyind 120 than tons reduec will be 160 as FActory 1 will reduce by 60 tons

So Range = 100 - 120 dollars per 20 tons

100 and 120 excluding