Question

Assume that a firm has the following marginal benefit of pollution (denoted E for emissions, measured in tons): MB=150-5 E e. Now assume that instead the government allocates each firm permits to pollute equal to the total current pollution minus 12 tons, but allows the firms to trade. Which firm will purchase permits and which firm will sell permits? Hint: Notice that total pollution reduction of firm 1 plus firm 2 will be 24 tons. f. How much pollution reduction will each firm undertake after they have traded permits? What will the total cost of pollution reduction be across both firms? g. What price will permits sell for? What would the total cost to each firm of complying with the cap-and-trade policy be? h. Explain in words why the total cost of reducing pollution is lower under cap-and-trade than with firm-specific pollution limits. 3. Assume that a firm has the following marginal benefit of pollution (denoted E for emissions, measured in tons): MB=150-5E a. How much would this firm pollute if pollution is unregulated? b. The government would like to reduce pollution from this amount by 12 tons and so implements a quantity constraint at the quantity in part (a) minus 12. What is the cost to this firm of reducing pollution by 12 tons? C. What tax would encourage this polluter to reduce pollution by the same 12 tons as the quantity constraint? What would the cost of this tax be to the firm? d. Now assume that there is a second firm with the following marginal benefit of pollution: M B =90-3 E2. How much pollution would this firm emit if pollution is unregulated and what would it's cost be to reduce pollution by 12 tons from that level? e. Now assume that instead the government allocates each firm permits to pollute equal to the total current pollution minus 12 tons, but allows the firms to trade. Which firm will purchase permits and which firm will sell permits? Hint: Notice that total pollution reduction of firm 1 plus firm 2 will be 24 tons. f. How much pollution reduction will each firm undertake after they have traded permits? What will the total cost of pollution reduction be across both firms? 8. What price will permits sell for? What would the total cost to each firm of complying with the cap-and-trade policy be? h. Explain in words why the total cost of reducing pollution is lower under cap-and-trade than with firm-specific pollution limits.

Answer 1

Step-by-step explanation:

E)cost of pollution is reduction in benefit of the firms.

MB=150-5E,. MB=90-3E

E=30-MB/5. E=30-MB/3

Joint MB,

E=60-8MB/15

MB=112.5-1.875E

Total pollution reduction=24

Total pollution=60-24=36

MB=112.5-1.875*36=112.5-67.5=45

Firm 1

MB=150-5E.

45=150-5E.

E=-105/-5=21

Reduction=30-21=9

Firm 2,

MB=90-3E

45=90-3E

E=-45/-3=15

Reduction =30-15=15

So firm 2 is reducing 15 units of pollution and firm 1 reducing 9 units of pollution.

As each firm have to reduce 12 units of pollution but firm 2 reducing 3 units more while firm 1 reducing 3 less units.

So, firm 2 is selling 3 units of pollution emission permit to firm 1.

F)firm 1 reduce 9 units and firm 2 reduce 12 units of pollution after trade.

Total cost of pollution reduction will total Benefit reduction by pollution reduction.

MB=112.5 -1.875E

TB=112.5E-0.9375E^2

TB at E=60

TB=112.5*60-0.9375*60*60=6750-3375=3375

TB at E=36

TB=112.5*36-0.9375*36*36=4050-1215=2836

Total cost of pollution reduction=3375-2836=540

G)price of permit= cost of extra pollution reduction by firm 2 or total cost from 9 to 12 by firm 2

MB=90-3E

TB=90E- 1.5E^2

TB at E=18

TB=90*18 -1.5*18*18=1620-486=1134

TB at E=15

TB=90*15 -1.5*15*15=1350-337.5=1012.5

Permit price=1134-1012.5=121.5

Total cost to firm 2 =1134

Net total cost to firm 2=1134-121.5=1012.5

Total cost to firm 1=150E-2.5E^2=150*9-2.5*9*9=1350-202.5=1147.5

Net total cost=1147.5+121.5=1269

H) the total cost is lower in cap & trade policy is because the firm who has higher cost of pollution reduction is paying the other firm who has lower cost of pollution reduction to reduce more pollution ,so that his part of pollution reduction can be completed.

And the amount he is paying is equal to the amount that is cost of other firm of reducing additional pollution units.

So the cost the firm is lower as he is paying lower amount than if he reduce pollution by itself.