{"id":1849,"date":"2017-03-24T23:04:59","date_gmt":"2017-03-25T03:04:59","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/uvicecon103\/?post_type=chapter&p=1849"},"modified":"2017-03-25T12:52:26","modified_gmt":"2017-03-25T16:52:26","slug":"solutions-case-study-sulpher-dioxide","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/uvicecon103\/chapter\/solutions-case-study-sulpher-dioxide\/","title":{"raw":"Solutions: Case Study - Sulpher Dioxide","rendered":"Solutions: Case Study – Sulpher Dioxide"},"content":{"raw":"1. How much will the firms pollute before policy intervention?<\/strong>\r\n\r\nWithout policy intervention, there is no benefit for a firm to decrease its pollution. Even though reducing the\u00a0first few units costs relatively little, the firm maximizes profits by polluting its full\u00a0amount of pollution, where the costs of abatement are 0. This results in Firm 1 polluting 10 million tons of Sulpher Dioxide, and Firm 2 polluting 20 million tons, for a total of 30 million tons.\r\n\r\n\"\"\r\n\r\n2. If the government implemented a cap and trade system, distributing a total of 12 million permits, with 6 million to each firm, who would sell and who would buy permits?<\/strong>\r\n\r\nSince we know that each firm is given 6 million permits, we need to compare\u00a0the marginal cost of abatement for each firm at that level. Drawing a line up from 6 million we see that for Firm 1, their marginal cost of abatement is $350, whereas Firm 2 faces a cost of $200. Since Firm 1 values pollution more that Firm 2, there are mutually beneficial exchanges where Firm 1 buys permits from Firm 2.\r\n\r\n\"\"\r\n\r\n3. How much would the seller be willing to accept, and how much will the buyer be willing to pay?<\/strong>\r\n\r\nAt 6 million permits, we can see that Firm 1 is willing to pay up to their marginal cost of abatement, or $350, and Firm 2 is willing to accept at least enough to cover their lost benefit from polluting, or $200. Notice that after Firm 1 buys\u00a0a permit from Firm 2, this relationship changes - Firm 1 will be willing to pay slightly less, and Firm 2 will need to be paid slightly more.\r\n\r\n4. What is the equilibrium price of permits, and the equilibrium quantity of Sulpher Dioxide production?\u00a0After the exchange of permits on the open market, how much does each firm emit?<\/strong>\r\n\r\nTo find the equilibrium price and quantity, we need to find a price level for permits such that the marginal cost of abatement for both firms is equal. By looking at our previous graph, and following what happens each time Firm 1 buys a permit from Firm 2, we see that Firm 1's marginal cost falls and Firm 2's marginal cost rises until they are equal.\r\n\r\n\"\"\r\n\r\nThe transactions continue until Firm 1 has 8 million permits and Firm 2 has 4 million units. At this point the marginal costs of abatement are equal so no mutually beneficial transactions exist. Equilibrium quantity is 12 million, as regulated by the government, and the market price for permits is $300.\r\n\r\n \r\n\r\n5. What are the total benefits and total costs to each firm from trading permits? Show that the trade was a Pareto Improvement<\/strong>\r\n\r\nFor Firm 1, buying more permits gives them the benefit of polluting more, which is equal to the reduction of the costs of abatement as shown in the green area. The cost is the amount they have to pay Firm 2, which is equal to the market price of the permit ($300) multiplied by the number they purchase as shown in the red area.\r\n\r\nNote that while Firm 1 is technically willing to pay more than $300, in the perfectly competitive market for permits we usually deal with, if Firm 2 tries to charge any more than $300, Firm 1 will purchase permits from another firm.\r\n\r\n\"\"\r\n\r\nCalculating costs and benefits:<\/span>\r\n\r\nBenefits\u00a0<\/strong>(green area):\r\n\r\n[$300 x (8-6)] + [($350-$300) x (8-6)]\/2\r\n\r\n=$650 million<\/em>\r\n\r\nCosts\u00a0<\/strong>(red area):\r\n\r\n[$300 x (8-6)]<\/span>\r\n\r\n=$600 million<\/em>\r\n\r\nSurplus:<\/strong>\r\n\r\n$650 million - $600 million\r\n\r\n=$50 million<\/em>\r\n\r\nFor Firm 2, selling\u00a0permits means they will have to pollute less. This cost of abatement is equal to the red area below, and is the down side for selling permits. This cost is outweighed by the benefit of selling permits at the market price of $300. The revenue Firm 2 receives\u00a0is depicted in the green area.\r\n\r\n\"\"\r\n\r\nCalculating costs and benefits:\r\n\r\nBenefits\u00a0<\/strong>(green area):\r\n\r\n[$300 x (6-4)] + [($350-$300) x (6-4)]\/2\r\n\r\n=$600 million<\/em>\r\n\r\nCosts\u00a0<\/strong>(red area):\r\n\r\n[$200 x (6-4)] + [($300-$200) x (6-4)]\/2<\/span>\r\n\r\n=$500 million<\/em>\r\n\r\nSurplus:<\/strong>\r\n\r\n$600 million - $500 million\r\n\r\n=$100 million<\/em>\r\n\r\nWe can see that since both firms benefited from the trade, that this is indeed a Pareto improvement from when they were each\u00a0emitting 6 million tons of Sulpher Dioxide. The total surplus gain is equal to $150 million ($50 million + $100 million).\r\n\r\n6. What is the\u00a0correct tax level to receive the same result as in question 2?<\/strong>\r\n\r\nThe tax level to give us the same result as before is equal to\u00a0the market price of permits. This price incentives the same action from Firms 1 and 2, but rather than making trades with each other, they are making decisions on whether or not to abate on the margin with consideration of the tax. They will abate as long as there marginal cost of abatement is lower than the tax rate.\r\n\r\n\"\"\r\n\r\n7. How much revenue will the government raise from the tax?<\/strong>\r\n\r\nThe government earns $300\/ton of Sulpher Dioxide emitted. Since total emissions are 12 million tons, the government will make $3.6 billion. ($300 x 12 million)\r\n\r\n8. What assumptions does the government have to make under cap and trade? What about under the carbon tax?<\/strong>\r\n\r\nUnder cap and trade the government has to make assumptions and decide on the\u00a0quantity\u00a0<\/span>to cap emissions, whereas under a carbon tax, the government has to make assumptions and decide on the\u00a0price<\/span> to tax emissions. If the government wants to reduce emissions by 50%, with a carbon tax it would have to know the marginal cost of abatement for each of the firms. With cap and trade, they just need to know how much firms are emitting. Of course, as mentioned in the following explanation of the EU policy, sometimes emissions will change as a result of changing demand, which can make it difficult to set the right quantity under cap and trade.\r\n\r\n9. If the government implemented a cap and trade system, distributing a total of 16 billion\u00a0permits, h<\/strong>ow much will emissions be reduced by as a result of this policy?<\/strong>\r\n\r\nIn this case, since we don't know the initial distribution of the permits, we can skip right to the result of the cap and trade. Knowing that firms will trade permits until the marginal cost of abatement is equal, we need to find a horizontal line where the total amount of pollution sums to 16 billion\u00a0tons of Carbon. As shown in the graph below, this occurs at a price of $0\/permit. This means that the government actually gave out\u00a0enough permits for the firms to continue to pollute at the levels they had before the cap and trade program, rendering the policy ineffective.\r\n\r\n\"\"\r\n\r\n10. If the government wanted to reduce emissions by 50% by purchasing permits, what is the minimum amount they would have to pay?\u00a0<\/strong>\r\n\r\nAfter trades, we know that Firm 1 will end up with 12 billion\u00a0permits, and Firm 2 will end up with 4 billion\u00a0permits. If the government wants to reduce emissions by 50% they will have to purchase 8 billion\u00a0permits to make the new pollution levels 8 billion. We can quickly identify that the equilibrium price for 8 billion\u00a0permits is $15, so one way the government could reduce pollution is offer $15 to the firms.\r\n\r\nNotice however that the government could get away with paying less.\u00a0As long as they pay the firms for the marginal cost of abating to 8 billion\u00a0tons of Carbon, the firms will be indifferent to abating or not.\r\n\r\n\"\"\r\n\r\nCalculating the total abatement costs:\r\n\r\nFirm 1<\/span> - Abating from 12 billion\u00a0to 6 billion\u00a0(Area A):\r\n\r\n$15 x (12 - 6) = $90\u00a0billion\r\n\r\nFirm 2<\/span>\u00a0- Abating from 4 billion\u00a0to 2 billion\u00a0(Area B):<\/span>\r\n\r\n$15 x (4 - 2) = $30\u00a0billion<\/span>\r\n\r\nTotal Costs to the Government\u00a0<\/span>\r\n\r\n$90 billion\u00a0+ $30 billion\u00a0= $120\u00a0billion\r\n\r\nAs shown,\u00a0trying to purchase permits out of the market can become quite expensive.","rendered":"

1. How much will the firms pollute before policy intervention?<\/strong><\/p>\n

Without policy intervention, there is no benefit for a firm to decrease its pollution. Even though reducing the\u00a0first few units costs relatively little, the firm maximizes profits by polluting its full\u00a0amount of pollution, where the costs of abatement are 0. This results in Firm 1 polluting 10 million tons of Sulpher Dioxide, and Firm 2 polluting 20 million tons, for a total of 30 million tons.<\/p>\n

\"\"<\/p>\n

2. If the government implemented a cap and trade system, distributing a total of 12 million permits, with 6 million to each firm, who would sell and who would buy permits?<\/strong><\/p>\n

Since we know that each firm is given 6 million permits, we need to compare\u00a0the marginal cost of abatement for each firm at that level. Drawing a line up from 6 million we see that for Firm 1, their marginal cost of abatement is $350, whereas Firm 2 faces a cost of $200. Since Firm 1 values pollution more that Firm 2, there are mutually beneficial exchanges where Firm 1 buys permits from Firm 2.<\/p>\n

\"\"<\/p>\n

3. How much would the seller be willing to accept, and how much will the buyer be willing to pay?<\/strong><\/p>\n

At 6 million permits, we can see that Firm 1 is willing to pay up to their marginal cost of abatement, or $350, and Firm 2 is willing to accept at least enough to cover their lost benefit from polluting, or $200. Notice that after Firm 1 buys\u00a0a permit from Firm 2, this relationship changes – Firm 1 will be willing to pay slightly less, and Firm 2 will need to be paid slightly more.<\/p>\n

4. What is the equilibrium price of permits, and the equilibrium quantity of Sulpher Dioxide production?\u00a0After the exchange of permits on the open market, how much does each firm emit?<\/strong><\/p>\n

To find the equilibrium price and quantity, we need to find a price level for permits such that the marginal cost of abatement for both firms is equal. By looking at our previous graph, and following what happens each time Firm 1 buys a permit from Firm 2, we see that Firm 1’s marginal cost falls and Firm 2’s marginal cost rises until they are equal.<\/p>\n

\"\"<\/p>\n

The transactions continue until Firm 1 has 8 million permits and Firm 2 has 4 million units. At this point the marginal costs of abatement are equal so no mutually beneficial transactions exist. Equilibrium quantity is 12 million, as regulated by the government, and the market price for permits is $300.<\/p>\n

 <\/p>\n

5. What are the total benefits and total costs to each firm from trading permits? Show that the trade was a Pareto Improvement<\/strong><\/p>\n

For Firm 1, buying more permits gives them the benefit of polluting more, which is equal to the reduction of the costs of abatement as shown in the green area. The cost is the amount they have to pay Firm 2, which is equal to the market price of the permit ($300) multiplied by the number they purchase as shown in the red area.<\/p>\n

Note that while Firm 1 is technically willing to pay more than $300, in the perfectly competitive market for permits we usually deal with, if Firm 2 tries to charge any more than $300, Firm 1 will purchase permits from another firm.<\/p>\n

\"\"<\/p>\n

Calculating costs and benefits:<\/span><\/p>\n

Benefits\u00a0<\/strong>(green area):<\/p>\n

[$300 x (8-6)] + [($350-$300) x (8-6)]\/2<\/p>\n

=$650 million<\/em><\/p>\n

Costs\u00a0<\/strong>(red area):<\/p>\n

[$300 x (8-6)]<\/span><\/p>\n

=$600 million<\/em><\/p>\n

Surplus:<\/strong><\/p>\n

$650 million – $600 million<\/p>\n

=$50 million<\/em><\/p>\n

For Firm 2, selling\u00a0permits means they will have to pollute less. This cost of abatement is equal to the red area below, and is the down side for selling permits. This cost is outweighed by the benefit of selling permits at the market price of $300. The revenue Firm 2 receives\u00a0is depicted in the green area.<\/p>\n

\"\"<\/p>\n

Calculating costs and benefits:<\/p>\n

Benefits\u00a0<\/strong>(green area):<\/p>\n

[$300 x (6-4)] + [($350-$300) x (6-4)]\/2<\/p>\n

=$600 million<\/em><\/p>\n

Costs\u00a0<\/strong>(red area):<\/p>\n

[$200 x (6-4)] + [($300-$200) x (6-4)]\/2<\/span><\/p>\n

=$500 million<\/em><\/p>\n

Surplus:<\/strong><\/p>\n

$600 million – $500 million<\/p>\n

=$100 million<\/em><\/p>\n

We can see that since both firms benefited from the trade, that this is indeed a Pareto improvement from when they were each\u00a0emitting 6 million tons of Sulpher Dioxide. The total surplus gain is equal to $150 million ($50 million + $100 million).<\/p>\n

6. What is the\u00a0correct tax level to receive the same result as in question 2?<\/strong><\/p>\n

The tax level to give us the same result as before is equal to\u00a0the market price of permits. This price incentives the same action from Firms 1 and 2, but rather than making trades with each other, they are making decisions on whether or not to abate on the margin with consideration of the tax. They will abate as long as there marginal cost of abatement is lower than the tax rate.<\/p>\n

\"\"<\/p>\n

7. How much revenue will the government raise from the tax?<\/strong><\/p>\n

The government earns $300\/ton of Sulpher Dioxide emitted. Since total emissions are 12 million tons, the government will make $3.6 billion. ($300 x 12 million)<\/p>\n

8. What assumptions does the government have to make under cap and trade? What about under the carbon tax?<\/strong><\/p>\n

Under cap and trade the government has to make assumptions and decide on the\u00a0quantity\u00a0<\/span>to cap emissions, whereas under a carbon tax, the government has to make assumptions and decide on the\u00a0price<\/span> to tax emissions. If the government wants to reduce emissions by 50%, with a carbon tax it would have to know the marginal cost of abatement for each of the firms. With cap and trade, they just need to know how much firms are emitting. Of course, as mentioned in the following explanation of the EU policy, sometimes emissions will change as a result of changing demand, which can make it difficult to set the right quantity under cap and trade.<\/p>\n

9. If the government implemented a cap and trade system, distributing a total of 16 billion\u00a0permits, h<\/strong>ow much will emissions be reduced by as a result of this policy?<\/strong><\/p>\n

In this case, since we don’t know the initial distribution of the permits, we can skip right to the result of the cap and trade. Knowing that firms will trade permits until the marginal cost of abatement is equal, we need to find a horizontal line where the total amount of pollution sums to 16 billion\u00a0tons of Carbon. As shown in the graph below, this occurs at a price of $0\/permit. This means that the government actually gave out\u00a0enough permits for the firms to continue to pollute at the levels they had before the cap and trade program, rendering the policy ineffective.<\/p>\n

\"\"<\/p>\n

10. If the government wanted to reduce emissions by 50% by purchasing permits, what is the minimum amount they would have to pay?\u00a0<\/strong><\/p>\n

After trades, we know that Firm 1 will end up with 12 billion\u00a0permits, and Firm 2 will end up with 4 billion\u00a0permits. If the government wants to reduce emissions by 50% they will have to purchase 8 billion\u00a0permits to make the new pollution levels 8 billion. We can quickly identify that the equilibrium price for 8 billion\u00a0permits is $15, so one way the government could reduce pollution is offer $15 to the firms.<\/p>\n

Notice however that the government could get away with paying less.\u00a0As long as they pay the firms for the marginal cost of abating to 8 billion\u00a0tons of Carbon, the firms will be indifferent to abating or not.<\/p>\n

\"\"<\/p>\n

Calculating the total abatement costs:<\/p>\n

Firm 1<\/span> – Abating from 12 billion\u00a0to 6 billion\u00a0(Area A):<\/p>\n

$15 x (12 – 6) = $90\u00a0billion<\/p>\n

Firm 2<\/span>\u00a0– Abating from 4 billion\u00a0to 2 billion\u00a0(Area B):<\/span><\/p>\n

$15 x (4 – 2) = $30\u00a0billion<\/span><\/p>\n

Total Costs to the Government\u00a0<\/span><\/p>\n

$90 billion\u00a0+ $30 billion\u00a0= $120\u00a0billion<\/p>\n

As shown,\u00a0trying to purchase permits out of the market can become quite expensive.<\/p>\n","protected":false},"author":58,"menu_order":6,"comment_status":"closed","ping_status":"closed","template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1849","chapter","type-chapter","status-publish","hentry"],"part":28,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/uvicecon103\/wp-json\/pressbooks\/v2\/chapters\/1849","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/uvicecon103\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/uvicecon103\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/uvicecon103\/wp-json\/wp\/v2\/users\/58"}],"replies":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/uvicecon103\/wp-json\/wp\/v2\/comments?post=1849"}],"version-history":[{"count":6,"href":"https:\/\/pressbooks.bccampus.ca\/uvicecon103\/wp-json\/pressbooks\/v2\/chapters\/1849\/revisions"}],"predecessor-version":[{"id":1878,"href":"https:\/\/pressbooks.bccampus.ca\/uvicecon103\/wp-json\/pressbooks\/v2\/chapters\/1849\/revisions\/1878"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/uvicecon103\/wp-json\/pressbooks\/v2\/parts\/28"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/uvicecon103\/wp-json\/pressbooks\/v2\/chapters\/1849\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/uvicecon103\/wp-json\/wp\/v2\/media?parent=1849"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/uvicecon103\/wp-json\/pressbooks\/v2\/chapter-type?post=1849"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/uvicecon103\/wp-json\/wp\/v2\/contributor?post=1849"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/uvicecon103\/wp-json\/wp\/v2\/license?post=1849"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}