2. Assume that two firms have the following marginal abatement costs (with abate
ID: 1138207 • Letter: 2
Question
2. Assume that two firms have the following marginal abatement costs (with abatement measured in tons of pollution):
MAC1 =5AC1
MAC2=3AC2
a. The government would like to reduce pollution by 24 tons. It requires each firm to reduce pollution by 12 tons. What is the total cost of pollution abatement across both firms?
b. 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 abatement of firm 1 plus firm 2 will be 24 tons.
c. How much abatement will each firm undertake after they have traded permits? What will the total cost of pollution abatement be across both firms?
d. What price will permits sell for?
e. Explain in words why abatement costs are lower under cap-and-trade than with firm-specific pollution limits.
Explanation / Answer
a) The cost of acheiving a given level of pollution control is minimized by setting the marginal cost of pollution control equal for two firms (i.e. MAC1=MAC2). Using the information, it implies that, MAC1=MAC2.
5A1=3A2 or A1=0.6A2 (dividing by 5 on both sides)
Lets name the above equation as equation 1.
This is the first piece of information we need to solve the problem. The second piece of information we have is, we want to reduce pollution from total by 24 tons. This requires emissions to be reduced by 24 tons. Then mathematically, we can write as,
A1+A2=24 Lets name this as equation 2.
0.6A2+A2=24 (substituting A1 from equation 1)
1.6A2=24
A2=24/1.6
A2=15 Now A1 = ?
A1+A2=24 (from equation 2)
A1+15=24
A1=24-15
A1=9
Therefore, we have A1=9 and A2=15.
Total cost (TC)= VC+FC (Variable cost + Fixed cost)
VC= Total marginal cost & FC=0 (assume FC=0)
so TC1=MAC1=5A1=5*9=45
TC2=MAC2=3A2=3*15=45
Therefore, TC=TC1+TC2
TC=45+45=90
Therefore, total cost = 90.
b) As the government has allocated each firm to pollute 12 tons and total pollution (as we assume) to be 24 tons, therefore from our calculation of A1 and A2 from the equation A1+A2=24, we have A1=9 and A2=15. Therefore, firm A will sell permits as its total abatement is 9 tons which is less than 12 tons, whereas firm A2 will buy the emissions as it has more than the permissible value of 12tons. Therefore, firm A1 will sell the permits and firm A2 will buy the permits. Total cost = 90 (As calculated in part A).
c) The permit system will yeild cost effective allocation of pollution control. Since this correspons to A1=9 and A2=15, we can easily figure out the number of permits each firm should hold. Firm 1 has the permit to produce 12 tons (as from government permit it is total current pollution-12tons). As we assume A1+A2=24, so we assume that each firm has a permit of producing 24 tons of pollution. This means firm 1 initially emitted 24 tons of pollution and now has to reduce by 9 tons (as A1=9) so they will have (24-9)=15 tons of emissions left. This means they must hold 15 permits in order to comply with the law. Likewise, firm 2 starts off with 24 units and has to reduce by 15 tons, so they are left with 9 permits. This adds up to the total of (9+15)=24 tons, which we have assumed as the total no. of emissions permitted by the govt. Note: our answer will change if the total no. of emissions provided by govt. changes.As we have assumed here, the total is 24, so our permits for firm A1=15 and for firm A2=9. Ans: A1=15 and A2=9.
d) A firm should be willing to pay its marginal cost of emissions control for a permit. This is because if they have 1 permit, they can avoid the marginal cost of controlling that 1 unit of pollution. thus at the final allocation of permits, firm A should be willing to pay,
P1=MAC1= 5A1=5*9=45
P1=45
for a permit.
likewise, firm 2 will be willing to pay,
P2=MAC2=3A2=3*15=45
P2=45
for a permit.
Therefore, P1=45 and P2=45
Notice that. the firms value the permits the same. If they did not, they would want to trade permits.
e) An implication of Coase theorem is that under certain conditions the market equillibrium under the cap and trade system will be cost effective and independent of the initial allocation of the tradeable rights. That is, the overall cost of achieving a given aggregate emission reduction will be minimized, and the final allocation of permits will be independant of the initial allocation. We call this as the independence property. This property is important because it means that the government can establish overall pollution reduction goal for cap-and-trade system by setting the cap and leaving it upto the legislature to construct a constituency in support of the program by allocating the allowances to various interests without affecting either the environmental performance of the system or iits aggregate social costs. We examine the conditions under which the independence propert is likely to hold, both in theory and pratice.
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