Suppose you plan to reduce carbon emissions by a total of 384 units. Assume that we...

Suppose you plan to reduce carbon emissions by a total of 384 units. Assume that we have 3 polluting firms and q1, q2, and q3 are, respectively, the amount of pollution removed by each company that you choose to use so that the goal will be accomplished by any combination of methods such that q1 + q2 + q3 = 384. If the marginal costs of each removal method are, respectively, MC1 = $10 + $5q1, MC2 = $5 + $10q2, and MC3 = $5 + $20q3.

Question 1

Suppose an ambient standard is used, and each firm is asked to reduce its emissions by 128 units. Is this an economically efficient outcome? Why/Why not?

Question 2

How much should each firm reduce pollution by to achieve the pollution reduction cost-effectively?

Expert Solution

1. If each firm is asked to redue the pollution by the same amount, 128, then that is not an efficient outcome because each firm has different marginal cost curve. For example, the cost of reducing 2 units of pollution for firm 1 is 15+20=35, the same for firm 2 is 15+25=40 and form firm 3 is 25+45=70.

Clearly, these firms will incur different costs for reducing pollution by same amount and hence, this is not efficient because it is far more expensive for firm 3 to reduce the same amount as compared to firm 1. It seems ideal that costs would be lower when firm 1 reduces more pollution as compared to 2 and 3 and 2 reduces higher as compared to 3.

2. The most efficient outcome, as described in part 1 above, will happen where the marginal costs of all 3 firms will become equal. That is, where

MC1=MC2=MC3

The equations we have are

Q1+Q2+Q3=384
10+5Q1=5+10Q2
5+10Q2=5+20Q3
10+5Q1=5+20Q3

Solving these equations for Q1, Q2 and Q3, we get

Q1=219
Q2=110
Q3=55

As we can see, firm 1 has to reduce highest, firm 2 second and firm 3 lowest for cost to be most effective,

Rahul Sunny answered 1 month ago

Q1) Suppose you plan to reduce carbon emissions by a total of 384 units. Assume that...

Q1) Suppose you plan to reduce carbon emissions by a total of 384 units. Assume that we have 3 polluting firms and q1, q2, and q3 are, respectively, the amount of pollution removed by each company that you choose to use so that the goal will be accomplished by any combination of methods such that q1 + q2 + q3 = 384. If the marginal costs of each removal method are, respectively, MC1 = $10 + $5q1, MC2 = $5...

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