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In: Economics

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 + $10q2, and MC3 = $5 + $20q3.

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

Expert Solution

Answer )

We are given,

q1 + q2 + q3 = 384 .....eq(1)

MC1 = 10 + 5q1 .....eq(2)

MC2 = 5 +10q2 .....eq(3)

MC3 = 5 + 20q3 ......eq(4)

From eq(1) , we can write q1 as

q1 = 384 - q2 - q3 ......eq(5)

Substituting eq(5 )in eq(2) and equating it to eq(3) gives,

10 + 5(384 - q2 - q3 ) = 5 + 10q2

10 + 1920 - 5q2 - 5q3 = 5 + 10q2

1925 - 15q2 = 5q3

q3 = 385 - 3q2 ..... eq(6)

Substituting eq(6) in eq(4) and equating it to equation (3)

5 + 20(385 - 3q2) = 5 +10q2

5 + 7700 - 60q2 = 5 + 10q2

=> 70q2 = 7700

=> q2 = 7700/70

=> q2 = 110

Using eq(6) to find q3

q3 = 385 - 3q2 = 385 - 3(110)

q3 = 55

Using eq(5) t ofind q1 gives,

q1 = 384 - q2 - q3 = 384 - 110 - 55

q1 = 219

From the above calculations , we can conclude that Firm-1 should abate 219 units of pollution, Firm-2 should abate 110 units of pollution, and Firm-3 should abate 55 units of pollution in order to reduce the overall pollution in a cost-effective manner.

Rahul Sunny answered 2 years ago

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 +...

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