Question

2 Pollution Control There are three coal plants, currently emitting 120 units of coal emissions. The government determines they wish to cut emission in half to 60 units total across the three plants. Each plant has their own total control C costs for emissions: TC and marginal costs of: gi MC where q is the amount of emissions reduced per plant. 1. The gove nment requires each plants to reduce emissions by 20 units to achieve the new standard. What is the total cost of such a policy across all three plants? 2. Suppose in emissions control for ench plant and then set a per plant standard at these levels. How many units does each plant emit under this scheme? What is the total cost of such a policy across all three plants? See below for some help on setting this up. that the govern ment first uses the 2nd Equimarginal Principle to determine the efficient First, create three equations with three unknow ns, by setting MCI MC2 MC3 and solving for q3: using the poiey goal equation: ql MC2 and solving for q1; setting q2 q360 units. 3. What if the government instead allocated 2) po ntion permits per plant, and allowed plants to buy and sell permits from each other Eacli permit alowing them to emit one unit of coal emissions. Will plants be willing to buy and or se. permits to eaeh other If so, who buys and who sells? Pollution Control 2 There are three coal plants, currently emitting 120 units of coal emissions. The government determines they wish to cut emission in half to 60 units total across the three plants. Each plant has their own total control costs for emissions: TC,TC : TC 6 TC and marginal costs of: MC MCa 2 MCs 3 4 where q is the amount of emissions reduced per plant. 1. The government requires each plants to reduce emissions by 20 units to achieve the new standard. What is the total cost of such a policy across all three plants? 2. Suppose instead that the government first uses the 2nd Equimarginal Principle to determine the efficient emissions control for each plant and then set a per plant standard at these levels. How many units does each plant emit under this scheme? What is the total cost of such a policy across all three plants? See below for some help on setting this up. First, create three equations with three unknowns, by setting MC MC2 and solving for ql; setting MC2 MC3 and solving for q3; using the poliey goal equation: ql q23-60 units. 3. What if the government instead allocated 20 pollution permits per plant, and allowed plants to buy and sell permits from cach other. Each permit allowing them to emit one unit of coal emissions. Will plants be willing to buy and/or sell permits to each other? If so, who buys and who sells?

Answer 1

Answer;

1) q1 = q2 = q3= 20

Now total cost = 202/4 + 202/6 + 202/8

= 216.67

2) now at eqm, MC1 = MC2 = MC3

q1/2 = q2/3 ,

q1 = (2/3)*q2

Now MC2 = MC3

q2/3 = q3/4

q3= (4/3)*q2

Now as q1+q2+q3 = 60

So (2/3)*q2 + q2 + (4/3)*q2 = 60

So 3q2 = 60

q2* = 20

q1* = 40/3

q3* = 80/3

total cost = 200

3) now each is allocated 20 permits, now at eqm allocation of permit ,

MC1 = MC2 = MC3

Eqm permit price = 20/3

Now at q1= q2 = q3= 20

When each abates 20 units , & each emits 20 units,

Then MC1 = 20/2 = 10

MC3 = 20/4 = 5

So at eqm permit price = 6.67,

then firm 1 will buy permits from firm 2.