Suppose you have three production facilities that are polluting a river. Each em
ID: 1212263 • Letter: S
Question
Suppose you have three production facilities that are polluting a river. Each emits 20 units of pollution. Their marginal cost functions for reducing emissions are, respectively, MC1 = $6, MC2 = $8, MC3 = $10. a) If the objective is to cut emissions to a total of 30 units cost-effectively via a command & control type policy approach, how much reduction should be assigned by the regulatory authority to each firm? Show your work. b) What would be the total variable cost of controlling these emissions? (You may want to start by defining what total variable cost is.) c) What would be the total variable cost that would result from forcing each facility to control one-half of it emissions? Is this different from the cost associated with the cost-effective allocation? Why or why not?
Explanation / Answer
a) If the objective is to cut emissions to a total of 30 units cost-effectively via a command & control type policy approach, how much reduction should be assigned by the regulatory authority to each firm?Show your work
For the method to be cost effective maximum reduction in emissions should be done by the firm with least marginal cost.
Since MC1 = $6 is the lowest MC, so firm 1 will cut emissions by 20 units of emissions.
Now remaining 10 units of emissions will be cut by the firm 2 having a MC of 8.
So, Firm 3 with MC 10, will cut emissions by 0, as it is most expensive for firm 3 to cut emissions.
Thus Firm 1 cuts emission = 20 units
Firm 2 Cuts emission = 10 units
Firm 3 cuts emissions = 0 units
. b) What would be the total variable cost of controlling these emissions? (You may want to start by defining what total variable cost is.)
So, Total variable cost is the total cost of reducing emissions by 30 units.
Hence Total variable cost is the sum of total cost incured by each firm to reduce the required emissions
Total variable cost = Cost incured by firm 1 + by firm 2 + by firm 3
= 20*6 + 10*8 + 0
= 120 + 80 + 0
= 200
c) What would be the total variable cost that would result from forcing each facility to control one-half of it emissions?
Total variable cost = cost incured by firm 1 to reduce emissions by half + cost incured by firm 2 to reduce emissions by half + cost incured by firm 3 to reduce emissions by half
Total variable cost = 6*10 + 8*10 + 10*10 = 60 + 80 + 100 = 240
Is this different from the cost associated with the cost-effective allocation? Why or why
Yes, it is different from the cost associated with the cost-effective allocation because here each firm is reducing the emission by same amount where as in case of cost effective methos, reductions by each firm were based on their marginal costs, and firm with east marginal cost reduces the emissions by most.
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