Suppose you have three production facilities that are polluting a river. Each em

Question

Suppose you have three production facilities that are polluting a river. Each emits 10
units of pollution. Their marginal cost functions for reducing emissions are,
respectively, MC1 = $3, MC2 = $4, MC3 = $5.
a. If the objective is to cut emissions in half (to 15) cost-effectively, how
much reduction should be assigned to each firm?
b. What would be the total variable cost of controlling these emissions?
c. What would be the total variable cost that would result from forcing each
facility to control one-half of its emissions? Is this different from the cost
associated with the cost-effective allocation? Why or why not?

Explanation / Answer

a) facility 1 reduce emission by 10, facility 2 reduce by 5
b) total cost : 10*3 + 5*4 = 50 variable cost = 50/15 = 10/3
c) total cost : 5*(3+4+5) = 60 variable cost = 60/15 = 4. This is different from the cost efficient allocation because you are allocating 5 more to facility 3 (which is inefficient with MC3 = 5) while the efficient way would be allocating the 5 units to facility 1 (which is efficient with MC1 = 3)

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