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, and 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?