Assume for simplicity that there are two identified point sources discharging chemical wastes into a local water body. Currently, each source releases 30 units of effluent, for a total of 60 units. To improve water quality, suppose that the government sets an aggregate abatement standard of 30 units. The two polluters’ abatement cost functions are:

Point source 1:.................TAC₁ = 10 + A₁²

........................................MAC₁ = 2A₁

Point source 2:.................TAC₂ = 20 + 2A₂²

........................................MAC₂ = 4A₂

a. Suppose the government allocates the abatement responsibility equally across the two point sources so that each must abate 15 units of effluent. Graphically illustrate this policy, and explain why this abatement allocation does not yield a cost-effective solution. Support your answer numerically.

b. What cost condition is required for the government’s abatement allocation to be cost-effective?

c. Suppose that instead of using an abatement standard, the government institutes an effluent fee of $40 per unit of pollution. How many units of pollution would each point source abate? Is the $40 fee a cost-effective strategy for meeting the 30-unit abatement standard? Explain.