Be sure to answer all why questions.

Two firms can control emissions at the following marginal costs: MC1 = $200 q1 and MC2 = 100 q2, where qi are the amount of emissions reduced by firm i, i = 1, 2. Assume that with no control, each firm would be emitting 21 units of emission. Assume there is no background pollution.

a) Graphically, show the cost-effective allocation of control responsibility if a total reduction of 21 units of emissions is necessary. Be sure to correctly label the graph. Hint: q1 + q2 = 21.

b) Compute the cost-effective allocation of control responsibility if a total reduction of 21 units of emissions is necessary. Hint: This is the same as 1a) but solve mathematically, use algebra. Two unknowns and two equations, see hint in 1a for one equation. Second equation at the cost effectiveness solution, what two equations have to be equal?

Important: Why is the amount of controlled for firm 2 twice the amount controlled by firm 1?

c) Compute the cost-effective allocation of control responsibility if the ambient standard is 30 ppm, and the transfer coefficients which translate a unit of emissions into a ppm concentration at the receptor are a1 = 2.0 and a2 = 1.0. Hint: 2q1 + q2 = 33 ppm, the amount to be controlled. Why? Note, before control each firm was polluting 20 units of emission, which leads to 20*2 + 20*1 = 60 ppm. Why the 2 and 1? They relate units of emissions to ppm. Hint 2: be sure to change the MC curves to reflect ppm and not emissions.

Important: Why is the amount of control for firm 1 the same as the amount control by firm 2?