Question

Two firms can control emissions at the following marginal abatement costs. ?? 1= 200?1 and ??.2 = 100?1, where q1 and q2 are, respectively the amount of emissions abated for firm 1 and firm 2. Assume that with no control at all each firm would be abating 20 units of emissions or a total of 40 units for both firms. a) Calculate the marginal cost for abating 20 units of emissions for each firm. b) Calculate the cost-effective allocation of control responsibility if 40 units of abatement are required.

Answer 1

a)

Here there are 2 firms and their marginal abatement cots are MC1= 200q1 and MC2= 100q2, respectively where q1 and q2 are the amount of emissions abated for firm1 and firm2.

So MC for abating 20 units of emissions for firm1 = 200* 20 = $ 4000 and MC for abating 20 units of emissions for firm2 = 100*20= $ 2000.

b)

Now according to equimarginal principle, equating marginal abatement costs:

=> MC1 = MC2

=> 200q1=100q2

So, q2= 2q1............... (i)

So if the 40 unit abatement is required, => q1+q2 =40.

=> q1+2q1 = 40

=> 3q1= 40, => q1=40/3 = 13.33 units, => q2= 40- q1 = 40-13.33 = 26.67 units.

So the cost effective allocation is given by q1= 13.33 units & q2= 26.67 units.