Question

Suppose that two polluting firms have marginal abatement costs given by the following equations:

MAC1 = 50 – 5e1 and MAC2 = 40 – 4e2

where e1 and e2 are the emission levels of each firm respectively. The regulator’s goal is to reduce total pollution from the two firms to 8 units.

a) Suppose that the regulator requires that each firm reduce their emissions to 4 units (i.e. they use a uniform standard). Compute each firm’s total abatement costs under this uniform standard and show graphically.

b) Find the cost effective allocation of the 8 units of emissions to the two firms. Compute each firm’s total abatement costs under the cost effective allocation and show graphically.

c) Now, compare the results between parts a) and b). Which allocation of emissions (uniform or cost effective) does each firm prefer and why? Which allocation does society prefer and why?

Answer 1

Pls see table below for calculations

	8-e1	50-5e1	40-4e2
e1	e2	MC1	MC2	TC1	TC2	TC - Combined
0	8	50	8	50	216	266
1	7	45	12	95	208	303
2	6	40	16	135	196	331
3	5	35	20	170	180	350
4	4	30	24	200	160	360
5	3	25	28	225	136	361
6	2	20	32	245	108	353
7	1	15	36	260	76	336
8	0	10	40	270	40	310

It costs 200 for firm 1 and 160 for firm 2, for a combined cost of 360, if each has to reduce pollution by 4 units each.

b) The most cost effective allocation is 0 for firm 1 and 8 for firm 2, for a cost of 50 and 216, giving a combined cost of 266. It is the point in the left most end of the graph above.

c) firm 2 will not prefer the solution in part b unless there's an arrangement between firm 1 and 2 to share teh total costs of abatement. Society would prefer solution b irrespective of cost sharing arrangement between the firms.