Question

Suppose that there are three firms in a region that are producing a common emission. The marginal abatement cost (MAC) for each firm is given by: MAC1 = 240 – 2E1 MAC2 = 192 – 1.6E2 MAC3 = 320 – 2.67E3 The marginal damage function for the region is given as MD = (4/3)ET {where ET = E1 + E2 +E3}

a) Find the aggregate MAC for the region.

b) Find the socially optimal level of Emissions for the region

c) Suppose that the government imposes a Uniform Standard on the three firms that achieves the socially optimal level. What will be each firm’s MAC and TAC?

Answer 1

A) Aggregate MAC is Horizontal Summation of individual MAC

So E1 = 120-MAC/2

E2 = 120 -MAC/1.6

E3= 120-MAC/2.67

Aggregate MAC : E = E1+E2+E3

E = 360- 1.5*MAC

MAC = (360/1.5) - E/1.5

MAC = 240-2E/3

b) at social efficiency

Aggregate MAC = MD

240- 2E/3 = 4/3E

240= 2E*

E* = 120

c) uniform standard

E1= E2= E3 = E/3 = 40

TAC is integral of MAC

TAC1 = 240*E- E1​​​​​2

TAC2 = 192*E- .8E22

TAC3= 320*E- 1.33E3​2

Firm	MAC	TAC
1	240-2*40 = 160	8000
2	192-1.6*40 = 128	6400
3	320-2.67*40= 213.2	10,672