Question

Two firms, Firm A and Firm B, have the following marginal abatement cost functions: MACA = 180-3EA and MACB = 100 - 2EB. A new emission control program requires them to reduce the total or combined emissions to 80 units. To achieve this, the regulator provides Firm A with 45 transferable discharge permits and Firm B with 35 initially. Suppose that one permit allows one unit of emissions, and that the market for permits is competitive. In equilibrium,

(a)how many permits are traded in equilibrium?   

(b) at what price are permits traded?   

(c) what is the net social gain from trading permits?

Answer 1

Solution:

a):- MAC_A=180-3E_A

E_A=60-MAC_A/3

MAC_B=100-2E_B

E_B=50-MAC_B/2

Aggregate MAC:

E=110-5MAC/6

MAC=132-1.2E

Desired E=80

MAC=132-1.2*80=36

E_A=60-36/3=60-12=48

E_B=50-36/2=50-18=32

So ,In Equilibrium 3 permit are traded . Firm A bought three permit from firm B.

b):- The Equilibrium price of permit is equal to MAC at Equilibrium ,so permit price =36.

c):- TAC_A = 180E_A - 1.5*(E_A)²

Gain to firm a by trading=180*48 - 1.5×48×48 -180×45+1.5×45×45 -36×3 = 13.5

TAC_B=100E_B-(E_B)²

Gain of firm B by trading=100×32-32×32-100×35+35×35+36×3 = 9

Net social gain= 13.5+9 = 22.5

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