Question

Assume there are two polluting firms in two different cities. In
the business-as-usual outcome, Firm #1 would emit 20 units of
pollution (e_{1}=20) and Firm #2 would emit 20 units of
pollution (e_{2}=20).

Additionally, assume the marginal abatement costs for Firm #1
and Firm #2 are given below: MAC_{1} (x_{1}) =
0.5x_{1} & MAC_{2}
(x_{2}) = 2x_{2}

This pollutant is known to cause adverse health effects when in
high concentrations. Since the firms are in different cities,
assume the marginal social benefit of abatement differs across Firm
#1 and Firm #2. In particular: MSB_{1} (x_{1}) = 8
& MSB_{2} (x_{2}) = 18

a) (1 point) Suppose a cap-and-trade program is established between the two cities, and a total of 15 pollution permits are created. If each firm is given 7.5 of the tradable pollution permits, will the socially optimal outcome be achieved?

b) (1 point) Calculate the total costs, total benefits and net benefits of abatement in each city, under the cap and trade system. Ignore emission fees.

c) (1 point) What if you he had no policy at all? Would the no-action scenario achieve lower or higher Net Benefits than the cap and trade policy?

Answer #1

Given: BAU outcome: e1 = 20 units of pollution, e2 = 20 units of pollution

MAC1 = 0.5X1 , MAC2 = 2X2

MSB1 = 8, MSB2 = 18

a) Socially Optimum level of pollution for Firm1 : MAC1 = MSB1
=> 0.5X1 = 8 => X1 = 8/0.5 = **16 units of
pollution**

Socially Optimum level of pollution for Firm2 : MAC2 = MSB2
=> 2X2 = 18 => X2 = 18/2 = **9 units of
pollution**

Therefore, Socially optimum level of pollution = 16 + 9 =
**25 units of pollution.** Hence, Cap-and-trade
program will not achieve socially optimum outcome.

b) In case of Cap- and -Trade Policy

Total Cost = integration of MAC, Total Benefit = integration of MSB

for firm 1: Total Cost = = X12/4 = (7.5)2/4 = 56.25/4 = 14.06, Total Benefit = = 8X1 = 8*7.5 = 60

for firm 1: Total Cost = = X22 = (7.5)2= 56.25 , Total Benefit = = 18X2= 18*7.5 = 135

Net Benefit = total benefit - total cost

Firm1: 60- 14.06 = 45.94

Firm 2 : 135- 56.25 = 78.75

Net benefit = 45.94 + 78.75 = 124.69

c) In case of No Policy

Total Cost = integration of MAC, Total Benefit = integration of MSB

for firm 1: Total Cost = = X12/4 = (16)2/4 = 256/4 = 64, Total Benefit = = 8X1 = 8*16 = 128

for firm 1: Total Cost = = X22 = (9)2= 81 , Total Benefit = = 18X2= 18*9 = 162

Net Benefit = total benefit - total cost

Firm1: 128-64 = 64

Firm 2 : 162-81 = 81

Net Benfit = 64+ 81 = 145

Therefore, no-action scenario achieves higher Net Benefits than the cap and trade policy.

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