Question

Problem 1

Assume that there are two factories, each emitting 20 units of pollutants into the environment, for a total of 40 units in their region. The government sets an aggregate abatement standard (A_ST) of 20 units. The polluters' cost functions are as follows, where the dollar values are in thousands:

            Polluter 1:       TAC₁ = 20 + 0.75(A₁)²,                      Polluter 2:       TAC₂ = 15 + 0.5(A₂)²,                                           MAC₁ = 1.5A₁,                                                           MAC₂ = A_2.

1. What information does the government need to support an assertion that the 20-unit abatement standard is efficient?

2. Suppose that the government allocates the abatement responsibility uniformly, requiring each polluter to abate 10 units of pollution. Quantitatively assess the cost implications.

3. Now, assume that the government institutes an emission fee of $16 thousand per unit of pollution. How many units of pollution would each polluter abate? Is the $16 thousand fee a cost-effective strategy for meeting the standard? Explain.

4. If instead the government used a pollution permit system, what permit price would achieve a cost-effective allocation of abatement? Compare the costs of this allocation to the costs of using the uniform standard described in part (b).

Answer 1

A) for cost efficient abatement standard level

MAC should be Equalized across all polluters, in a way that total abatement done is 20 units

B) now A1 = A2 = 10

Then MAC1= 1.5*10 = 15

MAC2 =10

As two MAC are not equal, so it's not cost efficient

Now, TAC1 = 20+.75*10^2

= 95

TAC2 = 15+.5*10^2

= 65

Total cost = 95+65

=160

c) t = 16

then for each firm, it will abate till, MAC is less than or equal to 16

If MAC rises above t= 16, then firm will prefer to pay tax = 16,

thus at eqm, MAC = 16

so for polluter 1

1.5A1 = 16

A1 = 16/1.5 = 10.667

A2 = t = 16

.

no, it's not cost efficient strategy, though with this tax , MAC is Equalized across two polluters , & equals to 16

But, the total abatement done = 10.667+16 = 26.6667 , exceeds the govt standard of 20 units,

Hence it's not cost effective

.

D) in permit system

At eqm, MAC 1 = MAC2 , & A1+A2 = 20

1.5A1 = A2

1.5A1 = 20-A1

2.5A1 = 20

A1* = 8

A2* = 12

then eqm MAC = 1.5*8

= $ 12

eqm permit price = $12

Now TAC1 = 20+.75*8^2 = 68

TAC2 = 15+.5*12^2

= 87

Total cost = 68+87

= 155

thus permit system leads to lowest Total abatement cost