Question

Question 3

Assume that there are two firms, each emitting 40 units of pollutants into the environment, for a total of 80 units in their region. The government sets an aggregate abatement standard (AST) of 30 units (total in the region). The polluters' cost functions are as follows, where the dollar values are in thousands:

Polluter 1: TAC1 = 15 + 1.5(A1)2, MAC1 = 3A1.

Polluter 2: TAC2 = 16 + 0.55(A2)2, MAC2 = 1.1A2,

a) What information does the government need to support an assertion that the 30-unit abatement standard is allocatively efficient?

b) Suppose that the government allocates the abatement responsibility uniformly, requiring each polluter to abate 15 units of pollution. Quantitatively assess the cost implications. How much would the policy cost to each firm, for the region overall?

c) Now, assume that the government institutes an emission fee of $10 thousand per unit of pollution. How many units of pollution would each polluter abate? Is the $10 thousand fee a cost-effective strategy for meeting the standard? Explain.

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

Answer 1

Answer:

given

Assuming that there are two firms, each emitting 40 units of pollutants. So total emitting of pollutant is 80 units.

the government sets an aggregate abatement standard (AST) of 30 units

The polluters' cost functions are as follows, where the dollar values are in thousands:

Polluter 1: TAC1 = 15 + 1.5(A1)2, MAC1 = 3A1.

Polluter 2: TAC2 = 16 + 0.55(A2)2, MAC2 = 1.1A2,

(a)information the government need to support an assertion that the 30-unit abatement standard is allocatively efficient is:

MAC1= MAC2

or 3A1= 1.1A2

A1 = 0.367A2

This is the first part of the solution.

now in second part,

A1+A2= (80-40)= 40

or, 0.367A2 + A2 = 40

1.367A2 = 40

A2 = 29.26

  A1 = 0.367A2

= 0.367*29.26

A1 = 10.73842

Put this values in TAC1 and TAC2,

TAC1 = 15 + 1.5(A1)2

= 15 + 1.5(10.73842)^2

= 15 + 172.97

TAC1 = 187.97

TAC2 = 16 + 0.55(A2)2

= 16 + 0.55(29.26)^2

= 16 + 470.88

TAC2 = 486.88

so, it is allocatively efficient.

(b)Suppose that the government allocates the abatement responsibility uniformly, requiring each pollutant to abate 15 units of pollution, policy cost to each firm, for the region overall is:

so total pollution emitting amount is 30 units which is equal to the abatement standards 30 units.

then,

A1+ A2= 30-30= 0

Then A1=A2=0

So, MAC1= MAC2=0

and, TAC1= 15, TAC2= 16

(d) Now, assuming that the government institutes an emission fee of $10 thousand per unit of pollution, no units of pollution would each polluter abate:

so it is known that,

P=MAC

Then, P1= MAC1

or, 10000 = 2.73A1

or, A1= 3663.003

and P2= MAC2

or, A2= 2.73*3663.003

A2 = 9999.99

These are the required abatement units:

if A1= 3663.003

Then, TAC1 = 15 + 1.5(3663.003)2

= 15 + 20126386.46

TAC1 = 20126401.46

and, TAC2 = 16 + 0.55(9999.99)2

= 16 + 54999890.000055

TAC2 = 54999906

so abatement cost is higher than before. So it is not efficient.

(d) Compare the costs of this allocation to the costs of using the uniform standard described in part (b):

on comparing ,we get, In part B, this situation is the most efficient.