Question

Suppose two companies emit a particular pollutant. The marginal cost of reducing business pollution 1 is MC1 = 400q1 while the corresponding marginal cost for business 2 is MC2 = 100q2 (where 1 q and 2 q are the quantities of pollutant emissions that the first and second companies reduce, respectively) . Without government intervention, enterprise 1 generates 100 pollution units and enterprise 2 generates 80 pollution units.

Cost effective allocation of pollution reduction requires that

MC₁=MC₂

400q₁=100q₂

4q₁=q₂

Regulation requires that

q₁+q₂=50

Set q₂=4q₁

q₁+4q₁=50

5q₁=50

q₁=10 (Amount of pollution reduction by company 1)

q₂=4q₁=4*10=40  (Amount of pollution reduction by company 2)

Calculate the pollutant emission charge that must be imposed in order to achieve a cost-effective result. What will be the tax burden of each business in this case?

Answer 1

Emission charge imposed = eqm value of MAC at cost effective solution

So Eqm MAC = 400*q1

= 400*10 = 4,000

So emission charge imposed on each firm = $ 4,000

So that new MC:

MC1' = 400q1 - 4000

At private eqm, MC1' = 0

q1 = 10, cost effective value

MC2' = 100q2-4000

At eqm, MC2' = 0

100q2 - 4000= 0

q2 = 40

tax burden:

since Firm 1 abates 10 units, so it emits 90 units

Total burden = 90*4000 = 360,000

Firm 2 abates 40 units, & emits now 40 units

So total tax paid = 40*4000 = 160,000