Question

Suppose that the MD = 5E and with its current technology, the firm’s MAC is given by MAC1 = 200 – 5E.

a) Determine the socially optimal level of emissions E.

b) Determine the emissions tax that would achieve the socially optimal level of emissions. Now suppose the firm can adopt a new technology that changes is MAC to New MAC2 = 160 – 4E Calculate change in costs for the firm from adopting the new technology when:

c) The government uses an emissions standard equal to your answer in (a) above

d) The government uses an emissions tax equal to your answer in (b) (Assume no change to standard or tax rate after the change in technology)

Now suppose the government adjusts the standard and/or the tax such that MD = New MAC. Calculate the change in total costs for the firm from adopting the new technology when:

e) The government adjusts the standard, and

f) The government adjusts the tax rate

Answer 1

A) Social optimal level of emission is where, marginal damage is equal to marginal abatement cost.

5E=200-5e

10e=200

E=200/10=20

So social optimal emission ia 20 units.

B) The emission tax Equal to marginal abatement cost or marginal damage at social optimal emission,will lead to social efficient emission.

So emission tax=5*20=100

C)In absence of regulation firm will emit,( with new technology)

0=160-4e

E=160/4=40 units.

So emission standard of 20 will result in 20 units of emission reeducation by firm.

So cost of reducing of emission,

TEC=160e-2*e^2

So total cost of reducing emission=160*40-2*40*40 -(160*20-2*20*20)=6400-3200-3200+800=800

Now with initial technology,

In absence of regulation,firm Will emit,

0=200-5e

E=200/5=40

So firm has to reduce 20 unit pollution

TC=200*e-2.5*e^2

So total cost of reducing 20 units=200*40-2.5*40*40. -(200*20-2.5*20*20)=8000-4000-4000+1000=1000

So due to new technology the abatement cost is reduced by 200.

D) initial technology,

tax =100$

The reduction cost =1000( solved in part c)

The tax of emitting 20 units=100*20=2000

Total cost=1000+2000=3000

With new technology,

Now firm will only emit,

100=160-4E

E=60/4=15 units

So emitting cost=15*100=1500

The reduction cost emission=160*40-2*40*40 -(160*15-2*15*15)=6400-3200-2400+450=1250

Total cost=1500+1250=2750

Reduction in cost=3000-2750=250