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) Determine the socially optimal level of emissions E.

MD = 5E

MAC1 = 200 – 5E.

So, 200 - 5E = 5E

E = 20

b) Determine the emissions tax that would achieve the socially optimal level of emissions.

As given

MAC1 = 200 – 5E.

Putting value of E

Tax t = MAC1 = 200 - 5 * 20 = 200 - 100 = 100

c) Now suppose the firm can adopt a new technology that changes is MAC to New MAC2 = 160 – 4E

The government will use emission standard equal to answer in a above.

If Standard set at E = 20, Old Technology will have TAC = $1000

New Technology has MAC2 = 160 - 4 *20 = 80

TAC from new technology = $800

Saving = 1000 - 800 = $200

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)

With tax = $ 100

Old MAC1 = 200 - 5E = 100 tax E = 20

New MAC2 = 160 - 4E = 100 tax E = 15

TAC , Old case = 100 * 20 * 1/2= 1000

TAX Bill = 100 *20 = 2000

Total = 1000 + 2000 = $3000

TAC, New Case = 25*100*1/2 = 1250

TAX Bill = 100 * 15 = 1500

Total = 1250 + 1500 = $2750

Savings = $3000 - $ 2750 = $250