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

Need help with part e and f

Answer 1

E = 20

Emission tax = 100

Change in cost = 2000 - 1600 = 400

Change in cost under fixed emission tax = 2000 - 1500 = 500

TAC = 1580.64

Tax bill = 1580.64.

Explanation:

Given that,

MD = 5E,

MAC1 = 200 -5E

a)     Socially optimal level of emission

              Marginal damage = Marginal cost

               5E = 200 - 5E

              10E = 200

               E = 20

b)     Emission tax that will attain socially optimal level of emission = (MAC at E =20)

    200 - 5E

    200 - 5*20

    200 - 100

   Emission tax = 100

c)     New MAC2 = 160 - 4E

And the government set emission standard (E= 20)

New MAC2 = 160 - 4*20

                    = 160 - 80

                    = 80

Cost = MAC*E

Cost = 80 * 20

         = 1600

Old MAC1 = 200 - 5E

               = 200 - 5*20

                = 200 - 100

               = 100

        Cost = 100 * 20

Cost = 2000

Change in cost = 2000 - 1600 = 400

d)     Emission tax set to = 100

160 - 4E = MAC2

4E = 160 - 100

E = 60 /4

E = 15

New cost when E=15, given (MAC = 100)

= 15 *100 = 1500

And old cost,

Old MAC1 = 100

200 -5E = 100

5E = 100

E = 20

Old cost when E = 20

                           = 20 * 100

                         = 2000

Change in cost under fixed emission tax = 2000 - 1500 = 500

e)     Under new technology

MAC2 = 160 - 4E

MD = 5E

MAC2 = MD

160 - 4E = 5E

9E = 160

E = 17.8

And resulting MAC2 = 160 -4E

MAC2 = 160 - 4*17.8

          = 160 - 71.2

MAC2 = 88.8

With standard equal to E = 17.8

TAC = 88.8*17.8

= 1580.64

f) Under tax rate t = 88.8, E = 17.8

Tax bill = tax rate* Emission

Tax bill = 88.8 * 17.8

Tax bill = 1580.64