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. What is the TOTAL Social Cost?

b) Determine the emissions tax that would achieve the socially optimal level of emissions. What is the total PRIVATE costs to the Firm?

Now suppose the firm can adopt a new technology that changes is MAC to New MAC2 = 160 – 4E Assuming no change to standard or tax rate after the change in technology, 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)

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

MD=5E (Marginal benefits of reducing pollution)

MAC1= 200-5E (Marginal cost of reducing pollution)

a. The socially optimal level of emissions or E will be at a point where MAC equals MD.

So, MAC=MD= 5E = 200-5E

or, 10E =200 ; E= 20.

Total cost of emissions = Amount of emissions × marginal cost of emissions

= 200E -5E²,

or, at E =20 , total cost = 2000- 500=1500  

b. In order to prevent firms to raise emissions beyond socially optimal levels, govt. may impose tax per unit of emissions.

So, tax = total cost of emissions at social optimal level / E

or, T = 1500/20= 75 per unit emission.

If firms emit at E=20 , then tax paid on emissions and abatement costs are same.

Total private cost to firm = MC× Q

Here MC is Marginal cost of production, and Q is quantity.

c. With new technology, optimal emissions levels is at-

MAC2= MD = 5E =160 - 4E

or, E = 160/9

• If govt. emission standard is E =20, then

MAC of firm is = 160 -4×20 = 80

Therefore total cost (at E = 20)= 80 × 20= 1600

So increase in total cost (at E=20)

= 1600-1500 = 100

If govt tax rate is 75 per unit, then total cost to firm = T × E = 75 ×20 = 1500

Change in costs =1500-1500 =0.