Question

1. Suppose a polluter initially faces marginal abatement curve MAC1 = 320-10E1 , but it has the possibility of investing in R&D and thereby lowering its marginal abatement cost curve to MAC2 = 160 – 5E2. Compute the cost savings to the polluter if it adopts the new technology (MAC2) after the introduction of an emissions tax of $100 per tonne. Compute the cost savings under a standard that is set at 20 tonnes. Explain why the tax provides a larger incentive to innovate than does the standard. (10 points)

Answer 1

Answer :

So, here “MAC1=320-10*E1”, => at the optimum without any tax the firm will choose “E1” such that “MAC1=0”, => E1= 320/10=32”. Now, after the introduction of tax of “100 per ton” the optimum “E1” is given by, “MAC1=100”, => E1 = (320-100)/10 = 22=E1”. So, here the total cost is given by.

=> Total Cost = total abatement cost + total tax

= 0.5*100*(32-22) + 100*22 = 500 + 2200.

=> Total Cost = 2,700.

For new technology “MAC2=160-5*E2”, => at the optimum without any tax the firm will choose “E2” such that “MAC2=0”, => E2= 160/5=32”. Now, after the introduction of tax of “100 per ton” the optimum “E2” is given by, “MAC2=100”, => E2 = (160-100)/5 = 12=E2”. So, here the total cost is given by.

=> Total Cost = total abatement cost + total tax

= 0.5*100*(32-12) + 100*12 = 1000 + 1200.

=> Total Cost = 2,200.

So, here the total cost savings is given by “2,700-2,200 = 500”.

Now, let’s assume that if a standard is set at “20 tones”, => at “E1=20”, => “MAC1=320-10*E1 = 120”, => her the total cost is given by, “0.5*(32-20)*120 = 720. Now, under the new technology at the emission level “E2=20” the corresponding “MAC” is given by “MAC2=60”, => here the total cost is given by “0.5*60*(32-20) = 360”. So, here the total cost savings is given by “720-360 = 360”.

So, here we can see that the cost savings is more under “tax” compare to under the “emission standard”. Now, under the 2^nd case the level of standard is fixed at “E=20” but at this level of standard “MAC2 > T=100”, => it is optimum to reduce the level of emission, but here we are not changing it, => optimum level of emission is not chosen, => cost savings is less under emission standard