Question

The town of Pollutionville has two smelting factories, Factory A and B. Each factory produces air pollution. Factory A’s marginal abatement costs are given by MACA=20-0.5eA. Factory B’s marginal abatement costs are given by MACB=40-eB. The Pollutionville City Council wants to introduce a constant per unit emissions tax that will reduce total emissions from the two factories by 18.75% cost-effectively. The total tax receipts the Council would collect from such a tax would be $ _______________.

Answer 1

Answer :

In absence of any regulation

Set MACA = 0

20 - 0,5eA = 0

eA = 40

Set MACB = 0

40 - eB = 0

eB = 40

Total emission = eA+eB = 40+40 = 80

Abatement required = 80*18.75% = 15

Desire level of emission = eA+eB = 80 - 15 = 65

Or

eB = 65 - eA

In cost effeciency

MACA = MAC2

20-0.5eA = 40-eB

Set eB = 65 -eA

45 = 1.5eA

eA = 30

eB = 65 - eA = 65 - 30 = 35

MAC at thus level of emission

MACA = 20-0.5eA = 20-0.5eA = 20 - 05*30 = $5

MACB = 40 - eA = 40 - 35 = $5

So, emmission after regulation =eAR = eA + eB = 30 + 35 = 65

Total tax receipts = T*eAR = 5*65 = $325