Question

Refer to the figure below to answer the following questions. 200 МАС, 160 МАС Tax 100 per tonne 30 10 15 40 Emissions (tonnes per year) 20

Compute the cost savings to this polluter if it adopts the new technology after the introduction of an emission tax of $100 per tonne. (Note: you are required to compute the actual $ value of the cost savings, not just compare areas in the diagram)

Compute the cost savings if this polluter adopts the new technology after the introduction of a standard set at 20 tonnes per year.

Which provides the greatest incentive to innovate, the emission tax or the standard?

Answer 1

Solution:

For the initial marginal abatement cost curve, MAC1, the tax line of 100 per tonne intersects it at 20 tonnes of emissions (which is the standard set), implying the optimal emission level to be 20 tonnes, same emission level is reached by both policies for initial MAC is same.

Cost by taxation: Since, to the right of 20 tonnes, cost of abating is lower than the cost of polluting (that is tax rate) so firm will prefer to abate that pollution. So, pollution emitted = 20 tonnes, and pollution abated = (40 - 20=) 20 tonnes.

Total cost = cost of polluting + cost of abating remaining

Total cost = (e + d +c) + (a + b)

Total cost = 20*100 + (1/2)*(40-20)*100 = $3000

By standard set policy, total cost = cost of abating those 20 units of emissions.

Total cost = (1/2)*(40-20)*100 = $1000

Now, with new technology, when MAC shifted down from MAC1 to MAC2, following the above reasoning:

With taxation, amount of pollution emitted = 15 units (intersection of tax line and MAC2); and pollution abated = (40-15=) 25 units

So, total cost = 15*100 + (1/2)*(25)*100 = $2750

So, cost saving in taxation = 3000 - 2750 = $250 (area a + c)

Under standard set policy of 20 tonnes, since abatement = 20 units, total cost = (1/2)*20*80 = $800 (look closely, it seems like 80 at intersection of MAC2 and 20 tonnes of pollution level)

So, cost saving under standard set policy = 1000 - 800 = $200 (area a)

Since cost saving is higher in case of emission tax, it provides a greater incentive to innovate (additional cost saved under emission tax = 50 that is area c).