Final answer:
To calculate the amount each region would abate under a carbon tax, we compare the marginal abatement costs (MAC) with the tax rate. Region 1 would abate 6 Mt, while Region 2 and Region 3 would not abate any emissions.
Step-by-step explanation:
The amount that each region would abate under a carbon tax of $30/tonne can be calculated by comparing the marginal abatement costs (MAC) with the carbon tax rate. In this case, Region 1 has a MAC of $5/tonne, Region 2 has a MAC of $10/tonne, and Region 3 has a MAC of $15/tonne. Since the carbon tax rate is $30/tonne, only Region 1 has a MAC that is lower than the tax rate.
To determine how much Region 1 would abate, we need to find the quantity at which the MAC is equal to the tax rate. So, we divide the tax rate by the MAC: $30/tonne ÷ $5/tonne = 6 tonnes. Therefore, Region 1 would abate 6 Mt (million tonnes) under the carbon tax.
Regions 2 and 3 have MAC higher than the tax rate, so they would not choose to abate any emissions under the carbon tax. Therefore, Region 2 and Region 3 would not abate any emissions under the $30/tonne carbon tax.