Question

The Reno City Council has passed a law requiring litter to be reduced by 108 pounds per day. The city can reduce litter near UNR campus (C), near downtown Reno (D), or both. The marginal abatement cost for campus is MAC_C=0.05A_C and the total abatement cost equation is TAC_C=0.025A_C^2. The marginal abatement cost for downtown is MAC_D=0.13A_D and the total abatement cost equation is TAC_D=0.065A_D^2 In each area, how much litter should be abated to meet the city's requirements at the least cost?

Answer 1

The Reno City Council has passed a law requiring litter to be reduced by 108 pounds per day

So, AC+AD=108 (equation 1)

The marginal abatement cost for campus is MAC_C=0.05A_C

The marginal abatement cost for downtown is MAC_D=0.13A_D

Applying the equimarginal principle and equating marginal abatement costs:

MAC_C=MAC_D

0.05AC= 0.13AD

or AC= 0.13/0.05 AD

Equating AC in equation 1

0.13/0.05AD +AD =108

On solving, we get AD=30

Computing the value of AC from equation 1, we get

AC= 78

Near UNR campus (C), 78 pounds per day litter should be abated and near downtown Reno (D), 30 pounds per day litter should be abated to meet the city's requirements at the least cost.