Consider a municipality A and an irrigation district B with the following marginal net benefit functions that describe net benefits from water consumption q.
MNBA = 72-12qA
MNBB = 30-qB
Recall marginal net benefits (MNB) shows the difference between marginal benefits and marginal costs. The quantity that maximizes net benefits is found where MNB=0.
a.) Assume the municipality A and the irrigation district B have two different sources of water. Assume it has been a very snowy winter and there is plenty of water for everyone. How much water should be processed and consumed by each?
b.) How much total surplus (net benefits) is enjoyed by each?
c.) Now assume it has been a less snowy winter and water supplies are limited. Each lake contains only 9 units of water for the season. What is the efficient water consumption for each?
d.) How much total surplus is enjoyed by each?
e.) Now assume the municipality and the irrigation district have to share water from a single lake. In the current year, only 9 total units of water are available to be shared between the municipality and the irrigation district. How should these 9 units be allocated to maximize net benefits? Show this result graphically.