Demand for water from the Sacramento River Basin (SRB) is given by inverse demand curve P = 5000 – 0.001Q where Q is in acre-feet of water. (An acre-foot of water is enough water to cover one acre of land, one foot deep in water ~ 300,000 gallons)

The marginal cost of pumping from the SRB is $200/acre-foot up until the maximum amount that can be pumped.

(a) Suppose “El Nino” doesn’t save Northern California from its current drought predicament and only 2 million acre-feet can be pumped from SRB this year. The state needs to decide how to allocate the water.

Draw the relevant diagrams illustrating the two options. (1) allocating the 2 million acre-feet by auction (selling it to the highest bidders), and (2) giving all consumers who would normally be served in a year without water constraints an equal share of the scarce resource. Label the consumer surplus, government surplus and deadweight loss of each option.

(b) Do the two options generate equal or dissimilar deadweight losses? Briefly explain.

(c) Describe any other considerations that might be relevant to policy makers when deciding between option 1 and option 2.

(d) Now suppose that El Nino saves the day and we can pump as much water from SRB as we would like. But, pumping water from the SRB impacts recreation opportunities, farming potential and ecosystems downstream.

In particular, the marginal damage from pumping water increases with the amount pumped. In particular, if Q acre-feet are pumped from the river, pumping one more acre-foot from the river causes damages of Q/5000. As an illustration, if 1 million gallons are pumped from the river, an additional acre-foot pumped causes $200 in damages downstream.

How much should be pumped from the river to maximize welfare? What is the deadweight loss if communities pump water until the marginal benefit is equal to the marginal private cost of pumping?