Demand for water

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) Initially, we have several wet years such that as much water can be taken from the Sacramento Rive r as
desired. If the government want the welfare-maximizing amount of water to be drawn from the river, what price
should it set and how much will be pumped?
(b) Suppose in a couple of years we’re back in a drought and only 2 million acre-feet can be pumped from SRB
in a particular year. The state needs to decide how to allocate the water.
Draw the relevant diagrams the following 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.
(c) Do the two options generate equal or dissimilar deadweight losses? Briefly explain.
(d) Suppose wet weather returns again to northern California and the quantity that can be pumped starts to
increase from 2 million acre-feet to the answer from part (a). Will the deadweight losses from option (1) and
option (2) in part (b) decrease at the same rate? Or will deadweight loss from one of the two options change
more quickly. Explain.
(e) Describe any other considerations that might be relevant to policy makers when deciding between option 1
and option 2.