Suppose the City of Berkeley decides to grant allocations of water from Strawberry Creek according to the appropriative doctrine. Next, due to significant administrative burdens, suppose only two individuals decide to apply for water allocations: Jesse [Arreguin] is the more senior user, and Carol [Christ] is the more junior user. Further, suppose the annual water flow in Strawberry Creek follows a uniform distribution from 0 to 100 acre-feet per year.


Jesse’s profits as a function of water use A are: πT (A) = 5000 ln(A), and Carol’s profits as a function of water use are: πN (A) = 12000 ln(A). Both Tom and Nicholas share the same cost function of water diversion capacity: C(A) = 5A2 + 1000. Finally, both Tom and Nicholas are risk neutral.


Required:

a. Draw graphs of both the PDF (g(·)) and CDF (G(·)) of Strawberry Creek’s annual flow.

b. How much water diversion capacity does Jesse build?

c. How much water diversion capacity does Carol build?