Joe and Matilda are two farmers, each cultivating some acreage of corn in Wisconsin. Their plots share a border and a reservoir straddles the boundary. Each draws water from the reservoir for their crops.
Joe's marginal net benefit for water is given by the curve MNBJoe: P = 24 - Q/3, and Matilda's marginal net benefit for water is given by the curve MNBMaddy: P = 16 - Q/4. Notice that prices are in $/acre-in and Q is in acre-in.
Annual precipitation is 40 in/yr, which results in 80 acre-in recharge to the reservoir.
A) Plot the demands for water on a figure as shown above. Mark all axes, intercepts, and curves.
Let Qwater = 80 acre-in, and have the curve MNBJoe intersect the Qwater axis at point J and the curve MNBMaddy hit the Qwater axis at point M. Determine the values of M and J (a.k.a. horizontal intercepts).
B) In two sentences, explain: What is marginal net benefit and why is it important to distinguish this concept from marginal benefits and marginal costs?
C) What quantity of water will Joe consume when water supply is not jointly decided on? Similarly, what quantity will Maddy consume in this situation? To simplify, assume that the cost is virtually zero.
(Hint: Essentially, what I am asking is whether or not the computed optimal quantities above are feasible given the limited water resource available to both parties)
Show calculations and explain in a sentence.
D) If the two farmers cooperate and decide water supply should be limited to the amount of annual precipitation, so that use equals yearly recharge:
i. What are the quantities Joe and Matilda consume at this price? Mark QJoe and QMaddy on the figure.
ii. Mark the equilibrium price on the graph above and calculate the value. Explain what this value stands for.