Q. 1.  Suppose you are a regulator in charge of allocating water between residential and agricultural users (farmers) in Southern California. You conduct a survey that finds that under the current split the average residential water consumer would be willing to pay up to $0.70 a gallon for the next gallon of water they consume while the increased market value of crop production from the gallon of water (after farmers pay their costs) to the most profitable farmer would be $0.20. Is the current allocation of water economically efficient (circle: yes or no)?  If not, in what direction should the water be reallocated?  In a sentence or two explain how we would expect these two quantities to compare to each other if net benefits were maximized.

Q2 You are tasked with evaluating a project for reducing nutrient (nitrogen and phosphorus) loading into the Gulf of Mexico (GOM). These nutrients make their way into the GOM by way of the Mississippi River and primarily come from the runoff of chemical fertilizer and animal manure from Midwestern farms. They can trigger hypoxia (look it up) in the marine ecosystem, leading to "dead zones", unattractive and toxic algae blooms, and fish kills. A consultant for the National Oceanic and Atmospheric Administration (NOAA) estimates the following "marginal benefit" curve to fishermen and other affected communities for reductions in nutrient loads from their baseline (2010) levels: MB = 10-.1Q. Q is in units of millions of tons of nitrogen removed (so 1=1,000,000 tons). MB is in millions of dollars per million tons (so 1 = $1,000,000).

a. Draw the marginal benefit curve for nutrient cleanup given the equation above. Explain why the downward slope of this curve is reasonable (hint: what does this imply for the extra damage done by each extra unit of pollution as it is released into the ecosystem?). Finally, explain why this is a "demand curve" for pollution abatement.

b. Graphically, show how the total benefits of nitrogen removal can be calculated from the marginal benefit function at a reduction of 10 million tons (Q=10). Calculate these total benefits numerically.

c. Using the logic developed in the previous question, come up with an equation that gives you total benefits. In other words, come up with an equation of the total area of the "rectangle" and "triangle" that make up total benefits for any level of Q. (Note that I showed how to do this in class for a specific example. You should also be able to check your work by seeing if your equation can replicate your answer for part b.) Graph this equation (by hand or feel free to cut and paste from Excel or a similar graphic program).

d. ) Intuitively, explain why total benefits increase at a decreasing rate as the level of pollution abatement increases.
Q3. This problem continues the analysis from question 2.

a. Another economic study finds that the marginal cost (MC) to farmers of nutrient runoff abatement is MC = .1Q. Graph this function & explain intuitively why it slopes upward in Q.

b. Following logic very similar to that in 2(c), find a formula for the total costs (TC) to farmers of a reduction in nutrient runoff.

c. (10 points) Graph the total benefits and total costs functions on the same graph (again, feel free to cut and paste from Excel or a similar program). At approximately what level of abatement are net benefits to society (including both coastal and farming interests) maximized?

d. Graphically and numerically find the quantity of runoff abatement such that marginal benefits of reduced runoff are exactly offset by the marginal cost of the reduction (your graph should use the MB and MC functions, not the total functions). Why is this the efficient level of pollution abatement?

e. (10 points) Suppose the status quo is zero abatement. Who wins and loses from moving to the efficient amount of runoff found in part d and by how much? Is there the potential to create a "win-win" out of this situation? How?

Q4  Consider the case of cleaning up chemical contamination at an industrial site. The marginal benefits of additional cleanup are decreasing as the amount of cleanup increases. However, the marginal costs of the cleanup are actually decreasing (rather than increasing) in the level of cleanup as well. The reason is that much of the cost of the cleanup involves first locating contamination and then digging to expose contaminated soil. Therefore, the most expensive unit to clean up is the very first. We can depict this graphically.

 First, if you were only looking at whether the first small increment of cleanup passed a benefit cost test, what would you conclude?

Second, does the "equimarginal principle" (MB=MC) lead to a situation where the net benefits of cleanup are maximized?