Answer all questions on this sheet of paper and turn in by the end of class on February 23rd. You may also submit your assignment via Blackboard, but it must be uploaded before the end of class on the 23rd. Do NOT email your problem set to me or the TA. Make sure that your answers are clear, legible, and concise.
1. Suppose you are a regulator in charge of allocating water between residential and agricultural users (farmers) in the Verde Valley. You conduct a survey that finds that under the current split the average residential water consumer would be willing to pay up to $0.85 a gallon for the next gallon of water they consume while the increased market value of crop production from the gallon of water (after costs) to the most profitable farmer would be $0.15. 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.
2. You are tasked with evaluating a project for reducing air pollution (specifically, PM2.5-aerosols or fine particulate matter with diameters less than 2.5 micrometers) in the Phoenix Metropolitan Area. PM2.5 is particularly hazardous because it is too fine to be filtered out by the upper respiratory tract, meaning that particles can be deposited directly into the lungs and brain causing lung cancer, burning eyes, sore throats, and headaches. Recent research suggests that long-term exposure to PM2.5 also results in reduced cognitive function. A consultant for the Environmental Protection Agency estimates the following marginal benefit curve to urban residents and other affected communities for reductions in particulate matter relative to (2016) levels: MB = 300-6Q. Q is in units micrograms of PM2.5 removed per cubic meter of air. MB is in dollars per Q.
a) Draw the marginal benefit curve for cleaner air 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 atmosphere?). Finally, explain why this is a demand curve for pollution abatement.
b) Graphically, show how the total benefits of PM2.5 removal can be calculated from the marginal benefit function at a reduction of 15 micrograms per cubic meter of air (Q=15). 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.
3. This problem continues the analysis from question 2.
a) Another economic study finds that the marginal cost (MC) to polluting factories of reducing PM2.5 emissions is MC = 4Q. 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 factories of a reduction in PM2.5 emissions.
c) 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 factories and residents) maximized?
d) Graphically and numerically find the quantity of air pollution abatement such that marginal benefits of reduced emissions 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? How does it compare to the level that either residents or factories would prefer (assuming they only care about their own benefits and costs)?
e. Suppose the status quo is zero abatement. Who wins and loses from moving to the efficient amount of air pollution found in part d) and by how much? Is there potential to create a win-win out of this situation? How?