AEM 4500 / ECON 3860 / AEM 5500: Resource Economics
Spring 2024
Problem Set #11: Water and Groundwater Policy
Part I. Agricultural Groundwater Use
As the CEO of Agricultural Extraction Management (AEM), you are extracting groundwater for agricultural use. The aquifer from which you are extracting does not receive any recharge, so the groundwater is a nonrenewable resource. AEM’s profits each year are given by:
R(E) −C(E, S),
where E is the quantity of groundwater extracted in units of gallons, S is the amount of groundwater remaining in the aquifer in units of gallons, R(E) is the revenue (in dollars) that AEM earns from crops you grow and sell using E gallons of water, and C(E, S) is the cost (in dollars) of extracting E gallons of groundwater when there are S gallons of groundwater remaining in the aquifer.
Let’s suppose the crop revenue is R(E) = r0Er1 , and the extraction costs are C(E, S) = c0 . Ec1 Sc2 .
AEM’s aquifer currently has a groundwater stock S0 of 45,000 gallons of groundwater in the year t = 0 . The discount rate is r = 0.04 , and interest is compounded discretely.
AEM would like to choose its groundwater extraction Et for each year from t = 0 until t = 15 so as to maximize the present discounted value of AEM’s entire stream of profits from groundwater extraction from t = 0 until t = 15 .
1) [10 points] Dynamic Optimization Problem
a. Explain why groundwater can be viewed as a nonrenewable resource.
b. What is the objective of AEM in words?
c. What is the objective function for AEM in words?
d. Write out the objective function for AEM as a mathematical function.
e. What are the choice variables for AEM in words?
f. Write out the choice variables for AEM as mathematical variables.
g. What are the constraints faced by AEM in words?
h. Write out the constraints faced by AEM as equations.
i. What is AEM’s dynamic optimization problem in words?
j. Write out AEM’s dynamic optimization problem as a mathematical dynamic optimization problem.
2) [10 points] Numerical Dynamic Optimization: Traditional Irrigation Technology
Let’s suppose AEM uses traditional irrigation technology, in which case the revenue parameters in your crop revenue R(E) = r0Er1 are T0 = 5 and T1 = 1.01; and the cost parameters in your extraction costs C(E, S) = c0 . Ec1 Sc2 are C 0 = 14,000, C1 = 1.6, and C2 = −1.2.
a. Using Excel Solver, solve AEM’s dynamic optimization problem to obtain the optimal values for groundwater extraction Et each year from t = 0 until t = 15 when AEM uses traditional irrigation technology. In other words, solve for the optimal values of E0 , E1 , E2 ,..., E15 . Explain how you do this, describing exactly what cells, values, and/or equations/inequalities you use for your objective, choice variables, and constraints in Excel Solver, and why. Make sure the objective, choice variables, and constraints you entered into Excel Solver to obtain your solution are saved in Excel Solver when you save and close your Excel file, so that they reappear if you re-open your Excel file and Excel Solver. Include the Excel file you used in the zipped file you submit, and indicate the filename of the Excel file in the writeup.
b. Using Excel, plot the optimal values for extraction Et and groundwater stock St over time, with year on the x-axis, when AEM uses traditional irrigation technology. Label the x- and y-axes using full words and including the units in parentheses. Include the Excel file with the plots in the zipped file you submit, and indicate the filename of the Excel file in the writeup. Include the plots in your writeup.
c. What is the present discounted value of the entire stream of profits when AEM uses traditional irrigation technology and its extraction is chosen optimally?
d. How much total groundwater does AEM extract over the 16 years from t = 0 until t = 15 when AEM uses traditional irrigation technology and its extraction is chosen optimally?
3) [10 points] Regression Analysis: New Irrigation Technology
Now let’s suppose there is a new irrigation technology that wastes less water. AEM has obtained data on the total extraction costs (in dollars) of using this new irrigation technology for different combinations of groundwater extraction E (in gallons) and amount of groundwater remaining in the aquifer S (in gallons); this data is provided in the Excel file:
“AEM4500_ECON3860_AEM5500_PS11_data_spring2024.xlsx” .
a. Using Excel Analysis ToolPak, fit AEM’s data on total extraction costs of using this new irrigation technology for different combinations of extraction E and stock S to the extraction cost function C(E, S) = c0 . Ec1 Sc2 for this new irrigation technology. In other words, estimate the parameters C0 , C1 , and C2 in the extraction cost function C(E, S) = c0 . Ec1 Sc2 for this new irrigation technology. Explain how you do this. Report your estimated values of C0 , C1 , and C2 in the writeup, with C0 rounded to the nearest integer, C1 rounded to 1 decimal place, and C2 rounded to 1 decimal place. Include the Excel file you used, including the Excel Analysis ToolPak regression output, in the zipped file you submit, and indicate the filename of the Excel file in the writeup.
b. How do the extraction cost parameters C0, C1, and C2 for this new irrigation technology compare to the extraction cost parameters C0, C1, and C2 for the traditional irrigation technology in Question 2? How do the extraction costs for this new irrigation technology compare to the extraction costs for the traditional irrigation technology in Question 2? Interpret the results.
4) [10 points] Numerical Dynamic Optimization: New Irrigation Technology
Now let’s suppose AEM is instead using new irrigation technology in Question 3 that wastes less water. Now AEM’s extraction costs C(E, S) = c0 . Ec1 Sc2 are lower, and the cost parameters C0 , C1 , and C2 are now given by the cost parameters C0 , C1 , and C2 estimated in Question 3. With this new irrigation technology that wastes less water, AEM now can plant higher-revenue, more water-intensive crops, so that the revenue parameters in AEM’s crop revenue R(E) = r0Er1 are T0 = 6 and T1 = 1.05.
a. Using Excel Solver, solve AEM’s dynamic optimization problem to obtain the optimal values for groundwater extraction Et each year from t = 0 until t = 15 when AEM uses the new irrigation technology that wastes less water. In other words, solve for the optimal values of E0 , E1 , E2 ,..., E15 . Explain how you do this, describing exactly what cells, values, and/or equations/inequalities you use for your objective, choice variables, and constraints in Excel Solver, and why. Make sure the objective, choice variables, and constraints you entered into Excel Solver to obtain your solution are saved in Excel Solver when you save and close your Excel file, so that they reappear if you re-open your Excel file and Excel Solver. Include the Excel file you used in the zipped file you submit, and indicate the filename of the Excel file in the writeup.
b. Using Excel, plot the optimal values for extraction Et and groundwater stock over time, with year on the x-axis, when AEM uses the new irrigation technology that wastes less water. Label the x- andy-axes using full words and including the units in parentheses. Include the Excel file with the plots in the zipped file you submit, and indicate the filename of the Excel file in the writeup. Include the plots in your writeup.
c. What is the present discounted value of the entire stream of profits when AEM uses the new irrigation technology that wastes less water and its extraction is chosen optimally?
d. How much total groundwater does AEM extract over the 16 years from t = 0 until t = 15when AEM uses the new irrigation technology that wastes less water and its extraction is chosen optimally?
e. Does AEM have a higher present discounted value of the entire stream of profits when AEM uses the traditional irrigation technology, or when AEM uses the new irrigation technology that wastes less water? Explain and discuss.
f. Is total groundwater extraction higher when AEM uses the traditional irrigation technology, or when AEM uses the new irrigation technology that wastes less water? Explain and discuss.
5) [10 points] Analysis and Policy Implications
Watch the following video on water conservation and management:
Lin Lawell, C.-Y. Cynthia. (2017). Water Conservation and Management. YouTube video. URL:https://www.youtube.com/watch?v=zo-NUx1fZC8&feature=youtu.be
Read the following articles:
Sears, Louis, David Lim, and C.-Y. Cynthia Lin Lawell. (2017). Agricultural groundwater management in California: Possible perverse consequences? Agricultural and Resource Economics Update, 20 (3), 1-3. URL:
https://s.giannini.ucop.edu/uploads/giannini_public/a5/84/a584e52a-3311-4716-9e28-48b9af5d0748/v20n3_1.pdf
Sears, Louis, Joseph Caparelli, Clouse Lee, Devon Pan, Gillian Strandberg, LinhVuu, and C.- Y. Cynthia Lin Lawell. (2018). Jevons’ Paradox and efficient irrigation technology. Sustainability, 10 (5), 1590. URL:https://www.mdpi.com/2071-1050/10/5/1590
Suppose policy-makers are considering a groundwater conservation program that gives AEM this new irrigation technology for free.
a. What are some advantages of a groundwater conservation program that gives AEM this new irrigation technology that wastes less water for free?
b. What are some disadvantages of a groundwater conservation program that gives AEM this new irrigation technology that wastes less water for free?
c. Explain how well-intentioned water conservation programs may have unintended consequences if they are not designed carefully and well.
Part II. Water Conservation
Choose a country other than the United States, and choose a water conservation program or policy that has been implemented in that country. In your responses to each question below, cite all sources of information thoroughly, carefully, and fully; and provide the full citation (including author, date, title, and any URLs, etc.) for all sources or references that you use. You will be graded on how thorough, accurate, thoughtful, high quality, original, well-researched, and well- documented your research, sources, analysis, and explanations are.
6) [10 points] Research
a. What country did you choose and why?
b. What is the name of the water conservation program or policy you have chosen?
c. When was the program or policy implemented?
d. Who is covered under the program or policy?
e. What geographical regions are covered by the program or policy?
f. Does the program or policy cover groundwater, surface water, or both?
g. Describe the program or policy. What does the program or policy do?
h. Describe the motivation for the program or policy and what the program or policy is intended to achieve.
7) [10 points] Economic Analysis and Policy Design
a. Define and explain each of the following notions of economic efficiency
i. static efficiency
ii. dynamic efficiency
iii. allocative efficiency
b. What is the appropriate notion of economic efficiency to use when evaluating this program or policy. Why? Explain.
c. Make the case for why this program or policy might be desirable, effective, and/or efficient.
d. Make the case for why this program or policy might not be desirable, effective, and/or efficient.
e. What are some possible unintended consequences of this program or policy? Explain.
f. What suggestions do you have to improve the policy to mitigate any possible unintended consequences?
g. What other suggestions do you have to improve the program or policy?
Part III. Honor Pledge and Problem Set Policies
8) [30 points] Honor Pledge and Problem Set Policies
a. Please hand write the following honor pledge in its entirety word-for-word by hand on paper in your own handwriting, and then sign beneath the handwritten honor pledge with your own handwritten signature.
I affirm that I have respected and upheld the highest principles of honesty, honor, and integrity on Problem Set 11, and that I have completed and written up Problem Set 11 separately on my own.
b. Include a scanned copy of the handwritten and signed honor pledge in the online submission.
c. Please upload and submit your problem set in a zipped file onto the course website. The zipped file should be named “__PS<#>.zip”, and should include a write-up of the answers in a pdf file entitled “__PS<#>_answers.pdf”, a scanned copy of the handwritten and signed honor pledge, as well as any and all Excel files used for the assignment. The writeup should be in pdf format, and should include all graphs, all calculations, derivations, results, tables, etc. For example, Barbara
McClintock’s first problem set would include a write-up of the answers in a pdf file entitled McClintock_Barbara_PS1_answers.pdf”, a scanned copy of the handwritten and signed honor pledge, as well as any and all Excel files used for the assignment; and all these files would be submitted in a zipped file with the name “McClintock_Barbara_PS1.zip” . Similarly, Mae Jemison’s second problem set would include a write-up of the answers in a pdf file entitled “Jemison_Mae_PS2_answers.pdf”, a scanned copy of the handwritten and signed honor pledge, as well as all Excel files used for the assignment; and all these files be submitted in a zipped file with the name “Jemison_Mae_PS2.zip” .
d. Please follow the problem set policies on the syllabus.
e. Please follow the policies in the syllabus, including those described in the “Code of Conduct”, “Course Copyright”, and “Teaching Philosophy” sections of the syllabus.
f. Students are encouraged to ask questions and actively participate during class and office hours. It is highly recommended that you come to office hours regularly with your questions.