Climate Change Economics Final Exam Summer, 2022
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
Climate Change Economics
Final Exam – Take Home Portion
Summer, 2022
Overview
The final exam has two parts. Part II is this take-home exam, Part I is the “in-class”/online exam during the designated examination time.
Due Date
Please submit your take-home final exam spreadsheet file to bCourses by Friday, August 12th, 5pm (Pacific Standard Time). No late submissions will be accepted. We expect all students to plan
accordingly and buffer in time to account for technical issues in uploading your final file. Students with DSP accommodations for exams will have until Sunday 14th at 5pm.
Rules for Take-Home Exam
You may NOT work together on any part of the exam. If a question is unclear, you should email Eli Lazarus (lazarus.eli@berkeley.edu) but you need to ask for clarification before 5pm on Wednesday, August 10th . Eli will post any answers to clarifying questions as an announcement on bCourses. You may use any source of information from this semester (including this semester’s past assignments, assigned readings, and slides) when answering the questions. Please do not consult any resources from prior semesters of the class. We have changed the exam in ways to spot references to earlier course materials and if we find evidence that you have done this, we will give you a zero for the take home final. Please don’t risk it.
Attached to this assignment is a version of the integrated assessment model that is correct. It is the base model from the Assignment 6 Solution file (without the specific policy answers). You have two options: (1) You can start with this provided file and do the whole exam based on it, i.e., not use your own model at all; or (2) You can use your own model, in that case make sure to cross check your model with the version of the model that is attached to this exam to make sure your version doesn’t have errors. Please indicate in your submitted spreadsheet which option you are choosing.
Afew guidelines:
- We are not grading on formatting or coloring. As long as we can clearly find all your results, answers, and graphs, then you will not be deducted points based on formatting.
- Please preserve ALL of your work and calculations – this means only copy & paste for Question 3 where you are specifically asked to do that. Create separate worksheets for each
set of calculations you complete. Failure to show all of your work in the spreadsheet you submit will negatively affect your grade.
- Units in your calculations should be consistent, and you should remember to label your final output with the units that you use. The order of magnitude of the dollar values (whether in trillions, or just dollars) shouldn’t change your calculations – just be sure to be clear which units your values are in.
Exam Questions
This section of the exam has two parts: 1) you will add a Ramsey discount rate to your computation of the Social Cost of Carbon and 2) do a number of sensitivity analyses on the Social Cost of Carbon.
Part I: Modeling
Overview
You will add support for Ramsey discount factors to your computation of the Social Cost of Carbon from Assignment 6. You should redo your Social Cost of Carbon set up, redo the constant discounting with new discount rates (3%, 2%, and 4%), and then add the calculations of the Ramsey discount factor and the associated SCC numbers. Whenever you are asked to report a SCC value in the final exam, you should report both the $/tC value and the $/tCO2 value.
Ramsey Discount Factors
The Ramsey discount factor is a bit more complicated than the constant discounting scheme you used in Assignment 6. Because the discount rate for each year depends on that year’s per capita consumption growth rate, we first need to compute the Ramsey rate for each year:
Tt(r) = p + gt (1)
Tt(r) is the Ramsey discount rate for year t, p is the pure rate of time preference (prtp) and gt is per capita consumption growth from year t − 1 to year t (so gt = , with ct being per capita
consumption in year t, and ct- 1 being per capita consumption from the previous year; you should use the per capita consumption numbers from the base model and not the model with the marginal emissions pulse. Due to the definition of the Ramsey discount rate you cannot compute it for the first year, so you should compute it for the second and all following years.
The equation for the Ramsey discount factor is
t
DFt(r) = 1 × ∏
(2)
This is tricky to put into Excel as is. Instead, you can use a recursive formulation that is mathematically equivalent:
DFt(r) = DF1
1
1 + tr
(3)
This gives you the discount factor for all but the first year. The discount factor in the first year is one by definition: DF0(r) = 1. You should use a default value of 1% for the pure rate of time preference.
Part II: Policy Analysis
Question 1: How does the Social Cost of Carbon changefor different pure rate of time preference rates?
You should compute the Social Cost of Carbon for two other pure rate of time preference rates, namely 0% and 2.5%. You can do all the calculations for this sensitivity analysis on the third worksheet along with the constant discounting just as you did for Assignment 6.
Question 2: How do non-discounted marginal damage estimates over time compare to discounted marginal damage estimates?
You should create a graph that has years on the x-axis and $ damage on the y-axis. You should then plot undiscounted marginal damages over time as one line, and then one additional line for discounted marginal damages for each of the six total discounting schemes (three using constant discount rates 2%, 3% and 4% and three using Ramsey discount factors based on the rates you used in the previous question). You should then create one additional graph that only has the six discounted marginal damages on it, i.e. this second graph will be almost identical to the previous one, only it will not show the undiscounted marginal damages.
Question 3: How does the SCC changefor different values ofthe climate sensitivity?
The IPCC states the equilibrium warming for a doubling of CO2 concentrations is likely in the range of 2 to 4.5° with a best estimate of 3° . The equation we use to compute the equilibrium warming is:
Ct
Cpre
⏟
This is 2 for
a doubling of
concentrations
We got the value for 入 (the climate sensitivity parameter in our model) by plugging in the numbers from IPCC and solving for 入:
3° = λ × 5.35 × ln(2)
⇒ 入 ≈ 0.8 = 0.8
(5)
You should solve this equation to compute the climate sensitivity parameter that gives a warming of 2° and a warming of 4.5° for a doubling of CO2 concentrations, and then run your model with both of these alternative climate sensitivity parameters (remember, you will need to make the change in the base and marginal run models). How does the SCC change for these two alternative
climate sensitivity parameters? You should report the SCC for each of these climate sensitivity parameters for all six discount-factor schemes we have used so far.
You should not create a different set of models for each of the climate sensitivity parameters. Instead, you should have your model set up to calculate the SCC under all 6 discount-factor schemes, then change your existing model to use a different climate sensitivity, copy and paste those SCC results to a new sheet, change your model again, copy your results, then change your model the third time and copy your SCC results to that same worksheet. You should end up with 36 SCC values: for each of the 3 climate sensitivity (入) estimates you will have 12 SCCs – 3 with constant discounting in terms of $/tC, 3 with Ramsey discounting in terms of $/tC, and then all 6 of those transformed to the units of $/CO2 .
2022-08-08