This assignment 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 analysis 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 in this week’s assignment. This is the only thing that will change compared to last week, i.e. you will not change any other aspect of the SCC calculation. You should add the calculations of the Ramsey discount factor and the associated SCC numbers to the same sheet you used last week to compute the SCC, i.e. you should keep around the SCC computations you created using a constant discount rate. Whenever you are asked to report a SCC value this week, you should just report the $/tCO2 value, and not the $/tC value.

Ramsey Discount Factors

The Ramsey discount factor is a bit more complicated than the constant discounting scheme you used  last  week.  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:

rt(r) = P + gt                                                                                                            (1)

rt(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; you should use the per capita consumption numbers from the base model and not the model with the marginal emission impulse). 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

                                                              (2)

This is tricky to put into Excel right away. Instead, you can use a recursive formulation that is mathematically equivalent:

                                                               (3)

This gives you the discount factor for all but the first year. The discount factor in the first year is

one by definition: DF = 1. You should use a default value of 1.5% for the pure rate of time

preference.

Part II: Policy Analysis

Question 1: How does the Social Cost of Carbon change for different pure rate of time preference rates?

You should compute the Social Cost of Carbon for two alternative pure rate of time preference rates, namely 0% and 3%. You can do all the calculations for this sensitivity analysis on the third sheet you created in Excel last week.

Question 2: How do non-discounted marginal damage estimates over time compare to discounted marginal damage estimates?

You should create a graph that as 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 3.5%, 2% and 5% from last week 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 change for different values of the 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:

ΔT)  = λ × 5.35 ln

C!

C*"+

:

This is 2 for

a doubling of   concentrations              (4)

We got the value for λ (the climate sensitivity parameter in our model) by plugging in the numbers from IPCC and solving for λ:

3° = λ × 5.35 ln 2 ⇒ λ = 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. 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 change your existing model to use a different climate sensitivity, copy those SCC results to a new sheet, then change your model again, copy your results etc.