PrintMaking Comparisons — the Discount Rate
We would like to be able to see whether one policy for reducing emissions of carbon is economically better than another. Different policies will call for different histories of reductions, and to compare them, we need to find a way to compare the expected future damages associated with each policy. A problem comes when we try to compare 200 million in damages at some time in the future vs. 20 million in damages today. Economists use something called a discount rate to do this. Here is an example to help you see how this idea works: imagine you have a pig farm with 100 pigs, and the pigs increase at 5% per year by natural means. If you do nothing but sit back and watch the pigs do their thing, you’d have 105 pigs next year. So 105 pigs next year can be equated to 100 pigs in the present, with a 5% discount rate. Thus, the discount rate is kind of like the return on investment. Now think about climate damages. If we assume that there is a 4% discount rate, then $1092 million in damages 100 years from now is $20 million in present-day terms. Here is how this works in an equation:This is a standard exponential growth equation is called Euler’s number and has a value of about 2.7. Now, let’s say we calculate some cost in the future — 8 million dollars 200 years from now — we can apply a discount rate to this future cost in order to put it into today’s context. Here is how that would look:
It is important to remember that this assumes our global economy will grow at a 4% annual rate for the next 200 years. The 4% figure is the estimated long-term market return on capital, but this may very well grow smaller in the future, as it does in our model. Although we’re not going to dwell on the discount rate any more in this exercise, it is good to understand the basic concept.
A simpler way of comparing future costs or benefits with respect to the present is to express these costs and benefits relative to the size of the economy at any one time — which our model will calculate. This gets around the kind of shaky assumption that the economy is going to grow at some fixed rate. These relative economic measures are easy to do — just divide some parameter from the model, like the per capita consumption, by the GDP. Below is a list of the model parameters that we will keep an eye on in the following experiments:
Below is a list of the model parameters that we will keep an eye on in the following experiments:
Global capital — the size of the global economy in trillions of dollars;
GDP — the yearly global economic production in trillions of dollars
Per capita consumption — consumption/population; this is a good indicator of the quality of life — the higher it is, the better off we all are; units are in thousands of dollars per person
Relative per capita consumption — annual per capita consumption x (GDP/initial GDP); again, a good indicator of the quality of life, in a form that enables comparison across different times; units are in thousands of starting time dollars per person
Sum of relative pc consumption — the sum of the above— kind of like the final grade on quality of life. If you take the ending sum and divide by 200 yrs, it gives the average per capita consumption for the whole period of the model run.
Relative climate costs — an annual measure of (abatement costs + climate damages) x (GDP/initial GDP); this combines the costs of reducing emissions with the climate damages, in a form that can be compared across different times; the units are trillions of dollars.
Sum of relative climate costs — sum of the relative climate costs — the final grade on costs related to dealing with emissions reductions (abatement) and climate; this is the sum of a bunch of fractions, so it is still dimensionless.
Global temp change — in °C, from the climate model