Some fun with discounting. From the inbox (via the resource econ e-mail list):
Haynes Goddard: As most of you know, William Nordhaus has major differences with Nicholas Stern's report. The following quote is taken from Nordhaus"The Stern Review on the Economics of Climate Change", May 2007, pages 25-6. I have a couple of comments and a question that I hope one or more of you can comment on.
"The effect of low discounting can be illustrated with a “wrinkle experiment.” Suppose that scientists discover a wrinkle in the climate system that will cause damages equal to 0.1 percent of net consumption starting in 2200 and continuing at that rate forever after. How large a one-time investment would be justified today to remove the wrinkle that starts only after two centuries? Using the methodology of the Review, the answer is that we should pay up to 56 percent of one year’s world consumption today to remove the wrinkle. (footnote 26). In other words, it is worth a one-time consumption hit of approximately $30,000 billion today to fix a tiny problem that begins in 2200. (footnote 27)
It is illuminating to put this point in terms of average consumption levels. Using the Review’s growth projections, the Review would justify reducing per capita consumption for one year today from $10,000 to $4400 in order to prevent a reduction of consumption from $130,000 to $129,870 starting two centuries hence and continuing at that rate forever after. "
...what is the point of presenting the argument as one of a one time present period investment (reduction on current consumption), rather than an investment project to be undertaken over a period of years? It would seem that a better way of putting it would be to ask how much does the world have to invest over the next two hundred years to prevent a specified annual damage that will last for ever starting in year 201. That is, what is the equivalent annual amount for two hundred years, or the annual per capita amount equivalent to the present period per capita reduction of $5600 at the indicated growth corrected discount rate of 0.001? This is $5600/(annuity factor for 200 years). If I have done my calculation correctly, the annuity factor is 181, the present value of the per capita investment (reduction in consumption) is $5600, and the equivalent annual per capita amount is about $31.
