Discounting for short-term benefits and costs (within say 20 years), or for purely commercial investments, is theoretically uncontroversial. Discounting for investments that pay off over the very long term (say, 100 years or more) is a more difficult matter, and in my view, has not been well resolved theoretically.

To get a feel for the issue, consider the following example. Suppose that there is some foreseeable catastrophic threat that would have its impacts in 200 years time. Suppose that this foreseeable threat could only be prevented by some action taken right now. Perhaps the problem is due to a comet that is passing by currently, and is forecast with a high degree of certainty to strike the earth on its next orbit, in 200 years.

Assume also that:

• World GDP will grow by 3 percent per year to $8 quadrillion (15 zeros) by 2205;

• The discount rate is 7.5 percent (that’s the sort of rate routinely used by bodies such as government departments);

• The value of all damage (including loss of life and environmental damage) is $4 quadrillion, in 2204 dollars – half the global GDP.

Now, the question is, what is the most that the current generation should be willing to pay to prevent this forecast catastrophe? To make it easy to comprehend the size of the result, express it as the value per head of current population. In other words, if we were to fund the preventative action with a levy on each of the current six billion people on earth, what is the most that it would be reasonable to ask them to pay (on average)?

Using standard discounting methods, the answer is 35 cents each. If you doubt this, do the following calculation: 4 x 10¹⁵/(1.075²⁰⁰ x 6 x 10⁹).

Can that be right? It seems to imply such callous disregard for the welfare of our distant descendents. The implied rationale is that an expenditure of any sum greater than 35 cents each ($2.16 billion in total) could be set aside in investments that would yield 7.5 percent return per year, and that this would compound to a value greater than the $4 quadrillion that is under threat. But would it? Why would this $2.16 billion grow more rapidly than the rest of the world economy (which, remember, is growing at 3 percent)? Perhaps it might do so early in the time period when it is a tiny proportion of the world economy, but what about late in the period when it will be (theoretically) a large share of the world economy? It is simply not plausible to suppose that it could keep growing at 7.5 percent while the rest of the economy grows at 3 percent.

Clearly, discounting in this way produces a nonsense answer. Perhaps we should apply a discount rate of zero. This has been seriously suggested by some. However, this implies that the average personal cost to current individuals could be as high as $667,000, which is about 180 times the current average GDP per person. Zero discounting doesn’t produce a workable and reasonable answer either. Why should we give up absolutely everything (and more) now to prevent a partial loss in the future?

How about discounting at the expected rate of growth of the world economy: 3 percent, for the sake of this discussion. This has been suggested by some eminent economists as the appropriate approach for large long-term public investments. It would yield a value of $1800 per head, half the global average GDP per head. This at least has some intuitive relationship to the event it is intended to prevent: it implies that to avoid losing half the world GDP in 2205, we should be prepare to give up as much as half the world GDP in 2005.

But is that reasonable? The idea raises all sorts of difficult questions?

• How certain can we be that the comet would actually hit? In reality, it might be deflected slightly by gravity as it passes another planet and miss us by a long way. Or it might not cause as much damage as predicted. Either way, our sacrifice might turn out to be more than could be justified.

• What might happen with technology over the next 200 years? The extraordinary advance in technology from 1805 to 2005 will probably seem small compared to the advance from 2005 to 2205. Diverting the comet in 2205 using some currently unimaginable technology might be a simple matter. We (the current generation) would have given up so much for so little gain to anyone.

• What is the risk of the earth being destroyed in between time by some other cataclysm?

• Is it fair to expect people today to give up half of our current wealth to prevent a loss that would still leave the world economy vastly larger than it is today (around 200 times larger, even after losing half of it)?

• On the other hand, is it fair not to give up an amount of wealth now in order to avoid a future generation losing 400 times as much?

• Is it simply a matter of wealth? Even with 400 (or 200) times as much wealth, the future generation would probably not be that much happier or more satisfied than we are today? Should we account for that, and if so, how?

• In what real sense could we consider $1 x 10¹³ in 2005 to be equivalent to $4 x 10¹⁵ in 200 years time? Given the likelihood of dramatic changes in technology, health, wealth, institutions, culture, religion, age distribution, and so on, surely it is a case of comparing apples and oranges.

• The losses would include loss of life and damage to environments on a world scale. How should they be valued? In thinking about our investment in comet diversion, should we value them from the point of view of the current generation, or their contemporary generation, or aggregate over a whole lot of generations? If the latter, who should be included and why? And even if we are happy with non-market valuation methods for current generations, how can we anticipate how future generations might value human life and the environment?

Overall, the question is vastly more complex and subtle than just choosing which discount rate to use. It pulls economics into areas of ethics and morality which we have not usually handled well, and it forces us to deal the deepest uncertainty about future outcomes and values. My guess is that we will make further progress in clarifying the issues, but that it will probably always remain a problem with no clear answer.