Exploring Clark's theorem

I'll bet that analysis made you pretty uncomfortable. I certainly don't like it much, but it's very difficult to find a way to attack the conclusion. Before we go any further, I want to explore a couple of key assumptions behind that theorem to illustrate just how deeply you have to look to figure out what's wrong.

Consider this scenario⁷:

• Assume we knew with certainty that a catastrophe would wipe out the world 200 years from now.

• Assume that the world's gross domestic product (the annual value of all goods and services produced in the world) grows 3% annually over that period.

• Then the world's GDP in 2205 will be about U.S. $ $8\times 10^{15}$.

• Now suppose we use a standard financial discount rate of 7% to determine the net present value of $ $8\times 10^{15}$:
  
  $$\$8\times 10^{15}e^{-(0.07)200} = \$6.7\times 10^{9} \quad .$$
  
  
  Now $6.7 billion is a lot of money, but it's only about a tenth of Bill Gates' net worth and its only a little more than $1 per person currently alive.

• Nonetheless, the conventional economic argument would suggest that if it cost us more than $6.7 billion dollars to prevent certain destruction of the planet two centuries from now, we shouldn't spend the money.

This scenario illustrates two fundamental flaws with the conventional approach to discounting future events, at least those that extend far into the future.

1. The conventional approach assumes that resources are substitutable for one another.

2. The conventional approach glosses over problems of intergenerational equity.