Infinite Economic Values??

Dave asks for my thoughts about this article on The Angry Economist. Russell is involved in an argument about recycling, and defending the proposition that a finite physical supply of some resource can have an infinite economic value:

Infinite value is the proposition that a finite amount of something can have an infinite amount of value. People who are not economists, and are stuck in the 1870's objective value see this as being obviously false. How could a finite amount of something be valued infinitely high?

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Infinite value is an inevitable result of relative value. Let's say that you were using natural resources at a certain rate, and you were increasing the relative value of these resources faster than you used them. Specifically, let's say that you produced a certain amount of value out of consuming the first half of a resource. You were able to double the value of a specific unit of the resource, so that you could consume half of the remaining resource and produce the same value. Like Zeno's paradox, the resource continues to produce value forever.

In the real world, you reach the atomic level sooner or later, and effectively run out of the resource. Does this invalidate the idea of infinite value? No, because in time, the substitutes for a resource become cheaper than the resource, and people will switch to those substitutes. What this means, though, is that people can consume resources as if they were infinite.

It's not clear which of Zeno's paradoxes he's referring to (here's a more technical explanation of them), but this talk of paradoxes is beside the point.

Talking about infinite values in an economic context is ridiculous. Economic valuations are ordinal, not cardinal — a person ranks their alternatives by their 1^st, 2^nd, 3^rd, (etc.) preferences, but cannot quantify (give a cardinal number for) the magnitude of the distance between any pair of preferences. "By how much do you prefer an apple to an orange?" cannot be sensibly answered.

(Before any mathematicians pounce on me, please note that economists and mathematicians don't define "ordinal" and "cardinal" in the same way. They're terms of art in each field.)

The concept of infinity does not apply to ordinal numbers as used in economics.

Russell's conclusion (that we shouldn't worry about running out of resources) is correct, but not on the basis of infinite values. At the end he switches to the correct reasoning — competition among goods will cause people to use less of a resource as its increasing scarcity causes it to become relatively more expensive compared to its alternatives.

It is possible for a resource to be completely used up, but this is not necessarily cause for alarm. For example, the extinction of the dodo bird, which never had much economic value even as its population dwindled to zero because its habitat was destroyed to be used for purposes with higher economic value. There were never infinite values involved.