You Cannot Just Define Away the Impossibility of Infinite Growth

More and more people in the world are questioning the possibility of human economies to grow infinitely. The ongoing destruction of global as well as regional ecosystems and the overuse of Nature’s resources are signs that something is going wrong. Nevertheless, mainstream (or neo-classical) economists – especially macroeconomists – seem not to be bothered. They still are claiming that economic growth is not only possible, it even is necessary to improve our well-being (for a critique see here). In some cases this may be true – nobody sane would argue that, let’s say, Nigeria doesn’t need economic growth. But one cannot (and should not) generalize this. Confronted with such arguments, (macro)economists either ignore them, or they answer by showing that in their models infinite growth is possible. They are just defining away the contrary.

All major macroeconomic models are founded on one particular assumption – the so called Cobb-Douglas production function. The function states that production Q is:

Q = ALβKα

where A is technology, L is labour, and K is capital, and α and β are the elasticity coefficients of the latter two (often assumed to equal 1 in sum, so for the discussion here it be defined that β = 1-α). L can be defined as natural resources as well (and will be thus interpreted in what follows).

After a long way through further assumptions and much mathematics, you arrive at an equation that is critical here:

η = n + μ/(1-α)

where η stands for the rate of economic (i.e., production) growth, n is the growth rate of natural ressources (labour), and μ is the rate of technological progress. When you look at this equation as macroeconomists do, you will see that if n is negative (i.e., in simplificated terms, if we are running out of natural ressources that are critical for production), positive economic growth is still possible if the rate of technological progress, weighted with its “importance” in the production function (α), is bigger than n. This is a convenient line of argument, since if humanity is to realize in the future that growth is not more possible (due to too few natural resources left or to population growth), the macroeconomist can just say that our technology is not improving fast enough. And this would be true, indeed. Would be.

The problem is that the whole argumentation is built on one critical, but flawed assumption. By using a multiplicatory combination of factors in the production function we assume that the factors are substitutable. In common language: natural resources shortage is not a problem as long as our technology is improving. Isn’t this insane?

What will technology (i.e., resource productivity – how much we can produce using a given amount of a resource) use us if we run out of the resource? Paraphrasing a famous example made by Herman Daly: can we build the same wooden house with less wood but more workers and/or more axes? And, to use a less extreme argument: what is the reason to assume that resource productivity/technological progress has no limits? Our technologies have been improving over hundreds of years. People in the Middle Ages weren’t be able to imagine all the sophisticated tools we are currently using in everyday life. That is fully true. The problem is that we cannot know with anything near certainty that this will go on forever. It may do so. But it may be (and the probability of both is equal, since unknown) as well that our technology is not going to improve significantly any more because we are arriving at some limits we don’t know of yet.

The question now is one of responsibility: do we want to proceed with “business as usual”, naively assuming that technology will solve all our problems – and running the risk of a catastrophe in case that we had been wrong? Or shall we rather back-pedal and think about whether it is possible that we (especially we in the industrialized world) already have enough?

P.S. I just found an essential text on the subject discussed above: “Nature in Economics” by Partha Dasgupta. It is really worth reading.


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