What’s the deal with “returns to scale”?

(Pedagogy for the economists)

It’s time to retire the concept of “returns to scale”, at least in our intro/intermediate microeconomics. I don’t think it’s doing anything useful for us, it’s meaningful only as a pure thought experiment, and I think it confounds understanding of more relevant types of return to inputs in production.

I confess that I have never quite been able to understand the returns to scale thought experiment anyway. Scale up all inputs by the same proportion; by what proportion does output scale up? I don’t get how the answer can be anything other than the same proportion, constant returns to scale. I’m picturing an exact replica of Earth in a parallel universe, with an exact replica of the organization or factory or whatever it is we’re thinking about. As long as things are deterministic, what could possibly make output in the replica on Earth-2 different than in the original on Earth-1? “Scale up all scale-able inputs” is cheating, so that’s not going to cut it.

The perennial confusion with the concept of “economies of scale” is perhaps an indication that returns to scale is not doing good work for us. Economies of scale seems a fuzzier concept, but it gets at what we’re really trying to express. If I want to increase output, how does my average cost of producing each unit change? This is not an Earth-2 story anymore, but rather one that admits increasing returns to a single input, “scale up all scale-able inputs”, arguably dynamic stories like learning by doing or getting “up to speed”, and so on. So it’s for sure less clean of a concept than returns to scale, but it doesn’t back us in to weird thought experiment corners.

The tension is related to that other slippery concept, the “long run”. The point of that one is that in the long run a producer can alter the amount of any input it chooses, but in the short run at least one input is locked in at a given amount. The long run buys us the important fulcrum of entry and exit in industry dynamics: the long run is the time in which you can shut down and get out of Dodge with no more assets or liabilities forevermore. All inputs taken to zero, since everything is variable in the long run.

It seems like such a small step from the long run concept to the returns to scale concept. But scaling up production is not the same beast as starting up or shutting down. The symmetry does not work. As a practical matter, shutting down might be a scaling down of factor zero, but the scaling up is never the true scaling up of the returns to scale exercise. As a theoretical matter, what we are talking about here is the relationship between average costs and amount of output in the long run; this is a technological question, and an input market question, not a scaling up question.

In sum, I think that a pedantic insistence on comprehending returns to scale can wait at least until mathematical microeconomics, where the true role and nature of the concept can be given space to breathe. At the lower level, I think the difficulty in having the concept “take” is ingrained in the idea and not a failing of the student. In my experience it impedes intuition and causes disproportionate pain, and so I think it can go.

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