Market Power versus Price-taking in Economic Growth

I was traveling when Paul Romer’s “mathiness” paper and blog post started a debate about how economic theory built with mathematical tools can be manipulated for purposes that are more political than scientific. There has been a ton of discussion about this, and for now I want to highlight this piece by Dietz Vollrath. If you assume that the relevant production function is well-defined and differentiable, his arguments make many things about this controversy very clear.

Meanwhile, Paul Romer has come back to this topic many times, and his latest, as of now, http://paulromer.net/the-norms-of-politics-ferguson-and-ehrlich/, pursues the science / politics point by bringing in two figures whom he criticizes for twisting words for political purposes and not admitting it when caught.

The Growth Economics Blog

I’m sure you’ve been breathlessly following along with the discussion on “mathiness” that Paul Romer kicked off (see here, here, here). Romer used several growth models to illustrate his point about “mathiness”, and his critique centered around the assumption of price-taking by firms and/or individuals in these papers. His argument was that these papers used “mathiness” as a kind of camouflage for their price-taking assumptions. Romer argues that the reasonable way to understand growth is to allow for market power by some firms and/or individuals over their ideas.

From what I can see, the heart of this is about replication. What Romer has asserted is that any aggregate production function must have constant returns to scale (i.e. be homogenous of degree one) in its rival inputs. The mental exercise here is the following. Imagine that tomorrow there was a perfect replica of the Earth floating next to…

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