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I was reading this article in VoxEU, where the authors (one is a Professor of Economics at Harvard University) make the case that an increasing average mark-up has accounted for much of the late productivity growth, since it leads to an increasing allocative efficiency.

However, isn't this exactly the oposite of what one would want? It seems that they are somehow mixing up the possibility of high profits due to one would usually think of as high productivity, with high profits due to market imperfections... Also, it's also as if the authors would defend a higher 'productivity' but at a lower output, than a lower 'productivity' at a higher output.

Here's a quote from the text which I find baffling:

«(...)this reallocation of market share from low- to high-mark-up firms has considerably improved the allocative efficiency of the US economy over the last 20 years. In fact, improvements in allocative efficiency account for about 50% of the cumulated growth in aggregate productivity during this period. This suggests that ‘true’ technological productivity growth has been even slower than previously imagined.(...)A high average mark-up reduces output and depresses the demand for labour and capital, generating low aggregate employment and low aggregate investment. It reduces the aggregate labour and capital shares, and increases the aggregate profit share.»

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allocative efficiency = Using resurces where they add the most value.

Example: The resources needed to create a branded t-shirt (or any other product with a strong brand) is the same as for the creation of a no-name t-shirt. However, the price/value of the branded product is considerably higher.

So, if you can switch production from cheap no-name products to more expensive branded products then output value increases but resource consumtion is unaffected. This value increase is separate from the resource reduction caused by an increase in productivity.

However, isn't this exactly the oposite of what one would want?

Depends on who "one" is. For american companies it is good, since it increases their profits. For the resource producers (seamstresses, cotton farmers etc) it is bad since it reduces the demand for their resources.

It seems that they are somehow mixing up the possibility of high profits due to one would usually think of as high productivity, with high profits due to market imperfections...

That depends on whether you consider branding a market imperfection. When measuring it is very difficult to distinguish quality and branding. If a no-name t-shirt costs \$6 and branded t-shirt costs \$30, how much of the price difference is due to quality and how much is brand name?

Also, it's also as if the authors would defend a higher 'productivity' but at a lower output, than a lower 'productivity' at a higher output.

From the quoted snippet it looks like they are describing the effects successful branding has had for US companies and for the US economy.

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