The CORE team's writings about labour productivity, real wages, markup and the price-setting curve

Question

I've been reading the free online economics handbook that's developed as part of the CORE-project (here). The book is a refreshing read, but I'm struggling to follow their discussion of the price setting curve and related matters. Specifically, I can't make sense of the explanation they're giving in this section for the thesis that real wages rise alongside labour productivity, with a fixed markup. True, when real wage = labour productivity * (1 - markup) as they're saying, real wages will rise proportionally with labour productivity, but in their discussion the markup itself depends on unit labour costs and therefore labour productivity. When I use the equations in Excel to see what the effect is of a rise in labour productivity is (with the markup partly depending on unit labour costs, and using nominal wage, labour productivity and price as independent variables) what changes is the markup and the shares that go to profits and real wages. The real wage itself remains exactly the same. In other words, the exact opposite of the thesis. What am I missing here? Mind, I'm not disputing it itself that real wages rise with productivity (I've read Blanchard's Macroeconomics in this regard), it's just I don't understand CORE's reasoning here.

It doesn't seem possible to share the Excel file, but it should be possible reproduce it yourself quickly.

Answer 1

The result with the markup should hold for the same reason as the result without the markup, which you accept.

That is because, in this case, the markup is constant. It is 1/elasticity, and the elasticity comes from the demand function parameters. Here it is unrelated to productivity (production function / technical capacity of the firm), i.e. as productivity changes, the markup does not change.

So, as labor productivity increases the markup is not changing (so for this argument it does not matter if it is there or not), and hence real wages must be increasing.