# Productivity and wages in a task-based model

In a task-based model like the one developed in Acemoglu&Autor 2011 with two types of worker, can the low type have a higher wage with respect to the high type?

More specifically: if the productivity of the "high type" is greater for each task in the economy, can we say that, regardless of the aggregate supply of labor, the equilibrium relationship is $w_h>w_l$?

Thank you in advance for any help!

• It would be helpful if you can give a brief outline of the model's setup, or at least give a link to the paper. – Herr K. Apr 3 '18 at 20:19

I guess you are referring to a situation in which abundand supply of high-skilled workers decrease productivity such that individual $$w_h < w_l$$ Considering Equation (5) in Acemoglu & Autor, $$H$$ and $$L$$ capture supply of both groups of workers. If $$\frac{H}{L}$$ becomes sufficiently high, I don't see why the relation between both wages should not become lower than 1.
• Check out the remarks in the paper below that equation. As far as I understand, if H/L becomes too high, high-skilled workers will do what low-skilled workers did before and vice versa. This is partly a consequence of the production function with one commodity and no differentiation between tasks. – E. Sommer Apr 6 '18 at 14:19
In that set-up, the wages are related by the following: $$w_h\geq w_l$$. But it can never happen the low skill earn more. This crucially comes from the fact the high skill have equal or higher productivity than low skill in any task.
By contradiction, if it's the case that $$w_l>w_h$$, then a firm could offer a higher wage to the high skill and substitute the low skill, thus increasing production.