<p>In that set-up, the wages are related by the following: <span class="math-container">$w_h\geq w_l$</span>. 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 <em>any</em> task. </p>

<p>By contradiction, if it's the case that <span class="math-container">$w_l&gt;w_h$</span>, then a firm could offer a higher wage to the high skill and substitute the low skill, thus increasing production.</p>

CC BY-SA 4.0
2018-10-23T10:27:16.350Z
2019-02-06T10:39:34.463Z
2019-02-06T10:39:34.463Z
Tecon
<p>I guess you are referring to a situation in which abundand supply of high-skilled workers decrease productivity such that individual <span class="math-container">$w_h &lt; w_l$</span>
Considering Equation (5) in <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.308.299&amp;rep=rep1&amp;type=pdf" rel="nofollow noreferrer">Acemoglu &amp; Autor</a>, <span class="math-container">$H$</span> and <span class="math-container">$L$</span> capture supply of both groups of workers. If <span class="math-container">$\frac{H}{L}$</span> becomes sufficiently high, I don't see why the relation between both wages should not become lower than 1. </p>

CC BY-SA 3.0
2018-04-06T13:15:48.810Z
Thank you for your answer. The problem is that I don't see how a worker who has a productivity higher than the other - in each task - could earn a lower wage. I don't have an intuitive answer to this problem, even though I see your point, and from the equation you mention it seems to be possible.
Tecon
CC BY-SA 3.0
2018-04-06T14:19:46.750Z
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
CC BY-SA 4.0
2018-04-05T12:23:47.837Z
2018-11-14T08:48:57.033Z
2018-11-14T08:48:57.033Z
E. Sommer
<p>In a task-based model like the one developed in Acemoglu&amp;Autor 2011 with two types of worker, can the low type have a higher wage with respect to the high type? </p>

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

<p>Thank you in advance for any help!</p>

CC BY-SA 3.0
2018-04-03T20:19:39.737Z
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.
<macroeconomics><labor-economics><inequality><productivity><technology>
Productivity and wages in a task-based model
Tecon
# Productivity and wages in a task-based model

(Asked by: username_0 on 2018-04-03)

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!

**Tags:** macroeconomics, labor-economics, inequality, productivity, technology

> **Comments:**
> **username_1**: 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.  

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## 2 answers

### Answer by username_0 on 2018-10-23. Score: 0 | Accepted answer

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.


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### Answer by username_2 on 2018-04-05. Score: 2

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](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.308.299&rep=rep1&type=pdf), $H$ 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.

> **Comments:**
> **username_0**: Thank you for your answer. The problem is that I don't see how a worker who has a productivity higher than the other - in each task - could earn a lower wage. I don't have an intuitive answer to this problem, even though I see your point, and from the equation you mention it seems to be possible.  
> **username_2**: 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.  

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