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Is the pooling equilibrium profit maximising for the firm?

I understand that when there are no ways for the firm to distinguish among highly productive and low productive worker the best the firm can do is to offer a wage which is based on the relative numbers of the type of workers in the labour force. From what I have understood this equilibrium is inefficient as the firm is now able to allocate workers to the most suitable task according to their level of ability. Hence the question: can the pooling equilibrium be considered as profit maximising?

Thank you in advance for any help!

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    $\begingroup$ It would be helpful if you tell us what model and equilibrium notion you are talking about. There are a lot of slightly different job market signalling models in the literature. $\endgroup$ – Michael Greinecker Jun 6 at 22:47
  • $\begingroup$ Thank you very much for your reply. I am just referencing to a basic (first year UG) model where schooling has zero impact on productivity. $\endgroup$ – James_ Jun 7 at 8:27
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As suggested in the comments, there are many different signaling models with firms and workers, and also what is the "standard model" to differnt people differs in details.

In most of those models, however, a firm does not make a profit in any equilibrium as the wage is equal to the expected productivity. In any separating equilibrium, the wage of the high type is equal to their productivity $w_{e=1}=\theta_H$, leading to a profit of $\theta_H-w_{e=1}=0$ from this type. Same for the low type, $w_{e=0}=\theta_L$. The pooling wage is equal to $E[\theta]$, again leading to a profit of zero.

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  • $\begingroup$ This does not answer the question. Is the attained profit of 0 maximal or not? $\endgroup$ – Giskard Jun 7 at 22:48
  • $\begingroup$ We would need to have more information about the details of the model to give a rigorous answer. In the model that I have in mind, any equilibrium has a profit of zero and therefore all of them attain maximal (and minimal) equilibrium profit. $\endgroup$ – Bayesian Jun 8 at 8:49

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