# Is the pooling equilibrium profit maximising for the firm?

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!

• 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. – Michael Greinecker Jun 6 at 22:47
• 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. – James_ Jun 7 at 8:27

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.