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!