A firm in perfect competition creates a new process that will lower its costs.  The firm has an employee who threatens to tell all other firms in the industry about how to implement this new technique. Economically speaking, will the firm be able to bribe the employee not to tell?

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I have added to your question because I recognize it as one that is sometimes seen in economics classes.  I hope this is what you were asking.

The firm in perfect competition will have an incentive to bribe the employee.  If they can keep the secret, they will make an economic profit, which is not typically possible in perfect competition.  They will be (economically speaking) willing to pay anything up to the amount of economic profit they are making.  

The employee can take the bribe or not.  Either way, he or she will make money.  If the employee (we'll say "she" here) sells her secret to all the firms in the market, she will get the same amount of money as if she takes the bribe from her firm.  This is because all of the firms in the market will pay as much as the economic profit they would gain.  Their economic profit would be equal to that of the dishonest employee's firm if it were to be able to keep the secret.

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