If you developed a new technology in a perfectly competitive market, what would be the best number of firms to sell your secret to? Assume that those who get the info keep the secret instead of selling it to still others.  Also assume that your new technology reduces the cost of production.

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This question assumes that I am an individual working for a company in a perfectly competitive market.  I know the secret of the new method but I do not benefit from it.  Therefore, I want to sell my secret to some number of other firms in the market.

In this case, I am essentially a monopolist.  Only I have the information  and I can sell it to whoever I want.  If I am in a monopoly, I will want to sell the secret up to the point where my marginal revenues equal my marginal costs.  This is the profit maximization point.  Of course, I essentially have no marginal costs for selling this secret.  Therefore, I will sell the secret until my marginal revenue is essentially zero.  This would mean that I would sell it to every firm in the market because they will all need it.  I will only stop selling when no one is willing to pay me anything for the secret.

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