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Person B is buying someone else's P Straps and trying to use the sale of the Adamantite Francesca to cover the cost of the P Leather, other materials for the Francesca, and make whatever profit he can. If Person B is lucky, he can find someone (Person C, or perhaps get in touch with Person A) willing to turn his Pterodactyls into P Straps for him, at a lower cost than the P Strap fetches on the Board, but it still increases his overhead.
. . .Persons A and B are trying to sell for the highest they can, while still actually selling their products. Lacking the need to pay off Person C, Person A can sell for less than Person B, often to the point that Person B cannot even make any profit. Person A is still able to make a profit, however, because he's not depending upon someone else to provide materials for him.
Why would Person B do this if he knows he can't compete with Person A's price? He wouldn't. The demand is there, but it's looking for a lower price than is being offered. It won't sell. The supply is not being depleted. If Person A can cut into his price and still make a profit, then so can Person C. And so he will, because if he does not, Person D (whom you conveniently omitted), someone who is willing to take the cut, will.
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The Specailization system prevents other people from intruding into the markets that A, B, and C are operating in, however, for they lack the requisite Specializations. That minimizes the competition, the need, to reduce the prices they are putting them up for. This ends up hurting the market, by reducing the number of sales (fewer can, or want to, pay), thereby reducing the total profit the crafters are able to generate, which reduces the amount they can craft to put up for sale, in a vicious cycle.
Persons A, B, and C are multiple people all competing for each other. You know this, so I'm not sure why you exaggerate the number of people involved. There are multiple Person A's, B's and C's all competing with each other's prices. It really only takes a few to drive prices down. But there are far more than that all competing with each other.