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minimum per person transaction cost

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Four people:

Person A whose profit is 84X-6X^2
Person B whose profit is $30-6X
Person C whose profit is $75-10X
Person D whose profit is $100-8X

Person A has property rights, meaning they can set the value of X from 0 to 8. Each person must have the same cost of negotiation with each other. What is the minimum per person transaction cost that would result in no bargaining at all?

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The expert determines the minimum per person transaction cost.

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Hi: I'm raising the bid one last time, but I just want you guys to know this is the most I can afford. Thanks for your help this past weekend, my exam is today.

Four people:

Person A whose profit is 84X-6X^2
Person B whose profit is $30-6X
Person C whose profit is $75-10X
Person D whose profit is $100-8X

Person A has property rights, meaning they can set the value of X from 0 to 8. Each person must have the same cost of negotiation with each other. What is the minimum per person transaction cost that would result in no bargaining at all?

* An OTA asked before what the condition of bargaining is. This is all the information, I don't exactly know what the OTA was asking. The idea is that person A sets X to 7, maximizing profits. Then person A must be compensated if she's going to move away from X = 7. So whats the minimum transaction cost where it wouldn't be worth it for anyone to pay her to move to, say X =6? You could pretty much disregard Person B & D because Person C has the highest damages (10X). So they would be willing to pay the most to get her to change X. If there's any information that seems to be missing, just make and assumption and tell me what the assumption was...

I really need this ASAP...

Assumption:
1. The transaction cost is ...

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