Boats and Docks

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A boat owner is caught in an unforeseeable storm and will lose her boat unless she docks. What happens? If the boat owner docks, the boat will do $500 worth of damage to the dock. If the boat owner does not dock, the boat owner will lose the value of her boat, either $900 or $100.

4. Overall Analysis

What Rule is the most efficient?

1. With all the assumptions in place, all the rules are equally efficient.

2. With high contracting costs, the liability rules are more efficient than the property rules.

3. With imperfect information and high contracting costs, the two sided liability rule is the most efficient.

What are the distributive consequences of each rule?

1. Under the property rules, whoever is enjoined is given the weaker bargaining position.

1. All Assumptions in place

General Rule

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Property rule protection for the dock owner. What this means is that if the boat owner attempts to dock, the sheriff will throw her off.

Expensive Boat

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$900

Game

Boat owner: Do I dock?

Yes

Dock owner: Do I allow the boat owner to dock?

Yes

0, -500 (Enjoined)

Yes, with a contract

-700, 200

No

-900, 0

No

-900, 0

Analysis

Explanation of Pay-off Nodes

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Since the dock is protected under the general rule, the position before bargaining is dock owner at 0 and boat owner at -900. By working together, they can both save $200.

Backwards Deduction

Dock owner: Yes, with Contract

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The dock owner would rather make $200 than $0.

Boat owner: Yes

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The boat owner would rather lose $700 than lose $900.

Equilibrium Outcome

Docked with Contract

-700, 200

Efficiency Outcome

Docked with or without contract

Is the Equilibrium outcome efficient?

Yes

Cheap Boat

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$100

Game

Boat owner: Do I dock?

Yes

Dock owner: Do I allow the boat owner to dock?

Yes

0, -500 (Enjoined)

No

-100, 0

No

-100, 0

Analysis

Explanation of Pay-off Nodes

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Since the dock is protected under the general rule, the position before bargaining is dock owner at 0 and boat owner at -100. The boat owner would be willing to spend up to $100. The dock owner will not accept anything less than $500. There is no opportunity to contract.

Backwards Deduction

Dock owner: No

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The dock owner would rather make no money than lose $500.

Boat owner: Either way

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Either way, the boat owner will not dock and will lose $100.

Equilibrium Outcome

No Docking

-100, 0

Efficiency Outcome

No Docking

Is the Equilibrium outcome efficient?

Yes

Neccesity Rule

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Neccesity Rule: Two Sided Liability (Qualified privelege)What this means is that the dock owner is liable for the boat's damage if he disallows the boat to dock, and the boat owner is liable for the dock's damage if she docks.

Expensive Boat

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$900

Game

Boat owner: Do I dock?

Yes

Dock owner: Do I allow the boat owner to dock?

Yes

-500, 0

No

0, -900

No

-900, 0

Analysis

Explanation of Pay-off Nodes

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The two sided liability rule holds each person accountable for the damage their actions cause: If the boat owner stays at the dock, she is liable for the $500 in damage that she does to the dock. If the dock owner denies dockage to the boat owner, he is liable for the $900 in boat damage that results. Is there opportunity to contract? The boat owner would not be willing to pay more than $500, since that is what she will have to pay if she docks against the dock owner's will. The dock owner will not accept any money under $500, since this is the amount he is due if the boat owner docks there. There is no opportunity to contract

Backwards Deduction

Dock owner: Yes

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The dock owner would rather pay nothing than have to pay $900.

Boat owner: Yes

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The boat owner would rather pay $500 than $900.

Equilibrium Outcome

Docked

-500, 0

Efficiency Outcome

Docked with or without contract

Is the Equilibrium outcome efficient?

Yes

Cheap Boat

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$100

Game

Boat owner: Do I dock?

Yes

Dock owner: Do I allow the boat owner to dock?

Yes

-500, 0

No

0, -100

No

-100, 0

Analysis

Explanation of Pay-off Nodes

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The two sided liability rule holds each person accountable for the damage their actions cause: If the boat owner stays at the dock, she is liable for the $500 in damage that she does to the dock. If the dock owner denies dockage to the boat owner, he is liable for the $100 in boat damage that results. Is there opportunity to contract? The most that the boat owner would be willing to pay is $100; the least the dock owner would be willing to accept is $500. There is no opportunity to contract.

Backwards Deduction

Dock owner: Yes

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The dock owner would rather make no money than lose $100.

Boat owner: No

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The boat owner would rather lose $100 than lose$500.

Equilibrium Outcome

No Docking

-100, 0

Efficiency Outcome

No Docking

Is the Equilibrium outcome efficient?

Yes

Reverse General Rule

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Property Rule Protection for the boat owner.What this means is that the sheriff will not allow the dock owner to kick the boat off the dock.

Expensive Boat

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$900

Game

Boat owner: Do I dock?

Yes

Dock owner: Do I allow the boat owner to dock?

Yes

0, -500

No

-900, 0 (Enjoined)

No

-900, 0

Analysis

Explanation of Pay-off Nodes

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The reverse general rule gives property rule protection to the boat owner. The dock owner cannot decide to keep the boat owner from docking. Is there opportunity to contract? The least the boat owner is willing to accept is $900, which is the cost of the boat. The most the dock owner is willing to pay is $500, which is what he pays if she docks. There is no opportunity to contract.

Backwards Deduction

Dock owner: Yes

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The dock owner has no choice under the rule.

Boat owner: Yes

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The boat owner would rather pay nothing than pay $900.

Equilibrium Outcome

Docked

0,-500

Efficiency Outcome

Docked

Is the Equilibrium outcome efficient?

Yes

Cheap Boat

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$100

Game

Boat owner: Do I dock?

Yes

Dock owner: Do I allow the boat owner to dock?

Yes

0, -500

No, with contract

200, -300

No

-100, 0 (Enjoined)

No

-100, 0

Analysis

Explanation of Pay-off Nodes

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The reverse general rule gives property rule protection to the boat owner. The dock owner cannot keep the boat owner from docking. Is there opportunity to contract? The most the dock owner is willing to pay to get the boat to leave is $500. The least the boat owner is willing to accept to leave is $100. Therefore, there is opportunity to contract. Splitting the gains to trade, the dock owner can pay the boat owner $300 to leave. This will leave the boat owner with a net profit of $200.

Backwards Deduction

Dock owner: No with contract

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The dock owner would rather pay $300 than pay $500.

Boat owner: No with contract

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The boat owner would rather gain $200 than lose $100.

Equilibrium Outcome

No Docking with contract

200,-300

Efficiency Outcome

No docking, with or without contract

Is the Equilibrium outcome efficient?

Yes

3. Imperfect information

Neccesity Rule

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Neccesity Rule: Two Sided Liability (Qualified privelege)What this means is that the dock owner is liable for the boat's damage if he disallows the boat to dock, and the boat owner is liable for the dock's damage if she docks.

Game

Expensive Boat

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$900

Boat owner: Do I dock?

Yes

Dock owner: Do I allow the boat owner to dock?

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The dock owner does not know which game he is playing

Yes

-500, 0

No

0, -900

No

-900, 0

Cheap Boat

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$100

Boat owner: Do I dock?

Yes

Dock owner: Do I allow the boat owner to dock?

r

The dock owner does not know which game he is playing

Yes

-500, 0

No

0, -100

No

-100, 0

Analysis

Explanation of Pay-off Nodes

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The two sided liability rule holds each person accountable for the damage their actions cause: If the boat owner stays at the dock, she is liable for the $500 in damage that she does to the dock. If the dock owner denies dockage to the boat owner, he is liable for either the $100 or the $900 in boat damage that results. Is there opportunity to contract? Since there is imperfect information, there is no opportunity to contract (?)There is no opportunity to contractPlus, high contracting costs prevent contracts.

Backwards Deduction

Dock owner: Yes

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The boat owner would rather pay nothing than something (whether or not that something be $100 or $900).

Boat owner: Depends on value of the boat

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The boat owner knows that the dock owner will allow her to dock. Therefore, if her boat is cheap, she will not dock because she would rather pay $100 than $500; and if her boat is expensive she will dock because she would rather pay $500 than $900.

Equilibrium Outcome

Expensive boat

Docked

-500, 0

Cheap boat

Not Docked

-100, 0

Efficiency Outcome

Expensive boat

Docked

Cheap boat

Not Docked

Is the Equilibrium outcome efficient?

Yes

One Sided Liability Rule

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Unqualified PrivelegeThe dock owner is liable for any damage done to the boat, but the boat owner is not liable for any damage done to the dock.

Game

Expensive Boat

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$900

Boat owner: Do I dock?

Yes

Dock owner: Do I allow the boat owner to dock?

r

The dock owner does not know which game he is playing

Yes

0, -500

No

0, -900

No

-900, 0

Cheap Boat

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$100

Boat owner: Do I dock?

Yes

Dock owner: Do I allow the boat owner to dock?

r

The dock owner does not know which game he is playing

Yes

0, -500

No

0, -100

No

-100, 0

Analysis

Explanation of Pay-off Nodes

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The one sided liability rule holds the dock owner responsible for the damage done to the boat, but does not hold the boat owner responsible for the dock. Is there opportunity to contract? No. High contracting costs disallow contracting.

Backwards Deduction

Dock owner: Either way

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Either way, the boat owner risks losing $400.

Boat owner: Yes

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Since docking incurs no costs on the boat owner, and not docking always incurs costs on the boat owner, the boat owner will always dock.

Equilibrium Outcome

Expensive boat

Either way

(0, -500) or (0, -900)

Cheap boat

Either way

(0, -500) or (0, -100)

Efficiency Outcome

Expensive boat

Either way

Cheap boat

Either way

Is the Equilibrium outcome efficient?

Not always

2. High Contracting Costs

One Sided Liability Rule

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Unqualified privelege. The dock owner is liable for any damage done to the boat, but the boat owner is not liable for any damage done to the dock.

Expensive Boat

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$900

Game

Boat owner: Do I dock?

Yes

Dock owner: Do I allow the boat owner to dock?

Yes

0,-500

No

0, -900

No

-900, 0

Analysis

Explanation of Pay-off Nodes

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The one sided liability rule holds the dock owner liable for keeping the boat off the dock, but does not hold the boat owner liable for damage done to the dock. Is there opportunity to contract? The least that the dock owner would accept would be $500. The most the boat owner would pay would be nothing. There is no opportunity to contractBesides, contracting costs are too high.

Backwards Deduction

Dock owner: Yes

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The dock owner would rather pay $500 than have to pay $900.

Boat owner: Yes

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The boat owner would rather pay nothing than $900.

Equilibrium Outcome

Docked

0, -500

Efficiency Outcome

Docked with or without contract

Is the Equilibrium outcome efficient?

Yes

Cheap Boat

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$100

Game

Boat owner: Do I dock?

Yes

Dock owner: Do I allow the boat owner to dock?

Yes

0, -500

No

0, -100

No

-100, 0

Analysis

Explanation of Pay-off Nodes

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The one sided liability rule holds the dock owner liable for keeping the boat off the dock, but does not hold the boat owner liable for damage done to the dock. Is there opportunity to contract? The least that the dock owner would accept would be $500. The most the boat owner would pay would be nothing.There is no opportunity to contractBesides, contracting costs are too high.

Backwards Deduction

Dock owner: No

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The dock owner would rather make no money than lose $100.

Boat owner: Yes

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The boat owner would rather lose nothing than lose $100.

Equilibrium Outcome

No Docking

-100, 0

Efficiency Outcome

No Docking

Is the Equilibrium outcome efficient?

Yes

General Rule

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Property rule protection for the dock owner. What this means is that if the boat owner attempts to dock, the sheriff will throw her off.

Expensive Boat

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$900

Game

Boat owner: Do I dock?

Yes

Dock owner: Do I allow the boat owner to dock?

Yes

0, -500 (Enjoined)

Yes, with a contract

-700, 200

No

-900, 0

No

-900, 0

Analysis

Explanation of Pay-off Nodes

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Since the dock is protected under the general rule, the position before bargaining is dock owner at 0 and boat owner at -900. Contracting costs deny this situation a contract

Backwards Deduction

Dock owner: No

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The dock owner has no choice.

Boat owner: Either way

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The boat owner will lose the $900 either way.

Equilibrium Outcome

No Docking

-900, 0

Efficiency Outcome

Docked with or without contract

Is the Equilibrium outcome efficient?

No

Cheap Boat

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$100

Game

Boat owner: Do I dock?

Yes

Dock owner: Do I allow the boat owner to dock?

Yes

0, -500 (Enjoined)

No

-100, 0

No

-100, 0

Analysis

Explanation of Pay-off Nodes

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Since the dock is protected under the general rule, the position before bargaining is dock owner at 0 and boat owner at -100. The boat owner would be willing to spend up to $100. The dock owner will not accept anything less than $500. There is no opportunity to contract.

Backwards Deduction

Dock owner: No

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The dock owner would rather make no money than lose $500.

Boat owner: Either way

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Either way, the boat owner will not dock and will lose $100.

Equilibrium Outcome

No Docking

-100, 0

Yes

Efficiency Outcome

No Docking

Is the Equilibrium outcome efficient?

Neccesity Rule

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Neccesity Rule: Two Sided Liability (Qualified privelege)What this means is that the dock owner is liable for the boat's damage if he disallows the boat to dock, and the boat owner is liable for the dock's damage if she docks.

Expensive Boat

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$900

Game

Boat owner: Do I dock?

Yes

Dock owner: Do I allow the boat owner to dock?

Yes

-500, 0

No

0, -900

No

-900, 0

Analysis

Explanation of Pay-off Nodes

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The two sided liability rule holds each person accountable for the damage their actions cause: If the boat owner stays at the dock, she is liable for the $500 in damage that she does to the dock. If the dock owner denies dockage to the boat owner, he is liable for the $900 in boat damage that results. Is there opportunity to contract? The boat owner would not be willing to pay more than $500, since that is what she will have to pay if she docks against the dock owner's will. The dock owner will not accept any money under $500, since this is the amount he is due if the boat owner docks there. There is no opportunity to contract

Backwards Deduction

Dock owner: Yes

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The dock owner would rather pay nothing than have to pay $900.

Boat owner: Yes

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The boat owner would rather pay $500 than $900.

Equilibrium Outcome

Docked

-500, 0

Efficiency Outcome

Docked with or without contract

Is the Equilibrium outcome efficient?

Yes

Cheap Boat

r

$100

Game

Boat owner: Do I dock?

Yes

Dock owner: Do I allow the boat owner to dock?

Yes

-500, 0

No

0, -100

No

-100, 0

Analysis

Explanation of Pay-off Nodes

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The two sided liability rule holds each person accountable for the damage their actions cause: If the boat owner stays at the dock, she is liable for the $500 in damage that she does to the dock. If the dock owner denies dockage to the boat owner, he is liable for the $100 in boat damage that results. Is there opportunity to contract? The most that the boat owner would be willing to pay is $100; the least the dock owner would be willing to accept is $500. There is no opportunity to contract.

Backwards Deduction

Dock owner: Yes

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The dock owner would rather make no money than lose $100.

Boat owner: No

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The boat owner would rather lose $100 than lose$500.

Equilibrium Outcome

No Docking

-100, 0

Efficiency Outcome

No Docking

Is the Equilibrium outcome efficient?

Yes

Reverse General Rule

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Property Rule Protection for the boat owner.What this means is that the sheriff will not allow the dock owner to kick the boat off the dock.

Expensive Boat

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$900

Game

Boat owner: Do I dock?

Yes

Dock owner: Do I allow the boat owner to dock?

Yes

0, -500

No

-900, 0 (Enjoined)

No

-900, 0

Analysis

Explanation of Pay-off Nodes

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The reverse general rule gives property rule protection to the boat owner. The dock owner cannot decide to keep the boat owner from docking. Is there opportunity to contract? The least the boat owner is willing to accept is $900, which is the cost of the boat. The most the dock owner is willing to pay is $500, which is what he pays if she docks. There is no opportunity to contract.

Backwards Deduction

Dock owner: Yes

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The dock owner has no choice under the rule.

Boat owner: Yes

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The boat owner would rather pay nothing than pay $900.

Equilibrium Outcome

Docked

0,-500

Efficiency Outcome

Docked

Is the Equilibrium outcome efficient?

Yes

Cheap Boat

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$100

Game

Boat owner: Do I dock?

Yes

Dock owner: Do I allow the boat owner to dock?

Yes

0, -500

No, with contract

200, -300

No

-100, 0 (Enjoined)

No

-100, 0

Analysis

Explanation of Pay-off Nodes

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The reverse general rule gives property rule protection to the boat owner. The dock owner cannot keep the boat owner from docking. Is there opportunity to contract? The most the dock owner is willing to pay to get the boat to leave is $500. The least the boat owner is willing to accept to leave is $100. Therefore, there is opportunity to contract. Splitting the gains to trade, the dock owner can pay the boat owner $300 to leave. This will leave the boat owner with a net profit of $200. Contract is blocked by high contracting costs

Backwards Deduction

Dock owner: Yes

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The dock owner has no choice.

Boat owner: Yes

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The boat owner would rather lose nothing than lose $100.

Equilibrium Outcome

Docking

0, -500

Efficiency Outcome

No docking, with or without contract

Is the Equilibrium outcome efficient?

No