Think about the oldest and most familiar principles of American law, property and proportional liability, in a new and surprising way, and learn to apply economic reasoning to an especially important and interesting aspect of life.

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Property and Liability: An Introduction to Law and Economics

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Think about the oldest and most familiar principles of American law, property and proportional liability, in a new and surprising way, and learn to apply economic reasoning to an especially important and interesting aspect of life.

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Property

Property is where law and economics meet, but it's not a simple concept. Property is not an object or a relation between people and objects, but a set of rights, relations among people over who is to control each of the many uses to which objects can be put. Different people may control different uses of an object, that is, have different property rights over its various uses, at the same time, or control the same use of the object at different times. When new uses create disputes, the law must define new property rights and allocate them initially to resolve the dispute – someone must be deemed to have won the dispute and be given initial ownership of the new rights. But once the former disputants are allowed to trade these rights among themselves, surprising results follow.

- Richard AdelsteinProfessor

Department of Economics

Hi, everybody. Welcome back.

When we last left our heroes, Tom and Alex, they were entering the courtroom to

litigate their dispute over the use of Rachel's alcove in Tom's house to test

sirens from 5:00 to 8:00 in the evening hour.

We'll recall what's at stake as well. They're arguing over the ownership of a

particular property right to Tom's house, the right to test sirens in Rachel's

alcove in the hours from 5 to 8. If Tom wins the case, he'll get the arrow

and he'll be able to test the sirens and not have to compensate Alex for the costs,

for the discomfort, the disutility, that the testing of the sirens imposes upon

Alex. On the other hand, if Hamilton wins the

case, then he'll be able to exercise that property right to Rachel's alcove,

negatively, by preventing Tom from testing the sirens in the alcove.

So, it does appear that it matters who wins.

It sounds as if, if Tom wins the case, he'll be able to test the sirens, but if

Alex wins the case, he'll be able to stop the testing of the sirens.

Our elderly court observer, Ron, however, has suggested that it doesn't really

matter who wins, and so let's test out his, his claim and see, in fact, if it

does matter who wins. Let's remind ourselves of the numbers at

stake, you will recall what they are. If the sirens are not tested, then the

full value of Tom's entire quiver of property right to this house, Jefferson,

is $1,000 and the full value of the quiver of property rights attached to Hamilton's

house, to Hamilton is $1,200. But if the sirens are tested, the value of

the quiver of property rights for Jefferson, which would now include the

right to test the sirens, rises to $1,500. But if so, the value of the property

rights associated with Hamilton's house falls from $1,200 to $1,000.

Again, Ron claims that it doesn't make any difference who wins the case, so let's

test out that claim by, in fact, seeing what happens in either case with either

outcome. The first outcome to consider would be if

Hamilton were to win the case. Remember what this means, at the end of

the case, the judge would go into her chambers, she would pull out a raw arrow

with no tag on it, she'd put a new tag on this arrow that says, the bearer of this

arrow has the right to test sirens in Rachel's alcove of Jefferson's house from

5 to 8 in the evening. And if Hamilton wins the case, then the

judge will have given that property right initially to Hamilton.

So, as they walk out of the courtroom, Hamilton has the arrow and Jefferson is at

least initially out of luck. In this initial situation, as you can see,

the full value of Hamilton's quiver of property rights is $1,200 because the

sirens are not being tested. I've indicated that with the locution,

Hamilton is worth $1,200. And similarly, Jefferson's quiver of

property rights, which does not include the arrow about testing those sirens, is

worth a $1,000 to him, as it was before. And so, as you can see, the total value of

the two properties, that is to say the total value of the two quivers of property

rights associated with the two houses, is $2,200 divided a $1,000 for Jefferson and

$1,200 for Hamilton. So, as they walk out the courthouse, it

appears that Jefferson is out of luck. Odd, it occurs to Jefferson, perhaps he

could try to buy the right from Hamilton. After all, it's not illegal to test the

sirens in Jefferson's house. It's only the case that Hamilton now has

the right to stop Jefferson from testing those sirens.

If Jefferson can get Hamilton's consent to transfer the arrow from Hamilton to

Jefferson, then Jefferson will be able to test the sirens.

But because Hamilton's been given the right by the court, the only way that

Jefferson can get the right is to purchase it from Hamilton.

And so, let's see what the purchase possibilities are.

Consider Jefferson. Jefferson is willing to pay anywhere from

0 all the way up to $500 to get the right. The right is worth $500 to him.

If he has it, his quiver of property rights is worth $500 more than if he

doesn't have it. So, he should be willing, if he is what

economists call, rational, to spend up to $500 to purchase that right.

By the same token, Hamilton has the right but the right is only worth $200 to him,

in the sense that if Jefferson has the right and uses it to test sirens, then the

worst that can happen to Hamilton is that he will incur a $200 loss in the value of

his quiver of property rights to his own house.

But since the value of the loss to Hamilton is only $200, Hamilton, if he is

rational, should be willing to sell that right for any sum over excuse me, over

$200. So, Hamilton should be willing to sell for

any sum over $200, and Jefferson should be willing to buy for any sum up to $500.

And so, as you can see, there's a $300 overlap in those range of, of acceptable

prices for the property right to both Jefferson and Hamilton.

So there's room for a deal in the range of prices for the property right between

$200, which is the minimum value that Hamilton will accept and $500, which is

the maximum that Jefferson will pay. Well, suppose they do some bargaining and

they discover that this overlap in their values exists and let's hypothetically say

that they agree to make a deal for the property right at $300.

This means that Jefferson will pay Hamilton $300 and in exchange, Hamilton

will transfer the arrow, the property right to test sirens in Rachel's alcove

from Hamilton to Jefferson. Once that transfer is made, the situation

changes. Now, sirens will be tested because

Jefferson has purchased the right for $300 from Hamilton.

As a result, Jefferson is now worth $1,500 because his quiver of property rights now

includes the right to test sirens but, in fact, he's had to pay $300 in cash in

order to get that property right. And so, if subtract that $300 in cash that

Jefferson has had to pay from the new value of his quiver of property rights, we

discover that Jefferson is now worth $1,200, which is $200 more than he was

worth before, when he didn't have the property right.

What about Hamilton? Well, Hamilton discovers that the property

right is now in Jefferson's hands, and as a result, the sirens are now being tested.

And as we've seen, once the sirens are tested, the value of Hamilton's quiver of

property rights falls to $1,000. But his pain is assuaged by the $300 in

cash that he's received from Jefferson. So,hamilton's worth is the $1,000 in his

quiver, plus the $300 that he's received from Jefferson, and the value of his total

rights is worth $1,300. So, as you can see, if Jefferson buys the

right for $300, the result will be that sirens are, in fact, tested.

Hamilton will be worth $1,300, $1,000 in his house plus $300 in cash.

Jefferson will be worth $1,200, $1,500 in his quiver of rights attached to his house

minus the $300 that he's had to pay in order to get the rights.

As you can see from the numbers, both of them are worth more after the transaction

than they were worth before the transaction.

And unsurprisingly, the total value of the two quivers of rights has been increased

from $2,200 before the sirens were tested to $2,500 once the sirens have been

tested. So indeed, if Hamilton wins the case,

interestingly enough, the final result will be that Jefferson is testing the

sirens anyway, because he's been able to purchase the right to test those sirens

from Hamilton. Suppose Jefferson wins.

In this situation, as we've seen, the judge goes into her chambers, comes back

with an arrow with the label, the bearer of this arrow has to write to test sirens

in Rachel's alcove from 5 to 8. And she gives the right, as [UNKNOWN,

bribery is illegal, she gives the right to Jefferson and now Jefferson walks out of

the courtroom with the arrow in his quiver.

Since he now has the arrow, initially, he will go home and start to test those

sirens. And as soon as he does so, he discovers

that he is worth $1,500. Actually, he knew this, and Hamilton was

worth a $1,000, because he's suffering, the pain and suffering, the $200 worth of

diminution of value that comes from the testing of the sirens.

Notice because Jefferson has the right, the sirens are tested, and when the sirens

are tested, the total value of the two properties rises to $2,500.

So now, symmetrically, we might ask, is it possible for Hamilton to make a deal

symmetrically with the earlier case so as to get that property right back from

Jefferson and for Hamilton to save the quiet of his dinner hour?

And the answer, of course, is no, he wont, and the reason is that Jefferson now

having the right will accept at the minimum, $500 dollars in order to sell it.

The right is worth $500 dollars to Jefferson.

He's the one who can make the money testing the sirens.

And if he has the right, he has the $500 profit that comes with siren testing.

So, if he's going to sell the right, somebody is going to have to make it worth

his while to do so, and they can only do that by offering him more than $500.

But as we've seen, Hamiliton is only willing to offer up to $200 to get the

right because that's the full value of the cost that the siren testing imposes upon

Hamilton. And so, what was a $300 overlap in the

earlier outcome, is now a $300 gap between the maximum price that Hamilton will pay,

$200, and the minimum price that Jefferson will accept, which is $500.

Since Hamilton can't pay enough to pry the right from Jefferson's hands, and put the

right in Hamilton's hands, so he can exercise it negatively, no transaction

will take place at all. The property right which was initially

allocated by the judge to Jefferson will stay with Jefferson and the sirens will be

tested. At the end of day, because there has been

no transaction, Hamilton is worth $1,000, Jefferson is worth $1,500, and the total

value of the two properties is $2,500. So, does it matter who wins?

Well, yes and no. Either way, the right ends up in

Jefferson's hands, the sirens are tested, and the total value of the two properties,

or the two quivers of property rights is $2,500.

But how that $2,500 is divided between Hamilton and Jefferson depends on who wins

the case and initially receives the right. As we've seen, the right is a valuable

object. It's worth, as it were, $300 in social

value. That is, it produces $500 of profit for

Hamilton, excuse me, for Jefferson, and $200 of cost for Hamilton, and the

difference between them is a net gain in social value if the sirens are being

tested. So, that property right has a value of

$300, a social value of $300. When the court awards the property right

to one or another of the two litigants, it's obviously giving either of them, the

winner of the case, something of real value.

And so, it makes sense that the winner of the case will end up with a larger share

of that total maximized value than if that party had lost the case and that's exactly

what happens here. In our numbers, in our hypothetical case,

Hamilton won the case when he won the case and sold the right for $30, the sirens

were tested, but Hamilton had $1,300 of value.

But if Jefferson had won the case, the sirens would still be tested and Hamilton

would have only a $1,000 worth of value. So, how that $2,500 is divided between the

parties, depends on who gets the valuable property right in the first instance and

that person, the one who gets the property right will wind up with a larger share of

the maximized value than that party would have wound up with, had the other side won

the case. And it's not a trick.

That is to say, the same result would apply if we were to change the numbers so

that the higher valuing owner of the property right is not Jefferson, as it was

in our example to this point, but we'll make Hamilton the higher valuing owner of

the property right and see what happens. To do this, I've changed the numbers in

our example. Jefferson's numbers are the same.

Without the sirens, his house is still worth a $1,000 to him.

With the sirens, that is with the property right to test the sirens in his quiver,

the full value of his quiver would be $1,500.

So, again, we'll look at Hamilton. If there are no sirens, Hamilton still

enjoys $1,200 worth of value from the quiver of property rights associated with

this house. But now, we'll make Hamilton's response to

the noise somewhat more serious. That is, we'll increase the cost that the

siren testing imposes upon Hamilton, from the $200 in our earlier example now to

$600, so that if the sirens are tested, the value of Hamilton's quiver of property

rights will drop from $1,200 down to $600. And so, we'll ask, does it still not

matter who wins the case? They go to court and once again, there are

two possible outcomes. Initially, if Jefferson wins, the sirens

are tested and if the sirens are tested, then Hamilton is worth $600.

That is to say, his house is worth 1,200 minus the 600 that comes about from the

siren testing itself and Jefferson's house, the quiver property rights is worth

$1,500 for a total property value of $2,100.

So, Jefferson has the right, the sirens are tested, and now the ball is in

Hamilton's court. Can Hamilton buy the property right from

Jefferson? Well, as we've seen, Hamilton will be

willing to pay anything up to, this is Hamilton, he'll be willing to pay up to

$600 to get that right, because that's the price that's, that the siren testing

imposes upon him, the cost that the siren testing imposes upon him.

Jefferson has the property right and as before, the property right is worth $500

to Jefferson. So, Jefferson will sell it for a value

over $500. And once again, there's an area of

overlap. Hamilton is willing to pay up to $600 to

get the property right, Jefferson is willing to accept anything over $500 in

order to get the property right, so there's a $100 overlap in their two range

of prices, two ranges of prices. So, again, let's hypothesis that Hamilton

purchases the property right to test the sirens from Jefferson for $550.

They'll split the difference between Jefferson's minimum price and Hamilton's

maximum price. So, Hamilton buys the right for $550.

That means that the right is transferred, the arrow moves from Jefferson to

Hamilton. And when Hamilton has the right, the

sirens are not tested. And Hamilton is worth $650, that is the

quiver of property rights to his house is worth $1,200 because the sirens are not

being tested but Hamilton has had to pay $550 in order to get that property right

so he's now worth $650, which as you can see, is more than he was worth before.

Summarily for Jefferson, Jefferson has now sold the property right, the sirens are

not being tested as a result and the value of Jefferson's quiver is a $1,000 because

the sirens are not being tested. But Jefferson is assuaged by the payment

of $550 for the right, so in addition to the $1,000 value of his quiver, he also

takes $550 in cash from Hamilton, and so Jefferson is now worth $1,550, more than

he was worth before. And because of this, the total value of

the two quivers is $2,200, which is greater than the total value of the

quivers had the property right remain with Jefferson.

So, if Jefferson wins the case and is given the property right because Hamilton

values the property right more than Jefferson does, Hamilton will be able to

purchase the property right, get the, the arrow and therefore stop the sirens from

being tested. And because Hamilton is the higher valuing

owner of the property right, when he has the property right, the total value of the

two properties is maximized, in this case, at $2,200.

Now, suppose that Hamilton wins the case, so that, as they walk out of the

courtroom, because Hamilton has the arrow, no sirens are tested.

Hamilton is worth $1,200, the value of his quiver with no sirens, and Jefferson is

worth $1,000, the value of his quiver with no sirens being tested, and the total

value is $2,200. Notice that's the same as the maximum

value that we saw in the other outcome. But here, that $100 overlap that Jefferson

won the case now becomes a $100 gap that Hamilton has won the case, now that

Hamilton has won the case. Jefferson is only willing to pay up to

$500 for a property right that will own him $500, but Hamilton will not sell his

property right for less that $600 because if Jefferson has that right and uses it to

test the sirens, then Hamilton will suffer that $600 cost.

Since Jefferson can't offer Hamilton enough to ply the right from Hamilton

hands, no deal is possible, the sirens are not tested.

Hamilton is still worth $1,200, Jefferson is still worth a $1,000 and the total

value of the two quivers of property rights is maximized at $2,200.

So, does it matter who wins? Again, either way, the right ends up with

the highest valuing owner, whom we'll abbreviate as the HVO, and the total value

of all the property rights in question is maximized.

But how that maximum total value is divided between the parties, as before,

depends on who initially receives the right.

So, next time, we'll formalize this result and call it a theorem.

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