All sides agreed that Byng had not acted unreasonably.

All sides agreed that Byng had done the very best he could to lift the siege and

all sides agreed that is was very unlikely that he would be able to lift

the siege with the leaking, unsuitable boats that he had at his disposal.

Nonetheless, Byng was court martialed for failure to do his utmost to relieve the

garrison at Minorca. In 1757, after a court martial, he was

shot for dereliction of duty. This raised quite a fuss because it

seemed the thing had been shot for offenses that certainly did not rise to

the level of seriousness that would, would deserve the extreme penalty that he

received. And in the midst of the controversy, the

great French writer, Voltaire, whose picture you see on the slide.

Had one of his characters say, memorably, in Britain, it is thought well to kill an

admiral from time to time to encourage the others.

So, let's talk about probability scaling a little bit.

If exchange or liability worked perfectly, that is, if everybody who

imposed a cost were identified and brought to pay compensation to the person

to whom they had inflicted a cost. If the system of exchange or the system

of liability worked perfectly, then every, and every cost imposer would have

an incentive to impose cost only where the cost imposition pays for itself.

That is to say, where the cost imposer derives more benefit, or economic value,

from imposing the costs than the costs that he's imposed upon his victims

itself. If that is the case, then it's possible

for the cost imposer to fully compensate the cost bearers for the costs that they

have born, and still have a little bit left over for himself.

That's what the next slide suggests. So that in this circumstance, cost

imposers, under perfect conditions, commit only what we might call efficient

acts of costs imposition. That is, acts of cost imposition that

produce greater economic value for the cost imposer then they produce economic

cost for the cost bearers. If a cost imposition is efficient, then

social welfare, measured by economic value, is increased by the commission of

the cost imposition, or the commission of the tort.

Because more social value, more economic wealth, has been created by the tort

itself, then cost has been created on the part of the people who have suffered as a

result of the torturous activity. And this leads to an efficient amount of

cost imposition, that is, the amount of cost imposition that maximizes the total

value of all property rights to the people who hold them.

But then the question arises, what if some cost imposers aren't caught and

therefore never have to pay compensation? Let's discuss a simple example of such a

situation. Suppose that there are a whole group of

cost imposers in our example, a whole range of steel plants, maybe 20 or 40 or

50 of them. And let's suppose every one of these cost

imposers is identical in the sense that each one imposes $100 cost on the victims

of their cost imposition. That is, the value of the good health

taken by each and every one of these 50 plants, let us say, is equal to $100.

But let's also assume that only one such factory in five is ever brought to the

bar of justice and made to pay compensation to the people who have borne

costs as a result of this activity. This means that the probability that any

one imposer will ever have to pay the fine is 1 out of 5 or 0.2.

So, the probability that I've indicated on the slide of 0.2 represents the

probability that any particular cost imposer will be the unlucky one who is

brought to bar and thus made to pay compensation.

Now, suppose some unlucky steel firm, the 1 in 5, is actually caught, actually

sued, and actually brought to bar in a tort liability suit for the damages that

that cost imposer has imposed. Recall that the cost imposition was at

the level of $100. So, if the liability judgement for this

cost imposer were to perfectly reflect the costs that the imposer had imposed on

his victims, then the liability price would be $100.

But if the liability price is $100, then in the future, because only one steel

plant in five is ever apprehended and made to pay a compensation price at all,

each steel plant faces not the real liability price of $100.

But what mathematicians would call an expected price, which represents the $100

price multiplied by the likelihood that any one steel plant is actually going to

be half, actually going to be made to pay that price.

So, if I believe that there's a one in five chance that I'll pay a 100 dollar

fine or a $100 liability payment. Then, the expected liability payment or

the expected price that I will pay for my cost imposing activity, which recall,

actually imposes a $100 worth of cost on my victims.

The price that I will expect to pay is much lower than that.

It's 0.2 times $100 or $20, and that price is inefficiently low.

If I only have to pay an expected cost of $20 for each act of pollution that

actually imposes $100 worth of cost, then I will impose more pollution than the

efficient allocation would prescribe. That is, I will take some entitlements

for whom I am not, in fact, the highest valuing owner.

Because the price that I actually have to pay for those entitlements is

substantially discounted by the fact that I'm not likely to actually be made to pay

at all. But if the price is scaled upward to

reflect the uncertainly of apprehension and it's scaled upwards, say, to $500.

Then, every steel plant in the future, where there's a 1 in five 5 that any

steel plant will be apprehended and made to pay compensation.

If the price, the liability price, is scaled upward to $500, then the expected

price that faces every steel plant is the probability of 0.2 that any steel plant

will, in fact, be captured and made to pay the compensation.

Multiplied by the now higher liability price for those poor firms that are

unlucky enough to be captured and have to pay compensation, the payment has been

scaled upwards to $500. So, 0.2 times 500 produces an expected

price of $100 in the future for every steel plant that pollutes.

Since each steel plant, by assumption, is polluting to the effect of $100 worth of

cost, then under this new scheme, where the unlucky steel plant which is caught

has to pay a much larger than $100 liability price.

The effect of this probability scaling have been to face each steel plant in the

future with an expected price that is exactly equal to the damages that its cos

imposition will actually impose, okay? So, if we abstract away from attitudes

about the riskiness that this situation poses for firms and we assume that firms

will behave the same way in the face of an expected price.

That they would behave in the face or a certain payment equal to the expected

price, then, cost imposers, under the higher penalty, will again impose only

those costs that pay for themselves. Just as they would under perfect

conditions, despite the fact that only some and perhaps a very few cost imposers

are ever caught or made to pay. And those that do pay will be made to pay

more, perhaps much more than would be justified by their own cost imposition so

as to provide the proper incentive for those who escaped the requirement of

payment. So, by scaling the probability up to

reflect the uncertainty that any given steel firm will be made to pay, we single

out a particular few of the steel firms who are unlucky enough to be the 1 in 5

who are caught. And we charge each of those steel firms a

liability price that is much greater than the actual liability, excuse me, the

actual level of the costs that the steel firm has imposed upon other people.

All steel firms impose a $100 cost, but the 1 in 5 that is caught has to pay a

$500 liability price, a disproportionate liability price.

So, they are punished disproportionately, the unlucky few, and perhaps very

disproportionately for what they have actually done.

So as to encourage the other steel plants who have been lucky enough to evade

punishment just like the unfortunate Admiral Byng.

I see I've spent a little bit more time talking about this than I thought I would

and so I'll consider the fourth of our possible solutions to the externality

problem in the next lecture.