The Problem of Social Cost 8

The Problem of Social Cost

 

Consider a railway, which is not liable for damage by fires caused by sparks

from its engines, which runs two trains per day on a certain line. Suppose that
running one train per day would enable the railway to perform services worth
$150 per annum and running two trains a day would enable the railway to per-
form services worth $250 per annum. Suppose further that the cost of running
one train is $50 per annum and two trains $ 100 per annum. Assuming perfect
competition, the cost equals the fall in the value of production elsewhere due
to the employment of additional factors of production by the railway. Clearly
the railway would find it profitable to run two trains per day. But suppose that
running one train per day would destroy by fire crops worth (on an average
over the year) $60 and two trains a day would result in the destruction of crops
worth $120. In these circumstances running one train per day would raise the
value of total production but the running of a second train would reduce the
value of total production. The second train would enable additional railway
services worth $100 per annurn to be performed. But the fall in the value of
production elsewhere would be $110 per annum; $50 as a result of the employ-
ment of additional factors of production and $60 as a result of the destruction
of crops. Since it would be better if the second train were not run and since it
would not run if the railway were liable for damage caused to crops, the conclu-
sion that the railway should be made liable for the damage seems irresistible.
Undoubtedly it is this kind of reasoning which underlies the Pigovian position.
The conclusion that it would be better if the second train did not run is
correct. The conclusion that it is desirable that the railway should be made
liable for the damage it causes is wrong. Let us change our assumption con-
cerning the rule of liability. Suppose that the railway is liable for damage from
fires caused by sparks from the engine. A farmer on lands adjoining the rail-
way is then in the position that. if his crop is destroyed by fires caused by the
railway, he will receive the market price from the railway: but if his crop is
not damaged, he will receive the market price by sale. It therefore becomes a
matter of indifference to him whether his crop is damaged by fire or not. The
position is very different when the railway is not liable. Any crop destruction
through railway-caused fires would then reduce the receipts of the farmer. He
would therefore take out of cultivation any land for which the damage is likely
to be greater than the net return of the land (for reasons explained at length
in Section III). A change from a regime in which the railway is not liable for
damage to one in which it is liable is likely therefore to lead to an increase in
the amount of cultivation on lands adjoining the railway. It will also, of course,
lead to an increase in the amount of crop destruction due to railway-caused
fires.
Let us return to our arithmetical example. Assume that, with the changed
rule of liability, there is a doubling in the amount of crop destruction due
to railway-caused fires. With one train per day, crops worth $120 would be
destroyed each year and two trains per day would lead to the destruction of
crops worth $240. We saw previously that it would not be profitable to run
the second train if the railway had to pay $60 per annum as compensation for
damage. With damage at $120 per annum the loss from running the second
train would be $60 greater. But now let us consider the first train. The
value of the transport services furnished by the first train is $150. The cost of
running the train is $50. The amount that the railway would have to pay out as
compensation for damage is $120. If follows that it would not be profitable to
run any trains. With the figures in our example we reach the following result:
if the railway is not liable for fire-damage, two trains per day would be run; if
the railway is liable for fire-damage, it would cease operations altogether. Does
this mean that it is better that there should be no railway? This question can
be resolved by considering what would happen to the value of total production
if it were decided to exempt the railway from liability for fire-damage, thus
bringing it into operation (with two trains per day).
The operation of the railway would enable transport services worth $250
to be performed. It would also mean the employment of factors of production
which would reduce the value of production elsewhere by $100. Furthermore it
would mean the destruction of crops worth $120. The coming of the railway will
also have led to the abandonment of cultivation of some land. Since we know
that, had this land been cultivated, the value of the crops destroyed by fire
would have been $120, and since it is unlikely that the total crop on this land
would have been destroyed, it seems reasonable to suppose that the value of the
crop yield on this land would have been higher than this. Assume it would have
been $160. But the abandonment of cultivation would have released factors of
production for employment elsewhere. All we know is that the amount by
which the value of production elsewhere will increase will be less than $160.
Suppose that it is $150. Then the gain from operating the railway would be
$250 (the value of the transport services) minus $100 (the cost of the factors of
production) minus $120 (the value of crops destroyed by fire) minus $160 (the
fall in the value of crop production due to the abandonment of cultivation) plus
$150 (the value of production elsewhere of the released factors of production).
Overall, operating the railway will increase the value of total production by $20.
With these figures it is clear that it is better that the railway should not be
liable for the damage it causes, thus enabling it to operate profitably. Of course,
by altering the figures, it could be shown that there are other cases in which it
would be desirable that the railway should be liable for the damage it causes.
It is enough for my purpose to show that, from an economic point of view, a
situation in which there is “uncompensated damage done to surrounding woods
by sparks from railway engines” is not necessarily undesirable. Whether it is
desirable or not depends on the particular circumstances.
How is it that the Pigovian analysis seems to give the wrong answer?
The reason is that Pigou does not seem to have noticed that his analysis is
dealing with an entirely different question. The analysis as such is correct.
But it is quite illegitimate for Pigou to draw the particular conclusion he does.
The question at issue is not whether it is desirable to run an additional train
or a faster train or to install smoke-preventing devices; the question at issue is
whether it is desirable to have a system in which the railway has to compensate
those who suffer damage from the fires which it causes or one in which the
railway does not have to compensate them. When an economist is comparing
alternative social arrangements, the proper procedure is to compare the total
social product yielded by these different arrangements. The comparison of
private and social products is neither here nor there. A simple example will
demonstrate this. Imagine a town in which there are traffic lights. A motorist
approaches an intersection and stops because the light is red. There are no
cars approaching the intersection on the other street. If the motorist ignored
the red signal, no accident would occur and the total product would increase
because the motorist would arrive earlier at his destination. Why does he not
do this? The reason is that if he ignored the light he would be fined. The
private product from crossing the street is less than the social product. Should
we conclude from this that the total product would be greater if there were no
fines for failing to obey traffic signals? The Pigovian analysis shows us that it
is possible to conceive of better worlds than the one in which we live. But the
problem is to devise practical arrangements which will correct defects in one
part of the system without causing more serious harm in other parts.

Conclusion

Notes

See Also

References and Further Reading

About the Author/s and Reviewer/s

Author: international

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