“What can you possibly mean by 'worth' if not what
you can purchase with it? Five shillings is worth a loaf
of bread, or a cup of wine, or a cheaply bound book of
poetry because that is what it will buy. Your tens of
thousands of negotiable guilders will buy you nine pounds
and
seven shillings because that is what someone will pay.”
Unlike most of what I
have included in this book, this story was deliberately
written to present economic concepts in fictional form. The
interrelated concepts are value and price, their meaning
worked out through three examples, all economic.
The first is the
simplest–value in exchange, market value, price, defined by
what someone else will give you for what you have. That is
the subject of the first example, quoted above.
The second example is
much less clear—the argument does not seem to entirely
convince the Cambist, although, fortunately for him, it does
convince two of the three judges. The Cambist has apparently
calculated the ratio of the life expectancy of the King,
given the life he chooses to lead, to that of a prisoner,
given the life he leads, and converted that into the ratio
between value of a day of the King’s life and a day of the
prisoner’s. How does that work?
The argument starts with
an invocation of the principle of revealed preference—what
people value is measured by what they do. The king
demonstrates that he has a low value for a day of his own
life by his willingness to do things that reduce the number
of days he will live. One might argue, although the Cambist
never actually does, that it is the King who ultimately
controls the prisoner’s life expectancy, hence that
controlling it in a way that makes it longer than that of
the King shows the King values a day of the prisoner’s life
more than a day of his own.
But that misses the
issue of what the king is selling days of life for. By
giving up a day of his own life the King gets the pleasures
of eating, drinking, smoking. He cannot get those pleasures
by giving up a day of the prisoner’s life. He could give the
prisoner those pleasures if he chose, with a corresponding
reduction in the prisoner’s life expectancy. But there is no
reason to expect the King to put the same value on pleasures
to himself and pleasures to the prisoner, so they do not
provide a common unit in which to measure value so as to
compare the value of one day of life to another.
The argument seem to be
based on use value, how much something is worth to an
individual as measured by what he is willing to give up to
get it. But to get relative use values of two different
things you need to observe someone who is choosing how much
of a third thing to give up to get each—which the Cambist
does not have.
The chief objective of
an author is to make a good story, even if, as in this case,
he is also trying to teach ideas to his readers. One of the
judges is the King. His verdict may be unconvincing as
economics but it suggest his dissatisfaction with his own
life of self indulgence. It thus foreshadows what will be
revealed in the story’s ending about the attitude toward his
own life of another libertine.
The third example is the
cost of a soul, although Lord Iron puts the question in
terms of the fair price. The Cambist gives, as his answer,
what it would cost Lord Iron to buy back his own soul. That
can be described as a price, although not a price in
exchange.
The three things the
Cambist is measuring are price, value and cost of
production. In the context of the story they have no obvious
connection with each other. The value of convertible
guilders is independent of both the cost to the Cambist or
Lord Iron of producing them and the value to them of
consuming them. The situation for the other two is a little
more complicated.
In the usual
economic context of a competitive market, on the other hand,
cost, price and value are not only connected, they are
equal. If I can buy bread for a dollar a loaf I will
increase how much bread I consume until the value to me of
one more loaf is a dollar–any less and I am giving up the
opportunity to buy loaves worth more to me than they cost.
Price in exchange equals (marginal) value. If I can produce
bread and sell it for a dollar a loaf I will produce more as
long as the cost to me of producing one more loaf is less
than a dollar. Price in exchange equals (marginal) cost.
P=MV=MC.
Why doesn’t that
relation hold here? Neither the Cambist nor Lord Iron is
producing convertible guilders; for both, cost of production
is higher than the market price. Neither is consuming them;
for both, value in consumption is less than the market
price. Economists, viewing individual actions as rational
behavior, see choice as the solution to a maximization
problem–adjust quantities consumed and produced to maximize
utility. The answer in this case is to reduce consumption
until you cannot reduce it any more because you are down to
zero, what mathematicians call a corner solution (see
figure). Quantity produced is a corner solution as well.
Price in exchange, on the other hand, is nine pounds and
seven shillings for some tens of thousands of negotiable
guilders. It is equal to a value–the value to whatever
buyer, in this case the glassblower’s shop, values the
guilders most, as reflected in what they are willing to buy.[1]
A day of the King’s
life has value in consumption to the king. It has no value
in exchange, because nobody is in a position to buy or sell
it. It does, however, have a cost of production–by reducing
his consumption of food that is tasty but bad for him by,
say, ten thousand calories a year, the king could produce an
extra day of life expectancy. Rational behavior implies that
you increase your production of a good that you yourself
consume as long as the value to you of consuming one more
unit is more than the cost to you of producing it–until cost
and value are equal. It was that equality that the Cambist
used in trying to measure the value of a day of the King’s
life.
Lord Iron’s soul is
of value to both Lord Iron and the Devil. The Devil already
owns it and has no interest in selling, so there is no price
in exchange. The only way Lord Iron can get it is by
producing it himself. He can do that at the cost of living a
humble life and does so, indicating that the value to him of
getting back his soul is at least as great as the cost.
[1]
More precisely, its value to the glassblower’s shop is at
least what the shop was willing to pay. In the model of
perfect competition–an infinite number of buyers and zero
transaction cost–it would be exactly what the shop was willing
to pay.