The Cambist and Lord Iron: A Fairy Tale of Economics

“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.