On price

Post-tea, pre-breakfast musings on prices, prompted by Donovan on inflation (of which more in due course).

Let us suppose that there is a world of things out there, things which are sorted into groups like oranges, apples and plums.

Let us suppose further that I have preferences about these things. So maybe I prefer oranges to apples. But we will also suppose that there is some tidy region of the brain which insists on transitivity in such matters, which means that if I prefer oranges to apples, and apples to plums, then I prefer oranges to plums. (Be warned: one can construct scenarios in which transitivity does not work for preferences about people, so maybe transitivity does not always work in real life).

We can then deduce that we can assign prices - positive real numbers - to things, prices which express our preferences. For the purposes of this discussion we exclude the possibility of zero or negative prices.

We might then wonder about the relationship of the price of two oranges to that of one orange. It seems reasonable to require the price of two oranges to be more than that of one orange, but not so reasonable to require it to be double. Which means that we cannot deduce that, while preferring oranges to apples, there will always be some number of apples which I prefer to one orange. The price of an increasing number of apples may converge to some number less than the price of an orange.

But putting that complication aside, one of the reasons for doing all this was to facilitate exchange. How do we bring some order into swapping apples for oranges?

So having constructed prices based on my preferences, we then construct prices based on someone else's. In general, even with a touch of normalisation to try to bring them into line, your prices are not going to be the same as mine. I might think that four apples are worth three oranges while you might think that two apples are worth seven oranges.

The up side of this is that if we swap my four apples for your seven oranges, we are both coming out ahead. I am getting extra oranges and you are getting extra apples. Trade, as one learns in elementary economics, is good for everybody. Everybody comes out ahead.

Then, if I get the idea that the world is full of people prepared to do swaps of this sort, perhaps I am going to adjust my preferences to align with other people's. If I know that you are very keen on apples, I will up my preference for apples in the knowledge that I can always do a good swap with you later.

And how do my preferences vary with my stocks? Does my preference for oranges decline as I accumulate the things? Or their supply? Does my preference for oranges increase as I learn about a world shortage of them? A world-wide failure of the orange crop? Or am I sensible, and just dump the whole orange thing in favour of plums?

Notwithstanding, maybe over time, all this will shake down and a stable, shared exchange rate between every pair of things will emerge. Perhaps there will be special markets specialising in particular sorts of swaps. Special markets with special market days.

Maybe given a bit more time, the local council, or other relevant authority, will invent a special thing called money, and the shared, stable exchange rate between any other thing and money will be its price. We get there in the end.

Perhaps there are people out there who make elaborate models on computers of systems of this sort, full of virtual agents with views about apples and oranges. People who go on to prove various elegant theorems about how systems of this sort pan out over time. Time to my mind being important as these systems do not settle down instantaneously, they evolve over time, in the course of lots of fruity transactions, time during which things may not be as optimal as one might like.

With the take-home being a glimmer of understanding about why one can go to university to learn about these matters and perhaps, afterwards, to write fat books about them.

PS: I remember now a story about trade in some far off island. The trader would come ashore and put up piles of stuff along the beach. He would then go back onto his boat to wait. The islanders would then take up some of the piles of his stuff, replacing them with piles of their stuff. Next morning, the trader would come and collect the piles. If he thought he had come out ahead, he would come back the following year and the whole process would be repeated.