2: Trade and Prices
Trade is the means whereby useful labour-saving tools or amusing luxuries find their way from manufacturer to user.
Trade always entails an exchange of some sort. If there is no exchange, then goods can only find their way to users either by being stolen or given away as gifts. In a perfectly idle society, it might not matter if goods were given away or stolen, but in a busy society when goods are stolen or given away as gifts their price is zero, and their users gain their full value without any of its costs, and their manufacturers and sellers lose the cost of producing them and see nothing of their value - a wholly one-sided transaction.
It is only when both buyers and sellers gain from a transaction that is not one-sided that trade will flourish. In a gift economy, or a theft economy, manufacturers of tools who found themselves gaining nothing from one-sided exchanges would stop making tools, or make them for their own use without offering them for sale. And as a consequence, in the absence of these useful tools, the idleness of a society would fall, and everyone would have to work harder, and everyone would be poorer.
Trade between two toolmakers
We may consider in some detail an example of trade between two individuals, one of whom makes and sells one useful tool, and the other another useful tool, such that both are more idle using both tools than they are if they do not trade, but simply have the use of their own respective tools. Both individuals are assumed to engage in exactly the same pattern of activities as they work to maintain themselves, using their tools in the process to expedite their work.
If two individuals, 1 and 2, who respectively make tool a (an axe) and tool b (a basket), and produce enough to ensure both always have use of both tools, and trade these tools with each other at prices Pa and Pb, then it's possible to examine exactly what's happening in this little trading system.
Since the lifetime of an axe is La, then to ensure that he always has at least one axe, man 1 must produce axes at the rate of 1/La. And if he is to ensure that both men always have an axe, he must produce axes at the rate of 2/La. And since the cost of making an axe is La hours, then he must work at the rate 2.Ca/La producing axes. And if man2 is do do the same making baskets, he must produce these at the rate 2/Lb, and work in their production at the rate Vb/Lb.
The gain (in labour time saved) to man 1 of using an axe is Va, and so over its lifetime La, he gains time at the rate Va/La. And in using a basket, he gains time at the rate Vb/Lb, so that the net rate at which he gains time is Va/La + Vb/Lb. And man 2 will also gain time at the same rate from using his own axe and basket.
In addition, since each is buying the tool that the other makes, and making this purchase once every tool lifetime, man 1 will spend at the rate Pb/Lb buying man 2's baskets. And man 2 will spend at the rate Pa/La buying man 1's axes.
And so the net gain will be the value gained from using the tools minus the cost of making them and the price paid for them. So in the case of man 1, the net gain is
G1net = Va/La + Vb/Lb - 2.Ca/La - Pb/Lb + Pa/La
and the net gain for man 2 will be
G1net = Va/La + Vb/Lb - 2.Cb/Lb - Pa/La + Pb/Lb
The price of tools is here denominated in days of work, and tools are paid for by the buyer in performing this amount of work for the seller. The nature of this and other sorts of money will be considered later.
Assume in case A that Va = 10, Ca = 2, La = 100, and Vb = 4, Cb = 1, Lb = 25, and set Pa = 6, Pb = 2. The dimensions of these variables are days.
G1net = 10/100 + 4/25 - 2.2/100 - 2/25 + 6/100 = 0.20
G2net = 0.20
So in case A, given these prices, both man 1 and man 2 enjoy an equal increase in idleness. But man 1's net money income is 0.06 - 0.08, or -0.02 days per day, while man 2's net money income is +0.02. So man 1 is doing work for man 2 at the rate of 0.02 days per day. This work may be in man 2's tool production, or some other work that he needs to do. When man 1 works at this rate for man 2, man 1's idleness decreases by this amount, and man 2's idleness increases by the same amount.
A different set of prices for the same tools, such as Pa = 8 and Pb = 3, produces a different outcome, case B.
In case B, man 1 ends up less idle than man 2, and man 1 performs 0.04 days of work per day for man 2. The relative prices of the two goods determine who works for who, and how the idle time produced by their tools is distributed between them.
When Pa = 8 and Pb = 2, the net money income of both men is zero, and they do no work for each other. But in this case, man 1's idleness is 0.22 and man 2's idleness is 0.18.
If the two individuals did not trade the tools they made, but simply used the tools they made for themselves then man 1's net gain from making and using axes would be
G1 = Va/La - Ca/La = 0.08
and the net gain for man 2 from making and using baskets will be
G2 = Vb/Lb - Cb/Lb = 0.12
instead of the 0.20 that both enjoy on average through trading their tools with each other. They are better off - more idle - trading than they are not trading.
Another circumstance to consider is where goods are sold at zero price. This is, in effect, what happens when tools are given away or stolen. Both producers will make enough tools to keep both supplied with tools.
In this case no equality of outcome results. And since an equality of outcome was achieved when the price of an axe was 6 hours, and the price of a basket 2 hours, this means that an equality of outcome can only be achieved by selling goods rather than just giving them away.
Useful tools that cost some amount of labour to produce, and save some amount of labour in use, must naturally exchange for some commensurate amount of labour: they have a price in labour. And while the cost and value of any tool are some fixed amount, the price is variable. Useful tools are always tools whose value is greater than their production cost, and anyone who makes such a tool would like to be rewarded with its full value, just as they would be if they were to use it themselves. But anyone who pays a price equal to the full value of such a tool will find that they gain nothing from the transaction. They get from the tool the value they paid for it. But if the price is set at the cost of the tool, then the seller gains nothing from selling it. So the price of goods must generally fall between cost and value if both buyer and seller are to gain from the transaction. Thus where tool price is P, V will be greater than P, and P will be greater than C:
V > P > C
One consequence of this is that goods will usually be sold at a price greater than their production cost. They will be sold at a profit. This profit is inherent in the nature of useful tools, which always have a value greater than their cost, and profit their users in the form of increased idleness.
When a tool is sold at cost, its buyer gains its full value, and its seller gains nothing. And when a tool is sold at its value, its seller gains its full value, and its buyer gains nothing. Somewhere in between these extremes there is a price where both buyer and seller gain equally. The gain in idleness for a buyer of tool t at price Pt is
( Vt - Pt ) / Lt
And the gain in idleness for the seller at this same price is
( Pt - Ct ) / Lt
So when both gain equally
( Vt - Pt ) / Lt = ( Pt - Ct ) / Lt
and Pt = ( Vt + Ct ) / 2
Which might be regarded as the 'fair' price for which a tool should be exchanged.
It might be expected that trading goods at 'fair' prices might result in a fair or equal net outcome, with all engaged in such trade ending up with equal idleness at the end of the day. But this is not the case.
In the simple 2-person trading system just considered, G1net is the gain of man 1 from making and trading tools, and G2net is the corresponding gain to man 2. If both are to gain equally
G1net = G2net
which, when expanded and simplified, reveals
Pa = Ca + ( Pb - Cb ).La / Lb
When prices of tools are set set in this ratio - the 'just' price - the outcome is an equal net increase in idleness. There are a whole set of 'just' prices, of which Pa = Ca, and Pb = Cb - pricing at cost - is one set.
With tool a and tool b, the axe and the basket, the 'fair' price of an axe is (10+2)/2 or 6 days, and the 'fair' price of a basket is (4+1)/2 or 2.5 days. And the 'just' price of Pb, assuming Pa=6, is 1 + (6-2).25/100 or 2 days. The latter are the prices used in case A above, and they indeed result in equal idleness.
The 'fair' price is not the same as the 'just' price. The one is the price which results in a buyer and seller of some good gaining equally from the transaction. The 'just' price is the set of prices which results in an equal gain among all buyers and sellers of all goods.
It is not intended to be meant here that the prices of goods ought to be fixed at 'just' prices, and that any other prices are in some sense unjust. Instead a set of 'just' prices, which produce an equality of idleness, should be seen as a reference point, akin to the zero on the axes of the coordinate system of a graph. If nothing else, with some sets of goods, or some special conditions, it may not be possible to find a set of just prices. 'Just' prices might also be seen as 'central' or 'equality' prices, in that they produce an equal outcome, and generally fall somewhere between the twin extremes of tool costs and values.
There may be some conditions where tools are sold at prices less than their cost, or bought at prices which exceed their value. A business facing bankruptcy may attempt to sell off its goods at whatever price they can get for them. And in extremis, someone may pay well over the odds for goods - as is reputed to have happened when, fleeing defeat in battle, Richard III cried, "A horse! A horse! My kingdom for a horse!" (an offer that no vendor seems to have taken up.)
The Price of Luxuries
The price of luxuries is subject to a similar logic as the price of tools. A high cost luxury will generally be sold at a price somewhere between its cost and its value. The cost of a luxury like a pack of cards is the time it took to manufacture the pack, by cutting out 52 pieces of card, and drawing all the suits on one side. The value to the buyer of this pack is all the hours he will enjoy playing cards with the pack.
There are, however, some fundamental differences between tools and luxuries. There are no gains in time from using luxuries. The 'value' of a luxury is, with respect to a tool, negative. Both buyer and seller use up or lose idle time in making cards and playing card games.
And while a useful tool will very often regularly save the same amount of work (e.g. a bicycle that saves an hour of walking each day), a great many luxuries will use up an indeterminate amount of time. The pack of cards bought in anticipation of numerous card games may slumber unused in a drawer, or be played furiously until dog-eared and bent.
It may be that the price of a great many luxuries is simply the reflection of the intensity of the buyer's wish to own them, quite regardless of how little or how often they might be put to 'use'.
A trade in luxuries and amusements may arise whenever there is sufficient idle time available to manufacture such luxuries, and to enjoy their use. However, since there is no necessity to make luxuries, it may that such trade will not arise at all, or that such luxuries as are made will be given away as gifts, or shared in common.
A secondary economy, trading luxuries, may be quite independent of a primary tool-trading economy. But it is possible that a primary economy may force a secondary economy into existence. For example, if some monopoly toolmaker makes and sells a tool at a price that is near to its value, with labour being the unit of currency, the toolmaker's idleness will rise as purchasers of his tool pay by performing work for him. And as more purchases of his tool are made, his idleness will rise. At first it may be supposed that debtors will act as his servants, perform routine everyday tasks for him. But debtors may also assist him in his tool production work as well, perhaps to the point where almost all production work is performed by them. But once all his work is being performed for him, and he has become almost perfectly idle, further purchases of tools cannot increase his idleness further. It is at this point that he will employ debtors to do quite unnecessary work for him. He may, for example, hire them to play music, or dance. Or he may hire them as ornamental gardeners or sculptors or architects or interior decorators. It may eventually be that almost all the work done for him entails the production of luxury art, sculpture, architecture, furniture, etc, on his behalf. In this process, these various luxury goods would acquire prices. And other equally prosperous toolmakers might also purchase these luxuries, perhaps bidding up the prices of some of them in the process. In this manner a secondary economy of luxury goods would come into existence, with a largely one-way flow of luxuries from tool buyers to tool manufacturers.
Such a secondary economy would collapse if tool prices fell to tool costs - perhaps as a consequence of competition among toolmakers acting to drive down tool prices. When tool prices are driven down, the idleness of toolmakers either does not increase, or increases at the same rate as those of the buyers, and there is no excess profit to spend on luxuries. And when tool prices are driven down, and excess profits are not spent on luxuries, the falling demand for luxuries will result in falling prices of luxuries. So tool and luxury prices will mirror each other.
Goods may acquire prices in a variety of ways. A process of haggling may result in a price being agreed. Or prices may be fixed by some authority at some level.
In practice, in the absence of any compelling authority, prices are likely to find their own level, rising when demand is strong, falling when it is weak.
Monopoly producers are always likely to raise prices as high as they possibly can, and their tool prices will approach tool values. Monopolies may arise in several ways, but the first producer of a new tool will generally hold a monopoly on it. And if he cannot meet the demand for it in the market, a monopolist will be able to push prices up towards value.
High monopoly prices for such tools will attract new producers, eager to share in the gains. However, as new producers appear, and the supply of tools they create begins to exceed demand, their share of the market will fall, and they will respond by dropping their prices slightly to regain market share. Prices will move downwards until those producers with the highest costs are driven out of the market altogether.
So if there are not enough producers of some tool, or - same thing - too many buyers, its price will rise to push some buyers out of the market, and encourage new producers to enter the market. And when there are too many producers, or too few buyers, prices will fall to attract new buyers, and drive high-cost or low-value producers out of the market. In this manner prices will respond to changing circumstances.
A further factor is the amount of money that is in the system. If there is little money around, buyers will not buy - not because they don't think the price is a good price, but because they have no money with which to buy a tool -, and prices will fall. Conversely, if everyone has a lot of money, prices will rise.
In this manner, prices will find their own level. These prices will seldom be just prices. If, however, competition between producers remains strong whatever the price level, prices will tend to be driven down towards cost. And pricing at cost, as already seen, produces a set of 'just' prices.
Author: Chris Davis
First created: September 2008
Last edited: June 2009