Value & Capital, CHAPTER IV, Section 2

In this section, Hicks begins to outline what he calls a "preliminary survey of the theory of Exchange."  He begins as follows:

Let us suppose that we have to deal with a world where the only objects of exchange are personal services.  The demand for these services will be governed by the laws set out in the preceding chapters;  so will the supplies.  All the complications of production and speculation are eliminated.  If we can get a clear idea of such an economic system, we shall certainly still be a long way from having a realistic model of the actual world; but we shall have a foundation on which to build, and which may be useful in itself for certain limited purposes.

He notes that the economist Léon Walras created the theory of general exchange equilibrium, and explains that he will be summarizing some work of Walras in the same way he previously summarized Pareto's work on the theory of value.

Hicks assumes an elementary case in which there are only two sorts of services and hence only two types of goods to be exchanged.  "Thus every person is either simply a buyer of X and seller of Y, or simply a buyer of Y and seller of X."  If perfect competition is assumed, there is only one price ratio to be determined -- that of X to Y.  The condition that the demand for X must equal the supply of X is available to help determine this price ratio.  Hicks notes that if this condition holds for X, then it must hold for Y as well.  Hicks's earlier investigations explained how the demand and supply for the two goods can be determined for a given price ratio.

Hicks notes that when the argument is extended to more than two goods, the number of prices to be determined will always be one less than the number of goods.  And he explains that if one of the commodities is chosen as a standard of value, then the rate of exchange between any two commodities must always equal the ratio of their prices in terms of the standard commodity.

For if not, one party or the other would always be able to benefit himself by abandoning direct exchange, and splitting the transaction into two parts:  first an exchange of one commodity for the standard, and then an exchange of the standard for the other commodity.

At this stage of the argument Hicks is assuming that the standard commodity has two of the qualities of money -- namely that it is an object of desire and that it is used as a standard of value -- but not any other qualities of money. Thus he is assuming that the standard commodity has "an ordinary place on the scale of preferences of an ordinary individual."  People who come into the market with supplies of the standard commodity may either spend it or reserve some of it as they see fit.