Value & Capital, CHAPTER V, Section 5

Hicks opens this section by stating his conclusion about the first of the two questions raised in the previous section.  His "tentatively negative answer" is as follows:  "If the market for a commodity X is stable, taken by itself, it is not likely to be rendered unstable by reactions through other markets."  He turns next to his second question -- that of whether a market for X that is unstable when considered by itself can likely be made stable by the reactions that happen through other markets.

In order for the market for X to be unstable when considered by itself, a rise in the price of X (with other prices given) will raise the excess demand for X.  (Looking back at the excess demand curve given in section 2 of this chapter, we can see that a rising excess demand curve already puts us in very strange territory.  Demand would have to outpace supply -- and increasingly so -- as the price for X rises.)  Reactions in other markets can only stabilize the market for X if they cause a lower excess demand for X, and Hicks argues that this is very unlikely.  Consider some other commodity Y, and assume for now that there are no income effects.  If Y is a substitute for X, a rise in the price of X should increase the excess demand for Y, thereby raising the price of Y;  this in turn should increase the excess demand for X.  If Y is complementary with X, a rise in the price of X should lower the excess demand for Y, thereby lowering the price of Y;  but because of the complementarity, this should increase the excess demand for X.  So in both cases the indirect reactions should increase the excess demand for X.  Thus, Hicks concludes, a market for X that is unstable, when taken alone, must be even more unstable when indirect effects are considered.

Hicks then goes on to acknowledge that this argument is not conclusive, because of potential complications when more than one other market is considered as well as the potential of income effects.  Hicks notes that the X-market will only be unstable to begin with, taken by itself, when income effects are large.  And if income effects tended to increase the demand for X when the price of X goes up, a similar effect could be possible when the price of Y changes.  As a result, the Y-market could exercise a stabilizing influence on an X-market that is unstable when taken by itself.  Hicks downplays the importance of this possibility but notes it as a possible exception to the rules he intends to set out in the next section of this chapter.

Hicks summarizes his conclusions about stability as follows:

There is no doubt that the existence of stable systems of multiple exchange is entirely consistent with the laws of demand.  It cannot, indeed, be proved a priori that a system of multiple exchange is necessarily stable. But the conditions of stability are quite easy conditions, so that it is quite reasonable to assume that they will be satisfied in almost any system with which we are likely to be concerned.  The only possible ultimate source of instability is strong asymmetry in the income effects. A moderate degree of substitutability among the bulk of commodities will be sufficient to prevent this cause being effective.

Finally, noting that if a system of exchange is stable at all it is likely to be perfectly stable, Hicks considers it "quite justifiable" to proceed to investigate how a perfectly stable system of multiple exchange reacts to changes in prices.