Value & Capital, CHAPTER VIII, Section 4

This section begins by asserting that the previous discussion of stability is sufficient to conclude that "a perfectly stable system of production equilibrium is a reasonable hypothesis."  The discussion then assumes that such a system exists and proceeds to examine its properties.  The rules derived in Chapter V for a general equilibrium system still apply, with some additional interpretation needed.

With a stable system, an increase in the demand for any commodity must raise its price (in terms of the standard commodity).  Conversely, an increase in the supply of any commodity must lower its price.  These properties hold for both factors and products.  The extent of such a price change depends on the degree of substitutability in the system.  This makes sense, since if it is easy to find a substitute for a commodity for which the demand increases, then some of the demand can be accommodated by the substitute (in other words, the given causes of increased demand might have caused an even greater demand had a substitute not been readily available).  Factors and products are considered to be in a relation of substitution.  "Thus, the more elastic the marginal productivity curve of any factor in terms of its product, the less will the price of any commodity (factor or product) be affected by a change in the demand (or supply) of it."  Again, this makes sense, as we may think of a little bit of the factor as "going a long way" in production of the product when the marginal productivity curve is highly elastic.  To look at it another way, a highly elastic curve has large quantities of product associated with small changes in price;  therefore a small change in demand must be associated with a very small change in price.

The discussion also points out that the effects on prices for various commodities that will result from a change in the supply or demand for some commodity depend "primarily on whether these other commodities are substitutes or complements for the first."  This is elaborated as follows:

To a first approximation, we may say that a rise in the price of a commodity X will be accompanied by a rise in the prices of all those goods which are directly substitutes for X, and a fall in the prices of those goods that are complementary.  But in the second place, we may have to allow for indirect effects through other prices ... . If a good is such that it is at the same time a direct substitute for X, and the complement of a substitute, the direct and indirect effects will pull in opposite directions.

Finally, "in the third place," there may be income effects.  A change in price may make some people richer and others poorer, and the overall effects on supply and demand may not cancel out.  The section closes by noting that

It is very difficult to say anything in general about this income effect;  sometimes its working can be guessed, but very often it can only be treated as a source of random error.

Value & Capital, CHAPTER VIII, Section 3

This section continues the analysis of the equilibrium of production, examining the stability of the equilibrium.  Because this analysis concerns the stability of markets, much of the book's earlier investigations can be applied here.

The previous chapter examined the effects of a change in price on the behavior of a single firm;  here we are interested in the effect on a group of firms.  As the author points out, "For the most part, this effect can be got by aggregating the effects on single firms, as we found we could aggregate the effects on private individuals; so far the group must obey the same laws as the single firm."  The complicating factor occurs when "the change in prices has the effect of altering the number of firms producing a particular commodity."  Hicks calls this "a notoriously tricky matter" and proceeds by considering two cases:  one in which the price change stimulates a new firm to begin production of a commodity X by using entrepreneurial resources that had not been used before, and a second in which such a firm takes entrepreneurial resources that previously had been used to make other products and transfers them to the production of X.  In the first case the production creates a new source of supply of X and a new source of demand for the factors used to produce X.  In the second case, the shift to production of X means that the supply of certain other products may diminish;  similarly, the demand for factors used to produce those other products may also diminish.  Hicks concludes that "in direction of change, though not perhaps in extent, the complications due to new firms are similar in character to those we have already covered."

Hicks argues that the only possible source of instability in the equilibrium of production is, as with exchange equilibrium, the presence of strong asymmetry in income effects.  This would imply, for example, (using the language of Chapter V) that "the sellers of X will have to be much more anxious to consume more X when they become better off than the buyers of X are."  In considering how likely it is for such an asymmetry to cause instability, Hicks notes that (as seen in the previous chapter) supply and demand from firms are not subject to income effects.  Therefore he proceeds by separately considering four different markets:
(1) The markets for products.  Here a fall in price makes consumers better off and entrepreneurs worse off;  therefore income effects exist on both sides here.  As with pure exchange, instability is only possible if the product in question is an inferior good, or if it is consumed to significant extent by the entrepreneurs.  Even if these conditions exist, however, the market will only be unstable if these effects dominate the substitution effects.  In the present case we have the substitution effects from consumers choosing between the given product and other commodities, and we also have the effect on production, which, as we saw in a previous section acts as a substitution effect.  Both of these effects work toward stability.
(2) The markets for factors.  Here a fall in price makes the suppliers of the factor worse off, while making the entrepreneurs who purchase the factor better off.  Hicks argues that the specifics of this case are likely to cause an income effect that could tend toward instability;  again, however, there are the stabilizing effects of both substitution by individual consumers (between leisure and consumption, for example) as well as the effect from production.
(3) The markets for direct services.  Here there is no production, so these markets work exactly as described for exchange.
(4) Markets for intermediate products.  In this case both the supply and demand come from firms, so there is no income effect;  hence these markets are necessarily stable.

Summarizing all these considerations, Hicks concludes that the situation is similar to that of the equilibrium of exchange, but in the present situation the absence of income effects leads toward stability.  Any danger of instability is concentrated in the markets for factors.  The section closes by examining the question of how likely it is that an instability in the factor markets could cause instability in the system as a whole.  His answer is as follows:

It would seem that it is not at all likely.  For we must always remember that the predominant relation on the technical side between factors and products reckons as a relation of substitution, and that it is usually a strong relation.  The possibility of considerable changes in the rate of conversion of factors into products as a result of quite small changes in relative prices is a strong stabilizing element.  It is this more than anything else which gives us ground for supposing that the general equilibrium of production will be stable in most ordinary circumstances.

Value & Capital, CHAPTER VIII, Section 2

To examine the workings of an economic system with both private individuals and firms, this section starts from the points of view of the private individuals and of the individual entrepreneurs who run the firms.  Every individual is assumed to have resources of one or both of the following two types:  (1) factors of production, which can be bought and sold on the market, and (2) entrepreneurial resources, which cannot be traded, but which can be used, in combination with the various factors, to produce marketable products.  Just because individuals have these entrepreneurial resources, however, does not mean they will necessarily use them;  it must be the case that using them will generate a positive surplus, given the market prices for the factors and products.  If so, such an individual will become an entrepreneur and use his resources to maximize the surplus.  Doing so will determine the individual's demand for factors and supply of products.  The surplus thus generated is then available for the entrepreneur to use (along with his other income) for consumption as a private individual.

A private individual, who either does not possess entrepreneurial resources or does not find it worthwhile to use them, has to decide how much of his supply of each factor he will sell and how much of each commodity he will purchase.  Again, the system of prices determines these decisions.

Hicks summarizes the workings of this system as follows:

Taking entrepreneurs and private individuals together, the demands and supplies of all sorts of commodities are determined, once the system of prices is given.  Strictly speaking, we have to distinguish four kinds of markets:  (1) the markets for products, where demand comes from private accounts (of private individuals and entrepreneurs), supply comes from the business accounts of entrepreneurs (that is to say, from firms); (2) markets for factors, where demand comes from firms, supply from private accounts; (3) markets for direct services, where supply and demand both come from private accounts; (4) markets for intermediate products, which are products for one firm and factors for another, so that supply and demand both come from firms.  In all kinds of markets, however, supply and demand are determined, once the price-system is given.

Hicks closes the section by noting briefly that, as in the theory of exchange, we take one of the commodities as a standard, and, if the number of commodities is n, we have n - 1 equations to determine the prices of the other commodities in terms of the standard.