Value & Capital, CHAPTER VIII, Section 6

This section examines the effects of an increase in the supply of some factor of production A. When the supply increases, without an increase in demand, the price must fall.  The techniques covered in previous sections can allow the effects on other prices to be worked out as well.

The text calls attention to one type of price effect it calls "particularly interesting."  This is the case of the effect on the price of some other factor of production that is used in the same industry or industries as factor A.  One possibility is that this factor, call it B, is complementary to factor A, and indeed, it has been pointed out previously that complementarity is the most likely relation among factors employed together in production.  The text notes that the direct effect in this case is to raise the price for B;  this makes intuitive sense, as the increased supply of A will lead to an increased quantity being used in production, which increases the demand for B.  But the text also notes that an important indirect effect will work in the opposite direction;  namely, the product produced from A and B is in a sense a substitute for them.  Hence B is a substitute for a substitute of A, which will tend to make its price fall.  Therefore

The net effect on the price of B is thus compounded out of two contrary tendencies, a direct effect tending to raise it, an indirect effect tending to reduce it;  either may be dominant.

If A and B are substitutes, then the combined effects will tend to reduce the price of B.

The section closes by noting that complementary factors are the commodities most likely to increase in price when the supply of a factor increases.  Even here, however, such a price

will only actually rise if the prices of their common products are little affected, that is to say, if the demands for the products are fairly elastic, or the products are good substitutes for other commodities. 

Value & Capital, CHAPTER VIII, Section 5

This section gives several examples of the kinds of analysis made possible by the results of preceding sections, specifically looking at what happens when there is an increased demand for a product.  (The next section will look at what happens when there is an increase in the supply of some factor of production.)

An increased demand for some product X will cause the price of X to rise and, in fact, will have a general tendency to raise prices "throughout the whole system."  Unless X is "a commodity of very great importance," however, the observed price increases may not be significant except for those commodities that are "nearly related" to the product X,   These commodities include factors employed in the production of X.

The increase in demand for X will only cause prices to decline for commodities that are "directly or indirectly complementary with X."  The author divides the complements into three groups as follows:
(1) Commodities complementary with X in consumption -- if the demand for X rises without a corresponding increase in demand for one of these complements, such a complement's price will tend to decrease, although the author notes that, in practice, there may be an increase in demand that masks the tendency toward a price decline.
(2) Products complementary with X in production -- products produced jointly with X will increase in supply as X increases in supply.  Again, absent an increase in demand for the complement, its price will fall.  (The author refers to this as "the familiar text-book case of wool and mutton.")
(3) Factors regressive against X -- As noted earlier in the book, regression is more plausible in the case of joint production than when there is a single product.  Here, the author notes that if any of the joint products are substitutes for X, their production will decrease, and hence the demand for factors needed to produce them may decrease as well.

The indirectly complementary commodities mentioned earlier are "either substitutes of the direct complements, or complements of the direct substitutes (whose prices rise)."  The latter includes such commodities as those that are "complements in consumption of other products whose prices had risen because they needed in their production some of the same factors as were needed for the manufacture of X."  The former includes factors of production for commodities complementary in consumption with X, as well as products for which "production is facilitated" by the decreased prices of these factors.

For those commodities the author calls "remoter indirect complements," the overall prevalence of substitution in a system will tend to "swamp much indirect complementarity."  Hence it is unlikely that their prices will fall.

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.

Value & Capital, CHAPTER VIII -- THE GENERAL EQUILIBRIUM OF PRODUCTION, Section 1

The opening paragraph of this section summarizes what has been covered in the book up to this point.  Chapters I-III explore "what determines the equilibrium of the private individual, and how he may be expected to react to changes in prices."  Chapters IV and V use the insights from the previous chapters "to elucidate the working of an economic system" consisting only of private individuals and in which the exchange of existing goods and services is the only economic activity. Chapters VI and VII introduce "a new kind of economic unit, the firm" and describe how a firm will conduct itself in the market.  At this point the stage is set "to examine the working of an economic system containing both kinds of units, private individuals and firms; so that the price-system does not only regulate exchange, but also regulates production."

Not surprisingly, the author, Sir John Hicks, calls the General Equilibrium of Production "an hypothesis of much wider applicability than the General Equilibrium of Exchange."  There are "quite a number" of economic problems where it can be applied safely, although it is possible to misuse it. In fact, Hicks claims that "the misuse of this system is one of the most fruitful sources of error in economic theory."  The reasons for this have to do with the areas of the economy that it abstracts away.

The section closes by enumerating the three "main deficiencies" of the system of the General Equilibrium of Production.  The first is that it leaves out the possibility of monopoly and imperfect competition.  The second is that "it abstracts from the economic activity of the State."  The third is that "it abstracts from capital and interest, saving and investment, and all that complex of activities ... earlier ... called 'speculation.'"  The book will treat this final deficiency in later chapters.

Value & Capital, CHAPTER VII, Section 6

Having treated some special cases in earlier sections, Chapter VII concludes in this section by summarizing what is known about the general case of a firm employing any number of factors to produce any number of products.  The summary still assumes that, "the factors ... co-operate with a fixed productive opportunity of limited capacity, so that the condition of increasing marginal cost is satisfied."  The discussion looks at what happens when a price of either a factor or a product changes (with all other prices being unchanged).

If there is a fall in price for some factor A, then the demand for A must increase.  If this happens, it must be balanced somehow -- either by the supply of some products increasing, or the demand for some other factors decreasing, or both.  Hicks goes on to explain:

The typical result of a fall in the price of a factor is then this:  that the supplies of products will expand, and the demand for other factors will expand too.  But to each of these general rules a limited amount of exception is possible, when the fixed resources are influential enough;  some factors may be substitutes for the first factor, some products may be regressive against it; the demands for substitute factors, and the supplies of regressive products, will decline.

Hicks explains in a footnote that regression seems to be more plausible in the multiple-product case than the single-product case.  If factor A plays an important role in the production of product X, then we may expect the output of X to increase when employment of A increases.  "But if the entrepreneur's fixed resources are devoted more to the production of X, they will be less available for the production of Y.  Thus A and Y may be regressive."

If there is a rise in the price of some product X, then the supply of X must increase.  Again, this effect must be balanced, and in this case it will be by an increase in employment of factors, a decreased output of some other products, or both.  Hicks also explains that

There are essentially the same reasons for expecting complementarity to be dominant among products as for expecting it to be dominant among factors (all the products must be complementary if the contribution to production of the entrepreneur's fixed resources is negligible).  Thus, though exceptions are possible, it is likely that the outputs of most of the other products will tend to rise.

Thus we would typically expect that an increased price of one product will cause an increased supply of other products and an increased demand for the factors.  "Substitute products and regressive factors will only be possible to a limited extent."

Although not stated explicitly, one can conclude that a price change for either a factor or product in the opposite direction of those assumed in the text will drive results in the opposite directions of those noted.

Hicks concludes by noting that these principles for the market conduct of a firm differ from those governing the behavior of an individual in two important ways:  (1) the income effect is absent, and (2) the general tendency will be for factors employed by the same firm to be complementary and for products jointly produced by a firm to be complementary.

This concludes Chapter VII.  Thank you for reading.

Noted in passing:  I am writing this post on the morning after Britain's vote to leave the European Union.  I wonder what Sir John Hicks would have made of this situation.  On the one hand, I tend to believe that he would generally support free trade and the economic integration facilitated by the EU.  On the other hand, some things I've read make me believe he had a tendency at times toward nationalist views, and I do think this vote was motivated largely by nationalism.