Value & Capital, CHAPTER IX, Section 2

This section discusses the analysis of economic dynamics by exploring the question of whether one could apply static analysis (of the sort presented in the book up to this point) and simply date all the quantities to the same moment in time.  The discussion notes that the main problem with such an approach is that "the adjustments needed to bring about an equilibrium take time."

A rise in the price of a commodity exercises, at once, only a small influence upon the supply of that commodity; but it sets entrepreneurs guessing whether the higher price will continue.  If they decide that it probably will continue, they may start upon the production of a considerably increased supply for a future date.  This decision will affect their current demand for factors;  the current position in the factor markets will thus be governed by the way entrepreneurs interpret the rise in the price of the product.

Similarly, the current supply of a commodity depends not so much upon what the current price is as upon what entrepreneurs have expected it to be in the past.  It will be those past expectations, whether right or wrong, which mainly govern current output;  the actual current price has a relatively small influence.

This is the first main crux of dynamic theory ... 

The author lays out two alternatives for how to proceed:  either incorporate the fact that quantities such as supplies and demands depend as much on expected prices as on current prices, or else "evade the issue by concentrating on the case where these difficulties are at a minimum."  He describes the first alternative as being "the method of Marshall."  He describes the second as
"(broadly speaking) ... the method of the Austrians."

The remainder of this section focuses on this second alternative, and in particular on what some Austrian-school economists called "the stationary state."  Hicks clearly states up front that "it is my firm belief that the stationary state is, in the end, nothing but an evasion" but he believes it to require attention because of the large part it had played in economic thought of the time.  He defines the stationary state as "that special case of a dynamic system where tastes, technique, and resources remain constant through time."  If entrepreneurs expect these constant conditions to remain in effect, then we can expect current prices to be the same as expected prices.  We can conclude that a price system in such a stationary state is the same as the static price-system already studied.  The explanation of this similarity with "the static world" notes the importance of a "'stationary' assumption that capital remains intact."

The discussion then notes that the static theory left out any account of the dependence of input-output (i.e. production) relations on the quantity of capital (in the form of intermediate products).  The author asks how this quantity of capital will be determined, with the answer being "through the rate of interest."  The assumption of a stationary state gives a relation between the (constant) size of the capital stock and the interest rate.  We have a second relation between the interest rate and quantity of capital stock by virtue of the effect of a stationary state on the (constant) level of saving.  This level "depends partly upon the propensities to save of the individuals composing the community, partly upon their real incomes -- and these depend again upon the size of the stock of intermediate products."  Thus there are two equations to determine the two unknowns:  size of capital stock and rate of interest.  While this is "a plausible theory of a stationary state" there are many complications that are left out.

The section closes with a discussion of the various real-world complications that are left out of the stationary state model.  The discussion also highlights the model's questionable assumptions and finishes the section with a withering criticism of the stationary state model.  If one does not assume a stationary state, then it is no longer valid to equate actual prices with expected prices, or interest rates from one period with those of another, or income with product, or money rates of interest with real rates of interest.  While it has always been known that the actual state of a real-world economy is never stationary, "stationary-state theorists naturally regarded reality as 'tending' toward stationariness;  though the existence of such a tendency is more than questionable."  The stationary state theory only "tells us that if we got to a stationary state, then (other things being equal) we should stick;  but it gives us no indication that we are in fact aiming for such a position;  for it can tell us nothing about anything actual at all."

Value & Capital, Part III -- THE FOUNDATIONS OF DYNAMIC ECONOMICS, Chapter IX -- THE METHOD OF ANALYSIS

In the first section of Chapter IX, the author, Sir John Hicks, introduces the subject of economic dynamics.  He describes it as being those parts of economic theory in which every quantity must be time-stamped.  (He actually uses the term "dated" but the concept of something's being time-stamped is probably fairly familiar to us in this age of e-commerce transactions.)  Up to now, the book has been concerned with "economic statics."  So in thinking about quantities of commodities consumed, or quantities of factors used to produce quantities of products, the discussion hasn't addressed questions as to when the consumption happens, or when the factors are available, or when the products will be finished.  In economic dynamics, we do address such questions.

Hicks goes on to explain that his rule of having abstained from looking at time-stamping ("dating") of quantities will have "great advantages" as he proceeds to examine the theory of economic dynamics.  This is because the methods of analysis he used in developing his static theory will be useful in analyzing dynamic problems.  He concludes this section as follows:

It is not obvious that anything like the same methods will do.  Nevertheless, we shall find, as we proceed, that there is a way of reducing the dynamic problem into terms where it becomes formally identical with that of statics.  Thus the results of static theory can be used after all; though almost all of them need drastic reinterpretation.

Value & Capital, Note to Chapter VIII -- CONVENTIONAL OR RIGID PRICES

Chapter VIII concludes with a note that examines what happens when some price is fixed.  Figure 22 shows supply and demand curves (S and D) for a single commodity, with the prices of all other commodities assumed to be fixed.  If the price of this particular commodity were not fixed, then it would move to the level represented by the intersection of the supply and demand curves.

If the price were fixed at a higher level (say at the level OL), then the demand curve implies that only a quantity ON would be sold, even though the supply curve implies that sellers would be willing to sell a quantity LT.  (Note that, by construction, the quantities ON, LP, and MQ are all equal.)  The note then argues that

The situation is therefore identical with that which would have arisen if a price OL had been fixed for buyers only, a price OM for sellers only, the difference between those prices being handed over as a bonus to those sellers who actually do make sales.  (Alternatively, we may suppose that a tax equal to LM per unit is laid upon the commodity, and the proceeds of that tax handed over to the sellers.  A process made familiar to us by the [UK] Ministry of Agriculture!)

The text points out that this construction retains an equilibrium in which supply equals demand, but "we have to sacrifice the rule that there is only one price in the market."  The real price is the assumed fixed price, and the text introduces the term "shadow price" to represent the price determined by equilibrium conditions.  In this context, the shadow price is OM.  The text notes that this shadow price is not the price that the sellers actually receive, so there is no income effect associated with it, but it does govern substitution effects on the supply side.

The text then assumes that demand for the commodity increases (represented by a change in the demand curve from D to D').  If the price remains fixed at OL, the amount bought will increase from LP to LP', and the shadow price will increase from OM to OM'.  The text points out the significance of the fact that the "supply will increase in just the same way (apart from the income effect) as if the actual price had increased from OM to OM'.  That is why the shadow price is important."  Any reactions in the markets for other commodities that are caused by changes in the supply of this commodity "will proceed as if there had been a real change in price; it is only is only reactions on the demand side which are cut off by the price-fixation."

Finally, the text considers an example in which there is "a minimum price for wheat, combined with jut sufficient restriction of supply to make the minimum price effective."  If there is an increase in demand, our model above shows that even though the fixed price doesn't change, there should be an increase in supply (as described by the supply curve).  Because this expansion in supply may come at the expense of some other crops (i.e. lower quantities of these other crops may be supplied), the prices of these other crops may rise, just as if the price of wheat had risen.

The note concludes that "The significance of this proposition (which is equally valid for maximum prices, when all term are reversed) is self-evident.  Price control can damp down a general rise in prices; but, unless it is absolutely complete, it cannot prevent it altogether."

Value & Capital, CHAPTER VIII, Section 7

This section explores in further detail some of the results of preceding sections by examining the role of "the standard commodity" (and considering what happens in the case where this is money).

Previous sections assumed an increase in the supply of factor A or in the demand for product X and examined the effects on the prices of other commodities, depending on whether these other commodities are substitutes or complements of the given product or factor.  The discussion in the previous section implicitly assumed that

... the amount of A offered at given prices increased, and the suppliers demanded nothing but some of the standard commodity in exchange.  If the standard commodity is money, this implies that they hoard all the income which they derive from the new units they supply.  Similarly, in [Section 5 of this chapter] it is implicitly assumed that the new demand is demand in terms of the standard commodity; so that if the standard commodity is money, the new demand comes from dishoarding, not from economizing on other goods.

If instead of making this implicit assumption we were to assume that the changes mentioned above were accompanied by changes in the demands for products, these latter changes would "produce an effect on general prices which goes in the opposite direction from the primary effect."  In particular, suppose that along with the increased supply of factor A there is an increased demand for products. The text argues that "prices in general" will only decrease if there is hoarding.  In other words, unless suppliers keep all their additional proceeds as money, they will spend some of it on products, which will tend to increase prices.  Conversely, suppose that along with the increased demand for product X there is a decreased demand for other products. Unless the increased demand for X comes from some dishoarding, all of the increased demand must be paid for through reduced spending for other products, thus decreasing their prices.

The discussion in the text also makes reference to the possible difficulties of calculating the net effect on prices of a combination of increased supply of a factor and increased demand for certain commodities.  Sometimes this can be simplified by choosing a representative consumption good as the standard commodity.  In other cases, there are obstacles to using this sort of device.  If there are any prices in the system that are fixed in terms of money, "severe intellectual contortions are needed" unless we choose money as the standard commodity.

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.