. 4
( 10)


on the prices of other goods is aggregated in the market so the quantity of
any one commodity that the market as a whole seeks to buy at a given price
depends heavily on the particular pattern of prices prevailing for other
goods. The concept of cross elasticity is of some importance in this con-
Cross elasticity gauges the degree of sensitivity of demand for one
product to price changes in a different product. Supposing there is a
50% rise in the price of college tuition; what can be said about the quantity
of college textbooks that will be bought at a given price? Very likely there
will be a decline. On the other hand, what is likely to happen to the de-
ward-sloping demand curve (for which the value of g is negative), marginal revenue,
therefore, will be less than price by a quantity p/e (disregarding the sign of e). The
more elastic the demand curve, the nearer the marginal revenue curve will lie to the
demand curve.
8 From the formula in the preceding footnote, it follows immediately that at a point
where elasticity is unitary, marginal revenue is zero. A special case is where total reve-
nue is unchanged for all points on the demand curve. For such a "constant outlay
curve," marginal revenue is zero, and elasticity unitary, for all points on the curve.

mand for the services of employment agencies that specialize in jobs for
high-school graduates? Clearly an increase is to be expected. The cross-
elasticity concept·ranks the various possible degrees of relationship between
prices of goods and demand for other goods.
Cross elasticity may thus be either positive or negative. Positive cross
elasticity exists between two goods when a change in the price of one, other
things remaining unchanged, causes the quantity bought of the other to
move in the same direction. This is likely to be the case when most of the
consumers consider the two goods as substitutes for one another. A rise in
the price of the one good would thus stimulate a switch to the other good.
Negative cross elasticity, on the other hand, exists between two goods when
a change in the price of one, other things remaining unchanged, causes the
quantity purchased of the other good to change in the opposite direction.
This is likely to exist where the two goods are regarded by the bulk of con-
sumers as complementary to one another. A rise in the price of one good
tends to raise the price of the group of complementary goods that are used
to satisfy some desire. This tends to reduce the quantity purchased of the
group as a whole and therefore also of each good in the group.
If the consumers relate the goods strongly to each other (that is, if they
are very close substitutes, or if they are almost invariably used together in
consumption), then the cross elasticities also will be of a high (positive or
negative) degree. (A measure of cross elasticity relates the percentage
change in the quantity bought of one commodity to a given percentage
change in the price of the other.) If the relation between the goods is weak,
then the cross elasticity between them will be very low. A price fall in
one good will cause only a slight shift of expenditure away from any one
other good (although the total shift may be considerable).

It must be emphasized that consumer demand constitutes a vibrant,
active market force, with a powerful positive impact on resource allocation,
prices, and other market phenomena. We must not allow the formal pres-
entation of demand analysis to create an image of market demand as being
merely passive, responding to changes in market prices but without itself
exerting any active influence on the market. Nothing could misstate more
grossly the true operation of demand in the market place. While a more
complete understanding of the operation of demand forces in the market
must wait until we discuss the determination of market prices, our discus-
sion of demand cannot close without making clear the positive nature of
this market force.
Consumers are human beings acting purposefully to improve their
positions. At any one time they find themselves able to choose among a

number of alternatives. As acting men they are intent on making sure that
no more desirable alternative exists other than those that they see before
them. To this end consumers are constantly experimenting with new
goods, new brands, and different stores. In selecting from among the avail-
able alternatives those they deem most attractive, consumers are at the
same time rejecting the remaining alternatives. In making these selections
and rejections, consumers are making known to the market the choices the
producers have to choose from. Consumers in the market place are not
only aware of the choices available at current prices but are aware that by
offering producers more attractive prices, they may themselves be able to
secure even more desirable buying possibilities.
Moreover, the true power exerted by demand forces can only be appre-
ciated by mentally relaxing the ceteris paribus assumptions underlying the
demand curve of a given instant. In the ever-changing complex of real
world conditions, consumers continually revise their relative valuations of
available alternatives. Producers are subjected to a steady flow of informa-
tion that apprises them of the most recently expressed preferences of the
market and helps them gauge possible future preferences. As a conse-
quence of changing demand patterns, it happens continually that the bids
made today by consumers, on the basis of yesterday's prevailing prices, pre-
vent all the desired choices from being successfully completed. It becomes
continually apparent to consumers, that is, that they must revise their opin-
ions of the actual choices they are free to make selections and rejections
among. When we have studied the complex of factors that affect the de-
cisions of producers, we will be in a position to understand the constant agi-
tation by which the market seeks to adjust the mutually offered alternatives
of producers and consumers to the ever-changing conditions on both sides
of the market.
It must be stressed once again that market demand does not present
itself as a single homogeneous force. It is not simply a matter of a single
"market" bid being placed for a quantity of a commodity being sold at a
given price. The aggregation of individual demand schedules into a
market schedule, and its expression by the market demand curve must not
mislead one into forgetting that market demand for a given good is the
force felt by the bids of individual buyers. Some of the buyers of the good
are more "eager" than others; that is, some buyers will be more active in
offering producers more attractive alternatives or will be more likely to
accept an alternative that other buyers reject. This must be kept in mind
when interpreting a market curve. For each buyer individually, too, it
must not be forgotten that his "eagerness" to buy a particular commodity
is not homogeneous. The very law of diminishing marginal utility, which
as we found is responsible for the characteristic downward slope of the
individual demand curve, makes implicit in such a curve the fact that buyers

display less "eagerness" for successive single units of the commodity. The
determination of price, we shall discover, depends quite fundamentally on
this "discrete" character of demand, on the fact that bargains are made
not with consumers as a whole but with individual buyers contemplating
the wisdom of acquiring additional units of a commodity.
Finally, we must draw attention once again to the way consumers adjust
to changes in the availability of goods and the consequences of this pro-
pensity for the demand of particular commodities. Suppose a sudden stop-
page occurs in the availability of a particular commodity or service; for
example, a cessation of commuter service occasioned by a strike. Consumers
of this particular service now find themselves barred from a previously avail-
able alternative. This will have an immediate consequence upon the
demand for both related and unrelated goods. Income allocated to com-
muter service most likely will be allocated to services that are substitutes
for commuter service. Taxicab service and car-rental services will now be
patronized by consumers on a larger scale, even at the previous prices. (Of
course, this will tend to exert a pressure on these prices to rise; but there
will be more of this in later chapters.) On the other hand, goods and serv-
ices in someway complementary to commuter service will experience a de-
cline in the quantity purchased at given prices. Newsstand literature that
is particularly suited for commuter reading, perhaps, will suffer such a
decline. Even the demand for entirely unrelated goods may alter some-
what as a reshuffling of income initiates a tendency toward a quite different
pattern of consumer equilibrium.
These short-run effects can be expected to give way, if the strike persists
so long as to force the complete closing down of the line, let us say, to a
permanent readjustment of consumer demand, other things remaining the
same. The human race has shown remarkable ingenuity at discovering
"substitute" goods and services, especially when allowed a long period of
adjustment. In our example we can expect the closing down of a com-
muter line to increase the "long-run" demand by the erstwhile commuter
communities for automobiles, to decrease the demand for new residences in
these communities, to increase the demand for new residences in other
communities, and so on.
This type of ability to adjust has important implications for demand
analysis. The point is sometimes expressed by saying that in the long run
the demand for a particular commodity is likely to be considerably more
elastic than in the short run. This means that given price changes can be
expected to cause more drastic shifts of demand away from the goods that
have become relatively more expensive, toward those that have become
relatively cheaper, as a longer period of adjustment is contemplated. As
human beings acting to improve their positions, consumers adjust to a

worsening of the available alternatives by seeking new ones. The discovery
and effective utilization of new methods to satisfy wants takes time.

The market demand schedule lists the different quantities of a given
commodity that will be asked for by the market as a whole at given prices.
It is made up of the sums of the individual purchases that would be made
by market participants at the different prices. The graphic representation
of this market demand schedule is the market demand curve.
The shape of the market demand curve depends on the individual
curves and is thus characteristically downward sloping. The proportion
in which the quantity purchased increases with a given percentage fall in
price measures the elasticity of demand over the given price range. If a
fall in price is associated with so great an increase in quantity bought that
total revenue increases, we call the demand elastic; if total revenue remains
unchanged, the elasticity is unitary; if total revenue declines, the demand
is inelastic. A perfectly inelastic demand situation is associated with a
demand curve that is vertical over the relevant range; a perfectly elastic
situation is associated with a horizontal demand curve.
From the point of view of the individual firm, the demand for his
product depends also on the prices charged by the firm's competitors. If
there is very little difference, in the opinion of consumers, between the
products of the firm and those available elsewhere, demand will be highly
elastic with respect to the prices charged by the firm. If the firm monopo-
lizes the production of his product, the elasticity of demand is the same as
that of the entire market for this good.
Associated with a demand curve are several revenue concepts: (a) the
total revenue of a given output, (b) the average revenue or revenue per unit
of output, and (c) the marginal revenue of any contemplated change in out-
put level. These three concepts are related arithmetically and change, with
changing level of output, in a way that depends on the elasticity of the
demand curve.
The relationship between consumer demand for any two goods is ex-
pressed in the concept of cross elasticity of demand. This concept relates
to the degree in which the quantity demanded of one good changes as a
result of a given percentage change in the price of another good. Cross
elasticity may be either positive (between goods that consumers regard as
substitutes for one another) or negative (between goods regarded as comple-
mentary to one another).
Demand is an active market force that constantly forces producers to
revise their estimates of the alternatives they can choose from. Market de-
mand expresses itself in bids for particular quantities of commodities by

particular individual buyers. Demand by consumers, where thwarted
from the attainment of particular objectives, adjusts by an increased demand
for substitute goods as part of a general reallocation of individual consumer
income. This adjustment takes time to become fully worked out, so that
the elasticity of demand for particular commodities tends frequently to be
higher as a longer period of adjustment is considered.

Suggested Readings
Marshall, A., Principles of Economics, 8th ed., The Macmillan Co., London, 1936,
Bk. 3, Ch. 4.
Stigler, G. J., The Theory of Price, rev. ed., The Macmillan Co., New York, 1952,
Ch. 3.
Stackelberg, H. v., The Theory of the Market Economy, Oxford University Press,
New York, 1952, pp. 164-171.

Market Process in a
Pure Exchange Economy

LJ NTIL NOW we have been concerned
with the way consumers make decisions when faced with the necessity of
choosing between alternatives given by the market. We assumed consumers
were faced with an array of products that could be bought at given prices.
We investigated the principles by which the consumer allocated his income
among the array of purchase possibilities, focusing attention in particular
on the kinds of changes in the data that could alter the consumer's alloca-
tion pattern.
This analysis, based as it was on the assumption of opportunities de-
termined externally, did not deal with the really essential elements of the
market process. We have been assuming that the facts governing the rele-
vant decision were presented in some definite but unexplained way by the
external world, as market data. Just as an individual is forced to adjust
himself passively to the physical laws governing his surroundings, so we also
assumed him to face the prices of the goods that he wished to buy as being
determined completely by impersonal and external forces. But the market
process is itself continually modifying, disrupting, and adjusting the market
phenomena that govern the decisions of the market participants. Our real
task is to understand this process.
A market process is the result of the interaction between the decisions
made by all the participants in a market. In a market system where
products are produced and sold to consumers by entrepreneurs who have
produced by combining resources purchased from resources owners, the
market process results from the impingement upon each other of the plans
made by consumers, entrepreneurs, and resource owners. Each of the par-
ticipants in the market, at any one time, makes his decisions on the basis

of what he believes to be given market data. Out of the mutual interplay
of these numerous decisions, and of their influence upon subsequent deci-
sions, the market process of price and production determination emerges.
In the previous chapters we investigated the elements of the market
process that must be explained by consumer theory. In Chapters 8 and 9
we will investigate those elements that must be explained by the theory of
production. These elements are based on the assumption of data given by
the market that the individual consumer or producer must passively adjust
himself to. In Chapters 10 and 11 we take up the full analysis of the com-
plex market process emerging from the compounding in the market place of
all these separate elements. The analysis in the preceding chapters, and in
Chapters 8 and 9, is introduced not primarily for its own intrinsic impor-
tance but as an indispensable help to the understanding of the complex
strands of cause and effect making up the market process.
The present chapter is introduced at this point as a step toward the
understanding of the market process in its full complexity. In this chapter
we show how a market process could emerge in a market made up of con-
sumers only. We imagine an economy where no production is possible;
all commodities are obtained costlessly by natural endowment. Exchange
could and probably would take place in such a society. The actions of
individuals in such an exchange economy would be governed by the prin-
ciples analyzed in the preceding chapters. Market phenomena would be
derived purely from the interaction of the decisions of the consumer par-
ticipants. Although this kind of market is unlikely to correspond to any
real society, its thorough analysis will prove extremely valuable for the
analysis of the more complex market processes involving production activi-
ties. There are chains of logic that apply with equal validity to any kind of
market. They can be perceived with especial clarity in a simple market
such as we consider in this chapter. We will be drawing heavily upon this
chapter when we come to consider markets, in Chapters 10 and 11, involving
production as well as simply exchange and consumption.

Any investigation of the process that determines prices and produc-
tion programs must take careful account of the competitive element inher-
ent in market activity. In the final analysis, the market process relies most
heavily upon this element. We may view the market process as the mecha-
nism that determines the opportunities that market participants find most
advantageous to offer other participants and that in this way also deter-
mines the particular opportunities that will be embraced in the market.
A market process may be defined as competitive when the opportunities

that market participants feel constrained to offer to the market are only
those opportunities
that they believe to be more attractive (or at least no less attractive) to
the market than comparable opportunities being offered by others.
Each market participant is forced to act with the realization that the oppor-
tunities he would like to offer to the market (that is, those that, if accepted,
would yield him the greatest advantage) will be rejected by the market (that
is, they will yield no advantage at all) if they are considered less attractive
than those made available by his competitors.
In general, then, the competitive market process tends to ensure that
each participant will offer to the market those opportunities that, if em-
braced, will prove most advantageous to himself”not out of all possible
opportunities that he could offer”but out of those opportunities he is able
to offer that he believes at least not less attractive to the market than those
of others. This is a very general proposition that applies to both buyers
and sellers and is sufficient to narrowly delimit the range within which
exchange opportunities emerge and are embraced in the market place.
Our task in this chapter is to reduce this general proposition to more specific
statements that can be applied to particular conditions.

The simplest possible case where we may observe and analyze the com-
petitive process at work is that of the market for a single homogeneous com-
modity, which cannot be produced by human action, but which is each day
obtained costlessly from nature by a large number of market participants.
The careful analysis of what can be expected to take place in this simplest
of cases will prove of great value in the analysis of the more complicated
cases to be taken up later.
Participating (at least potentially) in the market for our commodity
are all those individuals who, on the one hand, might be induced to buy
quantities of it if the price is low enough, and those who, on the other hand,
possess some units of the commodity and might be induced to sell quantities
of it if the price is high enough. Since we avert our eyes from everything
except the one commodity, competition can only take the form of offering
more attractive opportunities in terms of higher prices offered or lower
prices asked. The factor that determines the quantity of the commodity
a potential buyer might wish to buy at each of a series of different prices
(graphically expressed by his demand curve) is the marginal utility to him of
additional units of the commodity. Similarly, since production of further
units of the commodity is assumed to be impossible, the factor that de-
termines the quantity of the commodity its owner would be willing to sell
at given prices is the marginal utility to him of the units of the commodity

under consideration. (This can easily be seen by observing that what an
owner o£ the commodity does not sell, he is keeping for himself. Clearly
the quantity of the commodity he wishes to keep for himself depends on the
marginal utility of the relevant units of commodity as compared with what
can be obtained by selling them.) Our discussion in earlier chapters of the
significance of the law of diminishing utility will lead us generally to ex-
pect that at higher prices, all market participants will wish to hold less of
the commodity. The higher the price of the commodity, the less attractive
it generally becomes to hold a unit of it instead of what its value in money
could buy of other commodities. Fewer non-owners (and owners) of the
commodity will be willing to buy quantities of it, while more owners of the
commodity will be willing to sell it. On the other hand, the lower the price
of the commodity, the more attractive it generally becomes to hold a unit
of it instead of its value in other commodities. More non-owners of the
commodity will be willing to buy, while fewer owners will be willing to
sell (more of them, in fact, joining the non-owners in being prepared to add
to their holdings). If we assume an appropriate discrepancy between the
marginal utility of the product for some holders of it and that for others in
the market, we have a situation where conditions for mutually profitable
exchange exist. The problem is to explain the terms exchange will take
place upon.
The competitive process of price determination in a market such as
this can be grasped most easily by first imagining a quite impossible situa-
tion”where each market participant is fully aware of the quantities that the
rest of the market would wish to buy and sell at each possible price. This
"perfect knowledge" implies that each buyer and seller knows both what
sellers would be prepared to sell at each possible price (if it could be ob-
tained), and also what can be sold at each of these prices. In other words
each buyer and seller knows the limiting price above which a given quantity
of the commodity cannot be sold, as determined by the willingness to buy of
the most eager buyers; each participant also knows, for any given quantity
of the commodity, the limiting price below which it cannot be bought, as
determined by the willingness to sell of the most eager sellers.
In this situation it is easy to describe the outcome. The knowledge
possessed by the buyers and sellers will ensure that the prices asked for by
sellers will be similar to those offered by buyers, and will be within a nar-
row range”the limits of this range being easy to define. Our assumption
of perfect knowledge on the part of each buyer and seller means that he
knows the best offers available to him, as well as the best offers available to
others and against which he must compete. Each potential buyer knows
(a) the lowest price it is not necessary to bid above in order to induce each
given seller to sell given quantities, and (b) the highest price it is necessary
to bid above in order to ensure (if it proves desirable to do so) that given

quantities of the commodity are not bought by less eager buyers than him-
self. Similarly, each potential seller knows (a) the highest price it is not
necessary to go below in order to induce each buyer to buy given quantities,
and (b) the lowest price it is necessary to offer to sell below in order to
ensure (if it proves desirable to do so) that given quantities of product are
not sold by less eager sellers than himself.
It follows that the range of possible prices that may emerge in our
market must necessarily include only
those prices at w¬iich the quantity of the commodity that buyers would
be willing to buy (at these prices) is no greater and no less than the
quantity that sellers would be willing to sell (at these prices).
No exchange could take place at higher prices; buyers would not offer such
higher prices (nor, in fact, would sellers waste their time in asking these
prices).1 No buyer would offer such higher prices because he knows that
the lower price is quite sufficiently high to induce the more eager sellers
to supply all that buyers would ask at that lower price. (No seller would
waste time in asking such higher prices because he knows that buyers can
find an adequate number of sellers sufficiently eager to supply all the
units of product that would be asked for at the lower price.) On the
other hand, no exchange could take place at prices below the range specified
above: no sellers would accept lower prices. He would not do so because
he knows that the higher price is quite sufficiently low to attract all the
buyers necessary to buy what the sellers would offer at that higher price.
With perfect knowledge assumed, this definite outcome will emerge
immediately without haggling, or exploratory, "mistaken" acts of exchange
at "wrong" prices. Perfect knowledge would ensure that each participant
resign himself immediately to what he correctly believes to be the best
opportunity he can obtain. He knows that he cannot obtain a superior
opportunity because he knows that everybody else has the same perfect
knowledge that he does, thus even those who might otherwise be prepared
to provide superior opportunities know perfectly well it is unnecessary
for them to do so. (No seller, as we saw, would waste his time asking prices
higher than the above specified range.) Moreover (and this will be of the
utmost importance when we extend the analysis of our simple case to more
complex ones), there is an additional reason why a seller (for example)
would not waste his time asking the higher prices. And this is quite apart
from the fact that he knows he would find no buyer equipped, as he must
assume each buyer to be, with perfect knowledge, ready to buy at the higher

i A special case of great importance is where at any price greater than zero, the quan-
tity of the commodity that would be offered for sale exceeds the quantity that would be
bought. For such a good, it is clear, no finite positive price can be maintained; it becomes
a free good whose ownership does not yield command over other commodities through

prices. This additional reason is that the seller knows that were any
buyers to offer (inexplicably, and in error) a price higher than he really
need pay, he (the seller) could hardly expect to get the sale. He would
realize that such a buyer would be inundated with offers o£ numerous com-
peting sellers eager to sell at a price higher than they can get elsewhere. It
would be clear to any seller that this kind of error on the part of a buyer
would be immediately self-correcting.
The price resulting from this reasoning process has several interesting
properties that become apparent as one follows the logic of its determina-
tion. The price is so low, on the one hand, that almost all those who
buy at the price would have been willing (if this had been necessary) to
pay higher prices to secure what they are buying. On the other hand, the
price is so high that almost all those who sell at the price would have been
willing (if this had been necessary) to sell for lower prices. The reason
why all the buyers do not have to pay higher prices is that the marginal
buyers would not be willing to accept the last units bought, at any higher
price. Competition among sellers therefore ensures that no buyer pays
more than the marginal buyer. The other buyers thus gain what is often
termed a buyer's surplus, representing a sheer gain arising through their
purchases. Similarly, the reason why all the sellers do not have to sell for
lower prices is that the marginal sellers would not be willing to sell the
last units sold, at any lower price. Competition among buyers forces up
the prices received by all sellers to the price acceptable to the marginal
seller. The other sellers gain, in this way, a seller's surplus. The two-sided
competition of many sellers and many buyers forces price within the range
specified above”on the one hand, no higher than necessary to attract all
the sellers needed to sell what buyers would be willing to buy at the price,
and on the other hand, no lower than necessary to attract all the buyers
needed to buy what sellers would be willing to sell at the price.
The logic of the discussion may be presented also in a somewhat differ-
ent manner. Imagine two lists, one for sellers and one for buyers, in which
market participants are ranked in order of their eagerness to sell or to buy
the commodity. In the sellers' list the first line is assigned to the participant
prepared to sell a single unit to the market at a price lower than that offered
by anyone else; the second line is assigned to the seller prepared to sell a
second unit to the market at a price lower than anything offered by every-
body else (except the occupant of the first line). Of course both lines may
be occupied by the same person. And so on, each successive line raising
the price successive units can be induced to be offered to the market at.
In the buyers' list, similarly, the first line is assigned to the buyer prepared
to pay the highest price for a single unit of the commodity; the second line
is assigned to the buyer (who may be the same person as the first buyer) pre-
pared to pay a price for a second unit that is higher than anything that

would be offered anywhere else in the market (besides, of course, the price
that would be paid by the occupant of the first line). A comparison of
the sellers' and buyers' lists would reveal that the most eager buyers (those
high on the list) are prepared to pay much more for specified quantities of
the commodity than would be demanded by the most eager sellers (those
correspondingly high on the sellers' list). As one moved down both lists
this gap would gradually narrow since the prices on successive lines on the
sellers' list are rising, while those on the successive lines on the buyer's list
are falling. When the line is reached where the seller's offer is higher
than the corresponding buyer's bid, the unit has been reached where its
seller cannot expect to find a buyer for it. Any buyer sufficiently eager to
pay the high price the seller asks for it can find more eager sellers prepared
to sell for less. Conversely this unit is also the unit for which a prospective
buyer cannot find a seller. Any seller sufficiently eager to sell for the low
price the buyer offers for it can find more eager buyers prepared to buy for
more. The preceding unit, on the other hand (that relating to the pre-
ceding line in the list), can be sold since the buyer cannot find anyone
prepared to sell for less, nor can the seller find anyone prepared to buy for
more. The four prices represented by the offers and bids of the buyers and
sellers ranked on these two lines of the lists delimit the price range within
which equilibrium market price will be confined. The upper limit to the
range is the lower of the following two prices (out of the four): the price
corresponding to the buyer's bid on the higher of the two lines, and the price
corresponding to the seller's offer on the lower of the two lines. (A price
higher than the lowest of these two would either exclude a buyer necessary
to take the last unit offered for sale at this price, or it would attract a seller
of one unit more than can be sold at the price.) The lower limit to the
range is the higher of the remaining two prices. (A price lower than this
lower limit would either attract a buyer of one more unit than will be
offered for sale at the price, or it would exclude the seller of the last unit
necessary to supply all the buyers willing to buy at the price.) These
buyer-seller pairs involved in defining the upper and lower limits to the
price range are known in the literature as the "marginal pairs." 2
The logic of this kind of price determination throws immediate light
on the consequences of certain possible changes in the basic data. It is
clear, for example, that a change in tastes, which raises the marginal utility
of the product under consideration for the market participants, must have
the immediate effect of a rise in price (with no other changes in the data).
An increase in the marginal utility of the good means that for any given

2 See Böhm-Bawerk, E. v., Capital and Interest, Vol. 2 (translated by G. D. Huncke),
Libertarian Press, South Holland, Illinois, 1959, pp. 224-225. In the appendix to this
chapter, a translation into diagrams of the logic of the competitive price will be found,
together with further discussion of competitive price determination.

quantity of the commodity, buyers will be prepared, if they have to, to offer
higher prices. Similarly, sellers will be willing to sell given quantities of
the commodity only at higher prices. The resulting price will therefore
be higher than before the change. A sudden increase in the quantity of
the commodity that is in existence, on the other hand, will cause a fall in
price. The marginal utility of a unit of the commodity will now be lower
than before for holders of it. This follows from the law of diminishing
utility, since holders are on the average holding larger stocks of the com-
modity. The consequence is a fall in price according to the above outlined
logic of competitive price determination with perfect knowledge.

Our analysis of the competitive determination of price in a market for
a single unproducible commodity must now be extended to cover also the
case where knowledge is less than perfect. Certainly we have to expect
that in a real world, buyers and sellers will to some degree be ignorant of
the prices that they must offer or ask in order to outstrip competitors and
to attract advantageous exchange opportunities. It follows that some ex-
changes will probably take place, at least in the beginning, at prices signif-
icantly higher or lower than the price range defined in the previous section.
The important link between the case analyzed in the previous section
and the more realistic case we are now dealing with is that the price range
immediately realized in the preceding case must be recognized as being also
the equilibrium price range for the present situation. It will be recalled
from earlier chapters that a state of equilibrium is a state that would be
maintained unchanged so long as the basic data (of the situation being
analyzed) do not themselves change.3 By describing the price range defined
in the preceding section as being also the condition for equilibrium in the
present imperfect-knowledge case, we mean, then, that if by chance sellers
were to ask and buyers were to offer only prices lying within this range, no
upward or downward revisions of price would ensue for subsequent ex-
changes so long as the basic data of the case continued unaltered. This
is clearly the case, since prices in this range would clear the markets; all
bids made at this price would be accepted, since offers to sell precisely
the same quantity at this price are being made at the same time. No buyer
making a bid, and no seller making an offer needs to make revisions.
But this piece of information does not by itself tell us very much about
the prices that will actually be determined in the kind of market we are
attempting to grapple with. Without the perfect knowledge that we were
assuming in the preceding section, we can expect, as we have seen, the equi-

3 See especially in Ch. 2, pp. 22-23.

librium conditions to be established at the outset only by purest chance.
And if the prices and conditions that prevail at the outset are not those of
equilibrium, we are faced afresh with the problem of describing the com-
petitive process of market price determination.
We will assume that trading is carried on during trading "days." (A
trading "day" is a period of time so short that a course of action planned
for one "day" cannot or will not be revised during the day "itself.") We
will further assume that market participants do not have any reason to
consider any prices except those that will prevail "today"; in other words
we eliminate possible complications arising out of speculative behavior.
Nobody in our market is holding back from buying (selling) "today" merely
in the hope of lower (higher) prices tomorrow or later on.4 Market partici-
pants, whatever the degree of their knowledge of market conditions, can
be expected, then, to use their knowledge in the following obvious way.
Each potential buyer will bid prices for specific quantities of the commodity
only up to the point determined, first, by the marginal utility to him of the
commodity, and second, by the lowest price that he believes sufficiently
high to induce sellers to sell, as well as sufficiently high to outbid his less
eager competitors”in other words the lowest price he can buy at in the
market today. Similarly, each potential seller will offer quantities of the
product for sale at prices whose lower limit will be set, first, by the marginal
significance of the commodity to himself, and second, by the highest price
that he believes sufficiently low to induce buyers to buy, as well as sufficiently
low to eliminate any less eager sellers who may be in competition with him
”in other words the highest price he believes he can obtain in the market
The absence of perfect knowledge implies that some (probably most)
of the resultant bids and offers, on a given trading day, will be made in
error. Buyers will bid prices either higher than necessary to obtain what
they want or lower (and below what they might have been prepared to offer
if they had been better informed) than necessary to obtain what they want.
Similarly, sellers will offer to sell either for prices lower than necessary or
higher (and above what the sellers themselves, if better informed, might
have been willing to accept) than necessary to sell their commodities. It

4 For an outline of some of the complications introduced by the possibilities for spec-
ulation, see pp. 315-316 in the Appendix on multi-period planning.
5 Since we are assuming only imperfect knowledge, it is likely that participants are
aware that some of their expectations are likely to be mistaken. In our analysis, how-
ever, we will continue to assume that each participant is able to crystallize all his guesses
and doubts into a single-valued expectation he acts upon as if with certainty. The
reader will recognize this as a simplification; it is the task of a theory of uncertainty to
replace this simplification by a more sophisticated analysis of human action. For one
such theory see Shackle, G. L. S., Expectation in Economics, Cambridge University Press,
London, 1949.

will be observed that the mistakes that can be made are of two possible
kinds. First, bids and offers may be mistaken because
they unwittingly pass up superior opportunities (the particular market
participants are ignorant of) in favor of the inferior opportunities
(buyers offer to pay higher prices than they "really" need to; sellers offer
to sell for prices lower than those they can "really" secure elsewhere).
Second, bids and offers may be mistaken because
they deliberately pass up desirable opportunities in the erroneous
belief that still more attractive opportunities can be secured
(for example, buyers refuse to offer prices high enough to obtain what they
want, even though if better informed they would have done so, because they
believe the lower prices that they are bidding can buy the product some-
where in the market).
Two distinct possible reactions may emerge in the market consequent
upon, and corresponding to, these two kinds of "mistaken" bids and offers.
The first kind of error probably means that in some parts of the market, on
a given day, prices are higher than in others. Imperfect knowledge has
brought about an imperfect market which we may define loosely as one
where prices are not immediately uniform. This discrepancy between
prices will set into motion arbitrage operations on subsequent "days" as
soon as the discrepancy is discovered. That is, as soon as knowledge in-
creases just sufficiently for somebody to discover the consequences of the
previously imperfect knowledge, a part of these consequences will tend to
be eliminated. Men will buy where the price is low in order to sell where
it is high, and in so doing they will bring about a tendency toward a uni-
form price.
The second kind of error means that some prospective buyers and
sellers are disappointed”they find their bids to buy rejected as too low or
their offers to sell rejected as too high. We are entitled to assume that inso-
far as knowledge of market conditions for a given day is concerned, our
prospective buyers and sellers are capable of learning from experience
gained on previous days (although throughout our analysis we are holding
all the data of the situation”especially the buying and selling attitudes and
expectations of the participants”constant from each trading day to the
next). Buyers who yesterday found themselves disappointed in their bids
to buy (because they bid too low) will revise upward their estimates of the
prices necessary today to obtain the product; prospective sellers who found
themselves disappointed yesterday because they asked prices that were too
high will realize that they must lower them today if they are to meet the
competition of other sellers. In other words, the disappointment associated
with a seller's discovery during a trading day that "the price" of the product
is lower than he had believed simply means that on the following day he
will start with a lower and more nearly correct estimate of the price that

will clear the market. And similarly for buyers who discover that they had
a falsely optimistic estimate of market price.
The two kinds of reaction outlined in the preceding paragraphs make
up the agitation that characterizes a competitive market groping toward
the equilibrium position. It is clear that so long as prices are outside the
equilibrium range (which we found to be realized immediately in the case
where perfect knowledge is assumed), the market must seethe with changing
patterns of exchange activity. Prospective buyers and sellers change their
bids and offers, price discrepancies are discovered, exploited (and in this
way destroyed)”all this alters the opportunity patterns being embraced in
the market. The direction of these changes is toward the position described
by conditions of equilibrium. Supposing, to recapitulate, that all prices
asked and bid are initially above the equilibrium range; it is clear there
would be some unaccepted offers to sell. The disappointment of those
making these offers will teach them (even when some exchanges have taken
place at these higher prices) that the higher prices are above the highest
price that is low enough to sell the quantities of the products that they
would be willing to sell. Their subsequent bids, competing with each
other, will be lower”in the direction of equilibrium. On the other hand,
with all prices asked and bids falling initially below the equilibrium range,
the disappointment of unsatisfied prospective buyers in competition with
each other would raise the bid prices toward the equilibrium price range.
To consider the remaining possibility, if some bids are above and some
below the equilibrium range, and some selling offers are also above and
some below the range, then if not all the selling offers above the range are
accepted, nor all the bids below the range accepted, the same adjustments
will occur. But even if the bids below the range are exactly matched by
the offers to sell below the range, and the bids and offers at above the range
prices also match perfectly, the price discrepancies would invite arbitrage
activity. The commodity would be bought where its price is below the
range, and sold where its price is above the range. And this would go on
until the below the range prices rise, and the above the range prices fall,
to a single price. This single price can only lie in the equilibrium range.
Any other price would generate the disappointments and adjustments out-
lined above.
Besides explaining the way the competitive market process determines
prices, our analysis indicates also the way the market determines the quanti-
ties of the commodity that will be sold. In equilibrium of course, the
quantity sold is no greater and no smaller than that which both buyers
would be prepared to buy and sellers prepared to sell at the going price.
During the time equilibrium has not yet been attained, so that prices are
either all above, all below, or partly above and partly below the equilibrium
price range, we must generally expect a smaller quantity to be sold than

in equilibrium. This occurs because at prices higher than the equilibrium
price range, buyers will buy only a smaller quantity; while at prices below
the equilibrium price range, sellers will sell only a smaller quantity.
Our analysis, simple as it is, can be used to explain a host of matters.
It is easy to see, for example, how it could be used to explain a persistent
rise in the price of a commodity, or a persistent rise in the quantity of a
commodity sold. In these and similar cases, the analytical framework
enables the observer of the real world to look for those factors that his
theory suggests may play a key role in the explanation he is seeking. Our
analysis is also the foundation for the exploration of more complex situ-
ations, one of which we must now consider.

Still avoiding the complexities associated with existence of costs of
production, by assuming all commodities sold in our market to be non-
producible, we must now extend our analysis to the case where market
activity is possible in a number of different commodities. We may formu-
late the problem by first setting forth our assumptions. There are a
large number of potential participants in the market. Each potential
participant is endowed at the start of each day with an initial package
containing quantities of a number of different commodities. This package
we may call his daily "income." The package may be of different size
and composition for each market participant, and in his package a partici-
pant may find some of the included commodities present in greater quanti-
ties than others. All we need assume is that each day each participant is
endowed (by nature, since we exclude production) with the same package
as yesterday; no commodity is saved from yesterday. Each day, regardless
of yesterday's experiences, participants arrive on the market with the same
tastes as they possessed on the previous day. Thus, for any one participant
at the start of each day, the marginal utilities of the various commodities
on the market are exactly the same as they were at the start of the previous
day. Additional units of all available commodities are ranked on his
value scale in exactly the same order as at the start of the previous day.
Endowed with different initial daily incomes and tastes, different mar-
ket participants can be expected to arrive at the market each having a
different scale of values with respect to the various commodities. These
differences in relative significance attached by different people to marginal
quantities of the various commodities mean that opportunities may exist
for each of the various market participants to improve his position by
exchanging with other participants. Market activity will ensue. Goods
will be bartered until nobody is aware of further opportunities for mutually
profitable exchange. During the course of such a trading day, specific

quantities of the various commodities will have changed hands, and each
of the transactions will have been effected on particular terms.
Our problem is to discover what market forces are operative in deter-
mining (a) the quantities of the various commodities exchanged during
any one day, and (b) the terms these exchanges are made on. We must
discover further whether the market transactions of any one day can be
expected of themselves to bring about changes in the market transactions
of the following day. In other words, can we expect market participants
to revise their willingness to buy or to sell commodities at yesterday's rates
of exchange, purely as a result of yesterday's market experiences (that is,
without any changes in the basic data, incomes, tastes, and so on)? If our
analysis does lead us to expect such changes, we must further inquire into
the pattern that these changes will describe over time, whether these
changes may finally come to a halt, and, if so, into the conditions that
would be thus indefinitely maintained.
This description of the problem posed by the multi-commodity market
makes us immediately aware of a complication that was not present in the
case of the analysis of the single-commodity market. Our analysis of the
market for the single commodity was based on the notion of the existence
of a definite upper limit to the price that a potential buyer would be
prepared to pay for a commodity if market conditions forced him to do so.
Such an upper limit, of course, can be considered definite only on the
assumption of definitely known opportunities alternative to the purchase
of the commodity. So long as we were, as in the previous sections, confin-
ing our attention to the single commodity, such an assumption was appro-
priate. We were able to assume a specific pattern of prices governing the
availability of other goods, and, holding these other conditions unchanged,
we were able to proceed with our analysis.
In our present problem we are unable to proceed in this way. We
are now explicitly broadening the scope of our analysis to embrace an entire
group of commodities. We wish to investigate the process by which the
prices and quantities exchanged of all the commodities are determined.
The upper limits to the bids that a prospective buyer might be prepared
to make for a given quantity of one commodity cannot be thought of with-
out considering the market situation”itself an object of our inquiry”with
respect to all the other commodities. Our analysis of the multi-commodity
market must clearly take full account of this complication.

As in the single-commodity case considered in the preceding sections,
it proves pedagogically convenient to approach our task by attacking it
indirectly. Our principal aim is to explain the way the market transactions

of any one day force potential buyers and sellers to revise their market
plans, and, in so doing, to bring about alterations in the market transac-
tions for the following day. We wish to discover how the mutual impact
of numerous, possibly inconsistent, market plans, forges out new patterns
of exchange based on the disappointments encountered or opportunities
discovered in the course of exchange. We will, however, approach this
task by first explaining the relationships that would perforce have to exist
among the transactions in a multi-commodity market, if these transactions
be required not to lead to any plan revisions by market participants on
subsequent days. A firm understanding of the state of affairs, which would
lead nobody to make any alterations in his market activities, will clarify
the kinds of change that will occur under any other conditions.
At the start of each trading day, it will be recalled, we assume numer-
ous exchange opportunities to exist among the market participants. For
the transactions of any one trading day to be consistent with equilibrium
(so that they may be repeated without alteration on subsequent days), it
is necessary that they exhaust all possibilities of mutually profitable ex-
change. So long, for example, as the price pattern ruling on a particular
trading day does not set in motion exchange between two market partici-
pants, who might cheerfully have exchanged at some other set of prices,
it is obvious that sooner or later the situation will demand and achieve its
own correction.
If the equilibrium pattern of market transactions must be such as to
exhaust all possible opportunities for exchange, then these transactions
must clearly bring about a very special reshuffling of the pattern of com-
modity ownership. At the beginning of each day the commodities be-
stowed by nature on the economy are distributed among individuals in one
way. At the close of the day's market transactions, if these are to be con-
sistent with equilibrium, the pattern of ownership of commodities should
leave no two individuals in a position with respect to one another that
could present the conditions for mutually profitable exchange. The anal-
ysis of earlier chapters enables us to characterize such a pattern of com-
modity ownership with clarity. At the close of a day's market transactions
in an equilibrium market, the various commodities will be owned by mar-
ket participants in such a way that, with respect to marginal units of these
commodities, the value scales of all participants shall be identical.®
When the ownership of commodities has been redistributed in this
6 This identity, at the close of equilibrium trading, between the value rankings of
different market participants holds only with respect to the marginal units of (a) those
goods that each of the participants holds a stock of at the close of the day and (b) those
goods that can be bought and sold. With respect to a good that some participants
possess no stock of at the close of the day, all that can be said is that it ranks relatively
higher on the value scales of those who do hold some of it than on the scales of those
who do not.

way, through exchange, no further transfer of commodities between any
two commodity owners could possibly be proposed that would leave both
parties better off with the transfer than without it. This is obvious. Let
us suppose that one of the parties prefers the additional quantity of the
commodity that it is proposed he acquire over that he is to give up. Then,
since all participants have already attained identical scales of value, it
follows that the other party to the commodity transfer values the two
quantities of goods in exactly the same way. And this means that he
prefers the quantity of the commodity that it is proposed that he give up
over that it is proposed he acquire. No exchange opportunity can exist.
What the particular ownership pattern in a given situation must be,
if it is to fulfill the condition of identical value ranking by all market par-
ticipants, will depend on two sets of factors. On the one hand, it will
depend on the different tastes of the various market participants (since
these will govern their respective value scales); and on the other hand, it
will depend on the initial quantities of the various commodities each
participant is endowed with at the start of the trading day (since no own-
ership pattern can emerge that should leave anyone worse off than at the
start of the day). If one could discover the way a market participant,
owning a particular array of the various commodities, would rank addi-
tional units of these various commodities on his value scale; and if this
could be discovered also in turn for each of the possible cases in which
the array of commodities he owns might be somehow different,; and if cor-
responding sets of discoveries could be made in turn for each of the various
market participants”then, taking into account the initial commodity en-
dowments, we would have the data to determine the pattern of commodity
ownership that would prevail at the close of trading in an equilibrium
We may assume that these data are sufficient to determine uniquely
the required pattern of ownership at the close of trading in the equilibrium
market”namely, that pattern that yields identical scales of value with
respect to additional quantities of goods. The next step is to discover
what determines the transactions in the equilibrium market; that is, those
transactions that will lead to the above described final pattern of com-
modity ownership.
It will be recalled that a trading "day" is defined as being so short
that no plan changes can be made during a single day. Bids and offers
made at the start of a day are to be maintained unchanged throughout the
7 Whether or not the initial commodity endowments and the value scales of the vari-
ous participants do, in fact, permit the existence of such an ownership pattern (and of only
one such pattern), is a question, not of price theory proper, but rather of mathematics.
(In mathematical economics the proof that such a pattern does exist is known as an "exist-
ence theorem." We will assume that such a unique pattern does exist and that complete
knowledge of market data enables this pattern to be completely specified.)

day. It follows that in looking for the transactions of an equilibrium
market, we are looking for a single set of prices for the various commodities
that will permit market participants voluntarily to continue the reshuffling
of commodity ownership through exchange, until the ownership pattern
outlined in the previous paragraphs is reached. In the equilibrium mar-
ket there will be a single price for each commodity (clearly, two prices for
the same commodity must result in arbitrage activity on subsequent days,
altering either or both of the two prices). And with the required unique
set of prices for the various commodities expected to govern the market
throughout the day, in equilibrium, market participants will be induced
to buy and sell the various commodities in precisely those quantities that
will result in the final pattern of commodity ownership outlined above.
In other words, with these prices ruling, each market participant will con-
vert during the day his initial commodity endowment into a particular
commodity bundle more desirable to him than any other one available at
the market prices. The distribution of commodity bundles at the end of
the equilibrium trading day will be such that no opportunities for exchange
exist between any two participants; thus, no one is led to revise his market
plan for the following day.8
Now, the preceding paragraphs describe the conditions that would
have to be fulfilled before we could pronounce a multi-commodity market
to be in equilibrium. In the subsequent sections we will be concerned
with our principal problem”what goes in a multi-commodity market where
these conditions have not been fulfilled. At this point, the most fruitful
approach to this task will be to show that, exactly as was the case with the
single-commodity market, the equilibrium conditions would be immedi-
ately fulfilled if all participants possessed, and knew each other to possess,
perfect knowledge of all relevant market data.
Our analysis of the single-commodity market (with perfect knowledge)
proceeded from the following self-evident propositions. No prospective
buyer would be prepared to pay more for a commodity than its price
elsewhere in the market; nor would he waste time by offering to buy at a
lower price than that at which others are prepared to buy elsewhere in the
market. No seller would be prepared to sell the commodity for less than
it could bring elsewhere in the market; nor would he waste time trying
to sell it for more than the price it can be obtained for elsewhere in the mar-
ket. We may translate the logic of these propositions into corresponding
statements having reference to the multi-commodity market with perfect
Consider any participant in such a market, contemplating the con-
version of his initial commodity endowment into a preferred bundle by
8 Here, too, we will assume that such a set of prices is mathematically feasible and
can be derived from a complete knowledge of market data.

exchange in the market. He must sell some items and buy others; he
must calculate the price offers and bids he should make. It is clear that
the ratio between the price that he bids for one good and the price he
offers to sell a second good for
must not be different than the ratio of the prices these two goods can
be bought and sold at elsewhere in the market.
This is readily seen. Suppose the two goods in question to be A and B
respectively, and suppose the market price of A to be k times the market
price of B. Then our market participant, knowing this, will under no
circumstances make bids and offers to buy A and sell B (or, vice versa, to
sell A and buy B) that would yield a ratio between the price of A to the
price of B, either greater or smaller than k. He would not offer to buy
A at more than k times the price he is offering to sell B for. Such a course
of action would mean that he would give up more of B, in order to buy a
given quantity of A, than he would have to give up elsewhere in the
market; by the same token, he would be providing the market with quanti-
ties of B at a lower cost (in terms of A necessary to be sacrificed in exchange)
than is called for elsewhere. On the other hand, our market participant
would not offer to buy A at less than k times the price he offers to sell B for.
To do so would mean to ask a price for B that would be greater (measured
in terms of quantity of A required to be given up in exchange for a unit of
B) than is being asked elsewhere; by the same token, such a course of action
would mean an offer to buy A at a price that would be lower (measured
in terms of quantity of B offered in exchange for a unit of A) than sellers
of A can obtain elsewhere in the market.
It follows from these propositions that for each pair of commodities,
each of the perfectly informed market participants will seek in turn to
make price bids and offers bearing ratios that should coincide with that
reached by the other participants. Extending this to all the commodities,
it follows that each market participant will seek and is aware that each
of his fellow participants is likewise seeking, a unique set of relative prices
for all the commodities that should be common to all participants. With
each participant equipped with the same complete information concerning
individual tastes and initial commodity endowments, it is not difficult to
see which particular pattern of relative prices will immediately emerge from
their calculations. It can only be the particular set of relative prices that
we found to satisfy the conditions for an equilibrium market.9
No participant would make the error of entering the market in the
belief that some other set of relative prices, according to which he should
adjust his own buying and selling plans, would prevail. With perfect
9 The reader will observe that in this, as well as in parallel succeeding discussions,
our assumption of perfect knowledge includes also the assumption of the ability to make
instantaneous calculations of required information from the data.

knowledge, such a possibility (which would of course mean the violation
of the conditions for equilibrium) is precluded. With perfect knowledge,
a participant would know (and would know that everybody knows) that
any other set of relative prices would not bring the market, during the day,
into that pattern of commodity ownership that we found characteristic of
the close of a day in the equilibrium market. Such a set of relative prices
must then lead to the failure by some of the market participants to exploit
among themselves a number of mutually profitable, exchange opportunities.
Such a set of relative prices cannot be assumed to be allowed to prevail,
then, insofar as these interested participants can be counted upon to take
advantage of all opportunities for mutually gainful exchange. Knowing
this, each participant would correctly calculate what the set of market
prices will be. The conditions for an equilibrium market would be im-
mediately satisfied.

Our awareness of the relationships that would exist in a multi-com-
modity market in equilibrium, and our understanding of how these re-
lationships would be immediately realized in a world of perfect knowledge,
must now be used in extending our analysis further. We must now ex-
amine the multi-commodity market where knowledge is not perfect and
which cannot therefore be expected to fulfill equilibrium conditions. Once
again we assume that each day there is some initial endowment of a bundle
of commodities for each market participant; that these endowments may
differ among participants but are the same for any one participant from
day to day; and that while participants may differ among each other in
their tastes, any one participant arrives in the market each day with the
same tastes as yesterday, regardless of yesterday's market or other activities.
The imperfection of knowledge means that the typical participant
will know of the tastes and initial commodity endowments of only a small
number of his fellow participants, and he will have only fragmentary”
and possibly incorrect”knowledge of these. Were all these market par-
ticipants to come into contact with each other for the first time without
any experience whatsoever of earlier price relationships, the first exchange
transactions would probably be made, on a very small scale, within fairly
close groups of persons aware more or less completely of one another's
situations. Any buying or selling plans on a wider scale could be made
only on the basis of guesses regarding market conditions that very likely
would be proved mistaken. Even when the scope of exchange is broadened
to embrace the entire market, we must expect the individual buying and
selling plans of different participants to be made on information gathered,

for each of them, from the experience of only small segments of the market.
These plans will prove themselves mutually inconsistent; knowledge of
their inadequacy will be gained by the plan makers through the discovery
of superior opportunities lost because of adherence to such a plan, or
through the direct disappointment of goals sought to be achieved by the
plans. It will be instructive to work through in detail the simple logic
of such a sequence of /a\ plans made and executed on the basis of mistaken
knowledge; (b) the discovery of the unplanned sacrifice of desirable oppor-
tunities, or the non-attainment of planned objectives, due to this limited
knowledge and (c) the revision of plans for future trading, in the light of
the information gained from these market experiences.
Let us consider two market participants a and b. We will assume a
to start his day with a given, nature-endowed bundle of commodities, in-
cluding the commodities A and B, in such a proportion that he would
gladly give up a number of units (let us say any number up to m) of B in
order to gain a single additional unit of A. On the other hand, b starts
his day with an endowment such that his tastes would lead him to give up
a unit of A in order to acquire a number of units of B (let us say any num-
ber I or higher, with l<m).
Both a and b enter the market with estimates of the ratio between the
price of A and the price of B that will rule in the market during the day.
On the one hand, a expects the price of A to be k times the price of B;
that is, he expects to be able to acquire commodity A by selling commodity
B at the rate of k units of B for each unit of A acquired. On the other
hand, b expects the price of A to be n times the price of B (with k<l<m<n).
Thus, he expects to be able to acquire n units of commodity B in the market
for each unit of A that he sells in the market.
It is not difficult to understand the plans that a will formulate and
follow on the basis of his estimate. He believes it possible to acquire a
single unit of A for the sacrifice of k units of B. He does not think it
necessary to sacrifice any more than k units of B per unit of A; on the other
hand, he does not hope to be able to acquire a unit of A for the sacrifice
of less than k units of B. He will refuse, therefore, to enter into any trans-
actions that will yield less than one unit of A for the sacrifice of k units of
B. And, again, he will not waste his time in seeking to obtain more than
one unit of A for k units of B. Or, to repeat the sense of the previous
sentences in different words, a will refuse any transactions calling for the
sacrifice of more than k units of B per unit of A; and he will not waste
time seeking to obtain A at the sacrifice, per unit of A, of less than k units
of B. (Of course, were a to find that a unit of A could not only not be
obtained for k units of B, but could not even be obtained for anything
less than the sacrifice of more than m units of B, he would refuse to sell
B to get A, not only because he believes that better opportunities are

available but also because trade on such terms would, on our assumptions
above, make him subjectively worse off than at the start of the day.)10
Similarly, b will refuse to enter into any transactions to sell A and
buy B, which will yield him less than n units of B per unit of A, because
he is sure that he can obtain better terms elsewhere in the market. (More-
over, any transactions that yield, per unit of A, not only less than n units
of B, but even less than I units of B, will be rejected for the additional rea-
son that trade on such terms would leave b actually worse off than at the
start of the day.) n Again, b will not waste time seeking to acquire more
than n units of B in exchange for the sale of one unit of A. To repeat
these obvious propositions in different words, b will refuse transactions
calling for the sacrifice of more than one unit of A per n units of B; and
he will waste no time seeking to acquire n units of B in exchange for less
than one unit of A.
It is clear that a and b could both gain through mutual exchange, with
a selling B and buying A, and b selling A and buying B, at any ratio of the
price of A to the price of B lying between I and m. So long as a can obtain
a unit of A for less than m units of B, and so long as B can obtain at least
/ units of B for 1 unit of A, each can gain from trade. Since l<m, there
is clearly a range of price ratios that can create mutually profitable barter.
But it is equally clear that with their differing estimates of market con-
ditions, a and b will not come to terms with one another, since each believes
he can do better elsewhere. On the one hand, a will not give more than
k units of B for one unit of A; on the other hand, b will not accept less
than n units of B for one unit of A. Since k<n, no trade between a and
b can result. But let us consider the possible relations that these estimates
on the part of a and b may bear to the actualities of the market. A number
of cases may be considered in turn.
1. It is possible that both a and b might not be disappointed at all.
It is possible that a might find people willing to buy B from him and sell
A to him at prices yielding one unit of A for every k units of B. Similarly,
it is possible that B might be able to sell one unit of A and buy n units of
B. But together these possibilities simply mean that two prices exist in
a single market either for A, or for B, or for both. This can continue
only for as long as there is ignorance, among a and those with whom he deals,
of what is going on among b and those with whom he deals (and vice versa).
As soon as the price differentials are discovered, some market participants
will find that it is profitable to buy A in the area where a deals, and sell
it in the area where B deals; and to buy B in the area where b deals, and

10 In fact if the ratio of the price of A to that of B is very large, a will actually sell
some units of A in order to acquire B.
11 And for very low ratios of the price of A to that of B, b will even sell some units
of B in order to acquire A.

sell it in the area where a deals. In this way the price differentials will tend
to disappear, and in the course of time both a and b will revise their es-
timates of the price ratio between A and B, closer and closer together.
2. Another possibility is that the prices of A and B in the market are
such that one unit of A can be had in exchange for a particular number
of units of B that is greater than k but smaller than n. (In this and the
succeeding cases we ignore the possibility of more than one set of prices
for the various commodities in the same market, such as was considered
in the preceding paragraph.) It is clear that a will buy no A on these
terms, since he believes he can get A elsewhere in the market with a smaller
sacrifice of B. (And if the market prices are such that one unit of A re-
quires the sale of more than m units of B, then a would be actually worse
off by such a trade.) But at the end of the day a will find himself disap-
pointed in his hopes; he will not have bought any A with the proceeds
from the sale of B. He will have discovered that he has passed up profit-
able opportunities (to get A by sacrificing B at ratios calling for more than
k of B) in the vain hope of obtaining A for the sacrifice of only k of B per
unit of A. (Of course the lost opportunities would have been profitable
for a, on our assumptions, only if the A:B ratio, while less than ¬:k, was
not less than l:m.) In making his plans for the succeeding trading days,
a will revise downward his estimate of the relative price of B and revise
upward his estimate of the relative price of A.
As far as concerns b, the situation is rather similar. He will not sell
A in order to buy B, at the going rate of one of A to less than n of B,
because he thinks he can get n full units of B for the sacrifice of one unit
of A, elsewhere in the market. At the end of the day, he too is disap-
pointed. He will have discovered that he has passed up desirable op-
portunities (of getting something less than n units of B for the sacrifice of
a unit of A) in the vain hope of obtaining a more advantageous deal. (Of
course, the lost opportunities would have been desirable, on our assump-
tions, only if the A:B ratios, while greater than \:n, are no greater than
1:/.) In making his plans for the succeeding trading days, b will revise
upward his estimate of the relative price of B and revise downward his
estimate of the relative price of A.
3. A third possibility is that in the market, the price of A is less than
k times the price of B; thus, a unit of A is equivalent in the market to less
than k units of B.
(a) Let us consider b's reaction first. It should be clear that b will
react in exactly the same way we saw that he would react when the price
of A was more than k times (but less than n times) the price of B. He
would refuse to trade at market prices. He would do this (on our as-
sumptions) for two reasons. First, b would argue that if he wished to
buy B by selling A, he could do so much more advantageously (on his

estimation of market conditions) elsewhere in the market (where he expects
to secure as much as n units of B per unit of A sold.) Second, since we
assumed that under no circumstances would b buy B by selling A should
the relative price of B rise to the rate of less than / units of B per unit of
A sold, b will consider himself only to lose subjectively, that is, to be worse
off by trading A for B at market rates. (In fact b, after his discovery of
the market rates of exchange, might be tempted in the future to sell B and
buy A.) At the close of the day, b will have discovered how grossly he
had underestimated the relative price of B; and in making his plans for
the future, he will revise upward his estimate of the relative price of B
and revise downward his estimate of the relative price of A.
It is worthwhile to consider briefly, for this case, the impact of these
changes in b's plans upon the market. Suppose that the initial market
prices of A and B were at variance with the fundamental data of the mar-
ket in such a degree that with the given ratio between the market price
of A and that of B, too many people planned to convert A into B as against
those planning to convert B into A (in other words that the relative price
of B was too low and that of A too high). In this case b's original estimate
of the relative price of B was even lower than that "erroneously" ruling
in the market. Since the market as a whole "erred" in pricing B relatively
too low and A relatively too high, some of those who planned to sell A and
buy B must necessarily be disappointed. We have already seen that since
b's estimate of the relative market valuation of B was even lower, his plans,
too, were of course bound to be disappointed. (As it happens, b's misjudg-
ment of the relative market valuation of A and B may even have helped to
make the misjudgment by the market more serious in its consequences.
This can be seen by observing that if b had known that in the market one
unit of A could be had for so little of B, he might have sold B to buy A,
thereby helping to make less serious the general movement to convert A
into B.) In any event, as b's disappointment, along with that of others,
tends to raise estimates of the relative price of B and lower estimates of
the relative price of A, the market prices of subsequent trading days tend
to lower the number of units of B obtainable through the sale of a unit
of A. (This is so since we are observing that the terms transactions are
effected upon depend directly upon the estimates of prospective market
prices held by market participants.) This adjustment in the relative prices
of A and B will tend to eliminate the discrepancy between the quantity
of A, which people wish to convert into B, and the quantity of A, into which
people wish to convert B.
On the other hand, suppose that the market prices of A and B on the
initial trading day were at variance with the fundamental conditions of
the market, but, this time, in the opposite direction. Suppose, that is,
that the going prices induced too many people to plan to convert B into

A, as compared with those planning to convert A into B (in other words
that the price of B was relatively too high and that of A relatively too low.)
In this case b's original mistaken estimate of the relative prices of A and
B in the markets tends, if anything, to make less acute the immediate con-
sequences of the "erroneously" high relative valuation placed upon B by
the market. At the ruling relative market prices, it is true, too many
people are attempting to sell B and buy A, as compared with those who can
be induced at these prices to sell A and buy B. Inevitably, some of the
former will find their plans disappointed. But if b had correctly esti-
mated the relative prices of A and B on the market, he too might (as we
have seen) have attempted to sell B and buy A. (Of course b's own mis-
judgment of market prices led him to make plans to sell A and buy B on
terms that again could only be disappointed.) In any event the disap-
pointment of those who find that they are not able to sell B in order to buy
A at going market prices will result in lower estimates of the relative price
of B and higher estimates of the relative price of A. Similarly, b's esti-
mates of relative market prices will be revised (in the reverse direction)
toward the new relative market prices.
(b) Let us now turn to consider a's reaction to a market where one
unit of A is equivalent in value to less than k units of B (that is, less than
a has expected and planned for). Since a enters the market expecting (and
willing) to have to sacrifice k units of B in order to be in a position to
buy one unit of A, he will waste no time seeking more advantageous terms.
He might not, in fact, discover the unexpectedly favorable terms on which
he can convert B into A until the close of the day. At the close of the day
he will certainly revise his estimate of tomorrow's relative market price
of A downward, and that of B upward.
Let us suppose that the relative market price of A is too high, and
that of B too low, so that too many people are induced to convert A into
B, as compared with those wishing to convert B into A. Then if a's error
in the estimation of prices kept him back from converting B into A3 this
would tend to accelerate somewhat the market tendency lowering the
relative price of A and raising that of B. At the original prices, some
of those wishing to sell A and buy B are disappointed. If a remained in
ignorance of the opportunities that all these people are prepared to afford
him, more of them will have been disappointed than need have been the
On the other hand, if the relative market price of A is too low, and
that of B too high, so that too many people are led to attempt to convert
B into A, a's ignorance of what is available in the market would not make
any real difference to subsequent market movements. If a had known of
the opportunities available in the market for the conversion of £ into A
and was not to be disappointed in them, someone else instead would have

been disappointed. In any event the market would proceed to price A
relatively higher, and B relatively lower, than before.12

Thus far we have been proceeding on the assumption that any pro-
spective buyer of a commodity is able, in seeking out the best possible
terms, to choose from among a number of holders of the commodity. On
this assumption, any prospective seller of the commodity deliberating upon
the price he should ask for the commodity, knows, as we have seen, that
he will only be wasting his time if he demands a price any higher than the
lowest price asked by his competitors. The possibility of one seller charg-
ing a higher price for a commodity than another seller can arise only from
ignorance on the part of one or other of the sellers or the knowledge on
the part of the first seller that some prospective buyers are ignorant of
the opportunities made available by the second seller. Under these cir-
cumstances the market process ensures that the prices charged by the differ-
ent sellers will move toward each other until the equilibrium price range
is achieved. In other words the competitive market process tends to ensure
that no seller charge a price for a commodity higher than that which the
most eager among the sellers is prepared to accept in order to sell an ad-
ditional unit of it. This state of affairs assumes, of course, that although
the initial commodity endowments of the different market participants
are not alike, nevertheless each commodity is present in significant amounts
in the endowments of a considerable number of participants.
A special case arises when a particular commodity is present each day
in the initial endowment of only one of the participants. This participant
may of course be unwilling to sell any units of this rare commodity. He
may rank each unit of it, which he possesses, higher on his subjective value
scale than any additional quantity of any other commodity. But it is
possible that he might be glad to give up some of this rare commodity in
exchange for appropriate quantities of some other commodities (and this
is of course more likely to be the case when his endowment of the rare
commodity is large, and his endowment of other commodities meager). In
this situation the participant thus favored is in a position to act as a monop-
olist with respect to the commodity he has sole possession of.13
A monopolist is in the unique position of being able to demand a price
for the monopolized commodity without paying regard to prices charged
for the commodity by other sellers, since no such other sellers exist. Al-

12 Similar analysis may be employed to work out the consequences, for the plans of a
and b respectively, of a market where the price of A is more than n times the price of B.
l3The reader may imagine a group of islanders who have divided up their island into
equal holdings, in one of which oil is discovered.

though he knows, like the sellers of any other commodity, that for each
quantity of his commodity there is a price it cannot be sold above, for
him this upper limit is not set by the actions of other sellers of this com-
modity. This upper limit is determined by the subjective valuation of
this commodity of its prospective buyers as compared with other com-
modities. It is misleading, as we shall see, to say that the monopolist is
exempt from competition, but he certainly does not have to meet the
competition of other sellers of his commodity.
The competition that the monopolist does have to meet is from the
actions of sellers of other commodities. When the monopolist asks a
particular price for his commodity, any buyer of a unit of it, with a given
set of market prices for the other commodities, must sacrifice definite
quantities of one or more of these other commodities in order to be able to
buy the unit of the monopolized commodity. The lower the prices ob-
tained by the sellers of other commodities, the larger must be the quanti-
ties of these other commodities that must be sacrificed in order to buy a
unit of the monopolized commodity. Similarly, with given prices of the
other commodities, any increase in the price per unit demanded by the
monopolist again calls for larger sacrifices of other commodities in order
to acquire a unit of the monopolized commodity.
Thus, the monopolist who is attempting to convert his initial commod-
ity endowment into the most desirable commodity bundle possible through
exchange is faced with a special problem. Like every other participant in
the market, he must make estimates of the prices that will rule in the market
for all the other commodities. But whereas other participants must make
an estimate of the market price of every commodity that they sell (one
reason for this being that these prices will set the upper limit to those
that they themselves can demand), a monopolist is not obliged nor is he
able to estimate a market price for the monopolized commodity. He must
himself set the price. He knows that too high a price will lead many
prospective buyers to exchange their own commodities for commodities
other than the monopolized one (where they are able to secure better terms).
On the other hand, it is not difficult to perceive a lower limit to the price
that the monopolist might conceivably be willing to sell any given quantity
of his commodity at. This lower limit is set for a monopolist as for anyone
else by the point at which the subjective sacrifice involved in the sale
of the given quantity of the commodity ranks higher on the seller's value
scale than the additional quantities of other commodities whose purchase
would be made possible by the sale.
No matter what price he charges, the monopolist knows that he can
sell only a smaller quantity than it would be possible to sell at a lower
price. This, by itself, might mean that he would be refusing to sell some
units of the monopolized commodity, even though he actually values the

quantities of other commodities obtainable in exchange for those units
more highly than those units themselves. On the other hand, by keeping
the price higher and thus admittedly reducing the quantity of the monopo-
lized commodity sold, the monopolist may be able to obtain more in ex-
change for the units of his commodity, which he is able to sell at the high
price, than he could obtain by selling a larger quantity at the lower price.
Of course, the competition provided by the sellers of other commodities
may be so effective that the monopolist's most advantageous course of action
must be to charge a very low price indeed. In such a case any increase
in the price would reduce the number of units sold so drastically that the
increase in price for those remaining units that can be sold is insufficient
to make up the lost revenue. The elasticity of demand for the monopo-
lized commodity is of relevance in this regard. The strength of the competi-
tion of other commodities is reflected in the elasticity of demand of the mo-
nopolized commodity at all points on the demand curve. If the demand
curve for the commodity is inelastic at any particular price-quantity point, it
will be better for the monopolist to charge a higher price rather than
that corresponding to the point. With demand inelastic at a certain point,
total revenue is greater with the smaller quantity sold at the higher price.
The particular price that the monopolist will attempt to select will permit
a quantity to be sold that yields more revenue than any other price-quantity
combination. At this stage elasticity of demand will be unitary.14
One particular feature of the monopoly situation is especially worthy
of note. The monopolist's power to force buyers to pay higher prices is
a result of his ability to restrict the quantity of the commodity that he puts
on sale. It is this feature that distinguishes the monopoly price from the
competitive price. When a seller of a commodity is competing with other
sellers of the same commodity, he is not in a position to deliberately raise
the price by holding some of the commodity off the market. Were such
a competing seller to hold back some of his commodity, his customers would
14 The optimum price decision for the monopolist can be illustrated by a diagram.
Let AR be the market demand curve for the monopolized good. This line will therefore
be the monopolist's average revenue line, and the MR line will show his marginal reve-

Figure 7-1
nue. At the point P, marginal revenue is zero (and the point elasticity of demand uni-
tary). At this point the monopolist will be maximizing his revenue. Since he has no
costs (and we are ignoring his own demand for the good), this point is therefore the best
for him.

certainly not be prepared to pay higher prices in order to secure their share
of the reduced supply. They would simply buy elsewhere. But when a
monopolist holds back part of a supply of his commodity (even though
he might be able to sell all of it at a low price, and even though the supply
thus held back is perhaps of no use at all to him personally), he may be
in a position to drive up the price.13 Those most eager to obtain the com-
modity now find that in order to bid it away from other less eager
competing buyers, they must offer prices these other buyers are unable or
unwilling to match. The degree to which a monopolist may be able to
force up the price in this way, depends, as we have seen, on the degree
of competition provided by other commodities, reflected in the elasticity
of demand for the monopolized commodity.
So long as the number of monopolized commodities is not large, as
compared with the total number of commodities on the market, the exist-
ence of monopoly elements in an exchange market does not seriously upset
the analysis of this chapter. Monopoly elements will distort somewhat
both the pattern of prices of the various commodities and the quantities
of them exchanged in the market, but the logic of price determination is
not fundamentally altered. The results are different, but the market proc-
ess operates in an essentially unaltered manner. When we consider the
case of a monopolist-producer, we will return once again to an analysis
of the effects upon the efficiency of the entire market system that are intro-
duced by monopoly elements.

The analysis of this chapter places us in a position to understand the
seething agitation of changing prices that can be expected in any large pure
exchange market, even in the absence of any changes in initial commodity
endowments or changes in tastes.
Each participant in the market will be constantly scanning the latest
prices of the various commodities in making his market plans for the day.
Market participants will be constantly revising their estimates of the prices
they must expect to pay when buying the various commodities, and the
prices they can expect to obtain by selling them, in the light of their ex-
An interesting special case is where the monopolized good is present so plentifully
in the monopolist's endowment, that it would, under competitive conditions, have been
a free good. If the plentiful endowment had been distributed among the endowments
of many participants, none of them could have gained command over other goods
through exchange, by virtue of ownership of this plentifully endowed commodity. Un-
der competition there is so much of the commodity that even the lowest positive price
would bring forth a supply of it on the market in excess of the aggregate quantity that
participants wish to buy. The monopolist, by restricting the quantity that he offers to
the market, may be able to turn the free good into one that commands a positive price.

periences, and disappointments, in yesterday's market. In earlier sections
of this chapter we examined the kind of logic entailed in making decisions
concerning two commodities. In a market with many goods, the same
logic will be constantly applied to every possible pair of commodities and
every possible pair of groups of commodities.
The prices ruling on any one day will reflect the estimates for that day,
on the part of the market participants, of the entire set of relative market
prices. With these estimates in mind, each participant will seek to trans-
form his initial commodity endowment into the most desirable bundle of
commodities he can obtain by buying and selling in the market. His plans
will be made according to the logic of consumer choice discussed in earlier
chapters. He will go out into the market with a plan calling for the pur-
chase of definite quantities of specified commodities, and the sale of quanti-
ties of other commodities, all at the expected prices. These plans of the
various market participants, made on the basis of imperfect and fragmentary
knowledge, are almost certain to fail to mesh completely. There will in-
evitably be disappointed plans, as well as the realization that inferior op-
portunities have been seized at the expense of superior opportunities that
remained unknown.
These disappointments and discoveries will lead to a new set of esti-
mates for the following day and a new set of buying and selling plans.
This kind of agitation will proceed for as long as the set of prices expected
to rule in the market is in anyway different from those that fulfill the con-
ditions for the equilibrium market. Whenever the prices are such that
the relative values of any two commodities, A and B, induces too many
people to convert A into B, as compared with those wishing to convert B
into A, conditions exist that will bring about a readjustment in prices in
the direction of reducing previous "disappointments."
In this process of market agitation the market participants with the
keenest judgment of market conditions will be the most successful. Even
though in this chapter we are not allowing any commodities to be produced,
and are not permitting any activity to be based on speculation, there is still
a range within which the entrepreneur can exercise his peculiar function.
Whenever one man has superior knowledge of what is going on in the vari-
ous sections of the market, he is in a position to buy and sell more advanta-
geously than others. He will be able to buy the goods he wishes to buy
where prices are lowest, and sell those he wishes to sell where prices are high-
est. When his superior knowledge suggests that the same good is available
at different prices in the same market, he will engage in arbitrage to take ad-
vantage of the price differential. In this way some participants will buy
goods in the market only to resell them immediately at a profit. By this
kind of activity the superior knowledge of the entrepreneur is placed at the
disposal of all the participants in a market. More and more people dis«

cover that he is willing to pay higher-than-usual prices in those market areas
where the price of a good is low; more and more others discover that he is
willing to sell for lower-than-usual prices in those market areas where the
price of a good is high. The competition of all the market participants,
each seeking the best opportunities available in the market, places pressure


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