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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
exchange.
110 MARKET THEORY AND THE PRICE SYSTEM


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
MARKET PROCESS IN A PURE EXCHANGE ECONOMY 11 1


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.
112 MARKET THEORY AND THE PRICE SYSTEM


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.

SIMPLE PRICE COMPETITION WITHOUT 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.
MARKET PROCESS IN A PURE EXCHANGE ECONOMY 113


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
today.5
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.
114 MARKET THEORY AND THE PRICE SYSTEM


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
MARKET PROCESS IN A PURE EXCHANGE ECONOMY 115


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
116 MARKET THEORY AND THE PRICE SYSTEM


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.

THE MARKET FOR SEVERAL NON-PRODUCIBLE GOODS:
THE PROBLEM
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
MARKET PROCESS IN A PURE EXCHANGE ECONOMY 117


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.

THE EQUILIBRIUM SITUATION
FOR THE MULTI-COMMODITY MARKET
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
118 MARKET THEORY AND THE PRICE SYSTEM


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-

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