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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.
MARKET PROCESS IN A PURE EXCHANGE ECONOMY 11 9


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
market.7
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.)
120 MARKET THEORY AND THE PRICE SYSTEM


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
knowledge.
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.
MARKET PROCESS IN A PURE EXCHANGE ECONOMY 121


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.
122 MARKET THEORY AND THE PRICE SYSTEM


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.

THE MULTI-COMMODITY MARKET
WITHOUT PERFECT KNOWLEDGE
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,
MARKET PROCESS IN A PURE EXCHANGE ECONOMY 1 23


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
1 24 MARKET THEORY AND THE PRICE SYSTEM


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.
MARKET PROCESS IN A PURE EXCHANGE ECONOMY 125


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
1 26 MARKET THEORY AND THE PRICE SYSTEM


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
MARKET PROCESS IN A PURE EXCHANGE ECONOMY 127


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

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