5. Determination of Price, Equilibrium Price
One of the most important problems in economic analysis is the question, what principles
determine the formation of prices on the free market? What can be said by logical derivation
from the fundamental assumption of human action in order to explain the determination
It is most convenient to begin with a case of isolated exchange, a case where only two
isolated parties are involved in the exchange of two goods.
For example, Johnson and Smith are considering a possible exchange of a horse of the former
for some barrels of fish possessed by the latter.
The question is, what can economic analysis say about the determinants of the exchange
rate established between the two goods in the exchange?
An individual will decide whether or not to make an exchange on the basis of the relative
positions of the two goods on his value scale.
Thus, suppose the value scale of Smith, the possessor of the fish, is as follows.
His highest value, 103 barrels of fish.
His second highest value, 102 barrels of fish.
His third highest value, 101 barrels of fish.
His fourth highest value, a horse.
His fifth highest value, 100 barrels of fish.
His sixth highest value, 99 barrels of fish.
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If the horse in terms of the fish offered by Smith is 100 barrels or less, then Smith will make the exchange.
If the price is 101 barrels or more, then the exchange will not be made.
Suppose Johnson's value scale looks like this.
Johnson's highest value, 104 barrels of fish.
His second highest value, 103 barrels of fish.
3rd highest value 102 barrels of fish, his 4th highest value a horse, his 5th highest
value 101 barrels of fish, his 6th highest value 100 barrels of fish, his 7th highest
value 99 barrels of fish.
Then Johnson will not give up his horse for less than 102 barrels of fish.
If the price offered for his horse is less than 102 barrels of fish, he will not make
the exchange.
Here it is clear that no exchange will be made, for at Johnson's minimum selling price
of 102 barrels of fish, it is more beneficial for Smith to keep the fish than to acquire
the horse.
In order for an exchange to be made then, the minimum selling price of the seller must
Must be lower than the maximum buying price of the buyer for that good.
In this case, it must be lower than the price of 100 barrels of fish per horse.
Suppose that this condition is met, and Johnson's value scale is as follows.
Johnson's highest value, 84 barrels of fish.
Johnson's second highest value, 83 barrels of fish.
His third highest value, 82 barrels of fish.
His fourth highest value, 81 barrels of fish.
His fifth highest value, a horse.
His sixth highest value, 80 barrels of fish.
His seventh highest value, 79 barrels of fish.
Johnson will sell the horse for any amount of fish at or above 81 barrels.
This then is his minimum selling price for the horse.
With this as Johnson's value scale, and Smith's as previously described, what price will they
agree upon for the horse, and conversely for the fish?
All analysis can say about this problem is that since the exchange must be for the mutual
benefit of both parties, the price of the good in isolated exchange will be established
Somewhere Between the Maximum Buying Price and the Minimum Selling Price
That is, the price of the horse will be somewhere between 100 barrels and 81 barrels of fish.
Similarly, the price of the fish will be set somewhere between one eighty-first and one
one-hundredth of a horse per barrel. We cannot say at which point the price will be set.
That depends on the data of each particular case, on the specific conditions prevailing.
In particular, it will depend upon the bargaining skill of the two individuals.
Clearly, Johnson will try to set the price of the horse as high as possible, while Smith
will try to set the price as low as possible.
This is based on the principle that the seller of the product tries to obtain the highest
We cannot predict the point that the two will agree on except that it will be somewhere in this range set by the two points.
Of course, given other value scales, the final prices might be determinate at our point or within a narrow range.
Now, let us gradually remove our assumption of isolated exchange.
Let us first assume that Smith has a competitor, Brown, a rival in offering fish for the desired
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Johnson's highest value is 93 barrels of fish. His second highest, 92 barrels of fish. His third highest, 91 barrels of fish. His fourth highest, a horse. His fifth highest, 90 barrels of fish. His maximum buying price. Sixth highest, 89 barrels of fish. Seventh highest, 88 barrels of fish.
Brown's highest value is 84 barrels of fish, second highest 83 barrels of fish, third highest
82 barrels of fish, fourth highest 81 barrels of fish, his minimum selling price, fifth
highest a horse, sixth highest 80 barrels of fish, seventh highest 79 barrels of fish.
Brown and Smith are competing for the purchase of Johnson's horse.
Clearly, only one of them can make the exchange for the horse, and since their goods are identical
to Johnson, the latter's decision to exchange will be decided by the price offered for the
horse.
Obviously, Johnson will make the exchange with that potential buyer who will offer the
highest price.
Their value scales are such that Smith and Brown can continue to overbid each other as
long as the price range is between 81 and 90 barrels of fish per horse.
Thus, if Smith offers Johnson an exchange at 82 barrels per horse, Brown can compete
by raising the bid to 84 barrels of fish per horse, etc.
This can continue, however, only until Brown's maximum buying price has been exceeded.
If Smith offers 91 barrels for the horse, it no longer pays for Brown to make the exchange,
and he drops out of the competition.
Thus, the price in the exchange will be high enough to exclude the less capable or less
urgent buyer, the one whose value scale does not permit him to offer as high a price as
as the other, more capable buyer.
We do not know exactly what the price will be, but we do know that it will be set by
bargaining somewhere at or below the maximum buying price of the most capable buyer and
above the maximum buying price of the next most capable buyer.
It will be somewhere between 100 barrels and 91 barrels, and the exchange will be made
with Smith.
We see that the addition of another competing buyer for the product considerably narrows
the zone of bargaining in determining the price that will be set.
This analysis can easily be extended to a case of one seller and n number of buyers,
each offering the same commodity in exchange.
Thus suppose that there are five potential buyers for the horse, all offering fish, whose
His value scales are as follows.
Smith's highest value, 101 barrels of fish.
His second highest value, a horse.
His third highest value, 100 barrels of fish.
A's highest value, 100 barrels of fish.
His second highest value, a horse.
His third highest value, 99 barrels of fish.
B's highest value, 98 barrels of fish.
With only one horse to be disposed of to one buyer, the buyers overbid each other until
each must drop out of the competition.
Finally, Smith can outbid A, his next most capable competitor, only with a price of 100
barrels of fish.
We see that in this case the price in the exchange is uniquely determined once the various
This value scales are given at 100, since at a lower price A is still in the bidding,
and at a higher price no buyer will be willing to conclude the exchange.
At any rate, even if the value scales are not such as to determine the price uniquely,
the addition of more competitors greatly narrows the bargaining zone.
The general rule still holds, the price will be between the maximum buying price of the
most capable and that of the next most capable competitor, including the former and excluding
the latter.
Auction sales are examples of markets for one unit of a good with one seller and many
buyers.
It is also evident that the narrowing of the bargaining zone has taken place in an upward
The case of one-sided competition of many sellers with just one buyer is the direct converse of the above, and may be considered by merely reversing the example and considering the price of the fish instead of the price of the horse.
As more sellers of the fish competed to conclude the exchange with the one buyer, the zone of determination of the price of fish narrowed, although this time in a downward direction, and to the further advantage of the buyer.
As more sellers were added, each tried to underbid his rival to offer a lower price for the product than his competitors.
The sellers continued to underbid each other until all but the one seller were excluded from the market.
In a case of many sellers and one buyer, the price will be set at a point between the minimum selling price of the second most capable and that of the most capable competitor,
strictly at a point below the former and down to or including the latter.
In the final example above, the point was pushed down to be uniquely determined at the latter point, one one hundredth horse per barrel.
We have so far considered the cases of one buyer and more than one seller, and of one seller and more than one buyer.
We now come to the only case with great importance in a modern complex economy based on an intricate network of exchanges,
Let us, therefore, consider a market with any number of competing buyers and sellers.
Any product could be considered, but our hypothetical example will continue to be the sale of horses
in exchange for fish, with the horses as well as the fish considered by all parties as homogeneous
units of the same good.
The following is a list of the maximum buying prices of the various buyers, based on the
valuations on their respective value scales.
Buyers of horses.
First buyer, X1, maximum buying price, 100 barrels of fish.
Buyer X2's, maximum buying price, 98 barrels of fish.
Buyer X3's Maximum Buying Price, 95 Barrels of Fish
Buyer X4's Maximum Buying Price, 91 Barrels of Fish
Buyer X5's Maximum Buying Price, 89 Barrels of Fish
Buyer X6's Maximum Buying Price, 88 Barrels of Fish
Buyer X7's Maximum Buying Price, 86 Barrels of Fish
Buyer X8's maximum buying price, 85 barrels of fish.
Buyer X9's maximum buying price, 83 barrels of fish.
The following is a list of the minimum selling prices of the various sellers on the market.
Sellers of horses.
The first seller, Z1, has a minimum selling price of 81 barrels of fish.
Z2's minimum selling price, 83 barrels of fish.
Z3's minimum selling price, 85 barrels of fish.
Z4's minimum selling price, 88 barrels of fish.
Z5's minimum selling price, 89 barrels of fish.
Z6's minimum selling price, 90 barrels of fish.
The most capable buyer of horses we recognize as Smith, with a buying price of 100 barrels.
Johnson is the most capable seller, the seller with the lowest minimum selling price, at
81 barrels.
The problem is to find the principle by which the price or prices of the exchanges of horses
will be determined.
Now let us first take the case of X1, Smith.
It is clear that it is to the advantage of Smith to make the exchange at a price of 100
barrels for the horse.
Yet, it is to Smith's greater advantage to buy the good at the lowest possible price.
He is not engaged in overbidding his competitors merely for the sake of overbidding.
He will try to obtain the good for the lowest price that he can.
Therefore Smith will prefer to begin bidding for a horse at the lowest prices offered by
his competitors, and only raise the offered price if it becomes necessary to do so in
order to avoid being shut out of the market.
Similarly, Johnson would make an advantageous sale at a price of 81 barrels.
However, he is interested in selling his product at the highest possible price.
He will underbid his competitor only if it becomes necessary to do so in order to avoid
being shut out of the market without making a sale.
It is evident that buyers will tend to start negotiations by offering as low prices as
as possible, while sellers will tend to start by asking for as high a price as they think
they can obtain.
Clearly, this preliminary testing of the market will tend to be more prolonged in a new market,
where conditions are unfamiliar, while it will tend to be less prolonged in an old market,
where the participants are relatively familiar with the results of the price formation process
Let us suppose that buyers begin by offering the low price of 82 barrels for a horse.
Here is a price at which each of the buyers would be glad to make a purchase, but only
one seller, Z1, would be willing to sell at 82.
It is possible that Z1, through ignorance, might conclude the exchange with some one
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As the offering price rises, the least capable buyers, as in the previous case, begin to be excluded from the market.
A price of 84 will bring two sellers into the market, but will exclude X9 from the buyer's side.
As the offering price rises, the disproportion between the amount offered for sale and the
amount demanded for purchase at the given price diminishes, but as long as the latter
is greater than the former, mutual overbidding of buyers will continue to raise the price.
The amount offered for sale at each price is called the supply.
The amount demanded for purchase at each price is called the demand. Evidently, at the first
price of 82, the supply of horses on the market is one. The demand for horses on the market
is nine. Only one seller would be willing to sell at this price, while all nine buyers
would be willing to make their purchase. This reflects the progressive entry into the market
of the Sellers as the Price Increases and the Dropping Out of the Buyers as the Price
Increases.
As was seen above, as long as the demand exceeds the supply at any price, buyers will continue
to overbid and the price will continue to rise.
The converse occurs if the price begins near its highest point, thus if sellers first demand
At a price of 101 barrels for the horse, there will be eight eager sellers and no buyers.
At a price of 99, the sellers may find one eager buyer, but chances are that a sale will
not be made.
The buyer will realize that there is no point in paying such a high price, and the other
sellers will eagerly underbid the one who tries to make the sale at the price of 99.
Thus, when the price is so high that the supply exceeds the demand at that price, underbidding
of suppliers will drive the price downward.
As the tentative price falls, more sellers are excluded from the market, and more buyers
enter it.
If the overbidding of buyers will drive the price up whenever the quantity demanded is
is greater than the quantity supplied, and the underbidding of sellers drives the price
down whenever supply is greater than demand, it is evident that the price of the good will
find a resting point where the quantity demanded is equal to the quantity supplied, that is,
where supply equals demand.
At this price and at this price only, the market is cleared, that is, there is no incentive
5 for buyers to bid prices up further or for sellers to bid prices down.
In our example, this final or equilibrium price is 89, and at this price 5 horses will
be sold to 5 buyers.
This equilibrium price is the price at which the good will tend to be set and sales to
be made.
It is possible that the equilibrium point will not be uniquely determined at one definite
price.
Thus, the pattern of supply and demand schedules might be as follows.
At a price of 89, 5 are supplied and 6 are demanded.
At a price of 90, 6 are supplied and 5 are demanded.
The inequality is the narrowest possible, but there is no one point of equality.
In that case, if the units are further divisible, then the price will be set to clear the market
at a point in between, say 89.5 barrels of fish per horse.
If both goods being exchanged are indivisible further, however, such as cows against horses,
And the equilibrium price will be either 89 or 90, and this will be the closest approach
to equilibrium, rather than equilibrium itself.
Specifically, the sales will be made to the five most capable buyers at that price, X1,
X2, X3, X4 and X5.
The other less capable or less urgent buyers are excluded from the market, because their
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The minimum selling price is 89, is just able to make his sale at 89.
He is the marginal seller, the seller at the margin, the one who would be excluded with
a slight fall in price.
On the other hand, X5 is the least capable of the buyers who have been able to stay in
the market.
He is the marginal buyer, the one who would be excluded by a slight rise in price.
Since it would be foolish for the other buyers to pay more than they must to obtain their
supply, they will also pay the same price as the marginal buyer, that is, 89.
Similarly, the other sellers will not sell for less than they could obtain.
They will sell at the price permitting the marginal seller to stay in the market.
Evidently, the more capable or more urgent buyers and sellers, the supramarginal, which
which includes the marginal, obtain a psychic surplus in this exchange, for they are better
off than they would have been if the price had been higher or lower.
However, since goods can be ranked only on each individual's value scale, and no measurement
of psychic gain can be made either for one individual or between different individuals,
A little of value can be said about this psychic gain, except that it exists.
We cannot even make the statement, for example, that the psychic gain in exchange obtained
by X1 is greater than that of X5.
The excluded buyers and sellers are termed sub-marginal.
The specific feature of the clearing of the market performed by the equilibrium price
is that at this price alone, all those buyers and sellers who are willing to make exchanges
can do so. At this price, five sellers with horses find five buyers for the horses. All who wish to
buy and sell at this price can do so. At any other price, there are either frustrated buyers or
For Frustrated Sellers
Thus, at a price of eighty-four, eight people would like to buy at this price, but only
two horses are available.
At this price, there is a great amount of unsatisfied demand, or excess demand.
Conversely, at a price of, say, ninety-five, there are seven sellers eager to supply horses,
but only three people willing to demand horses.
Thus, at this price there is unsatisfied supply or excess supply.
Other terms for excess demand and excess supply are shortage and surplus of the good.
Aside from the universal fact of the scarcity of all goods, a price that is below the equilibrium
price creates an additional shortage of supply for demanders, while a price above equilibrium
Some creates a surplus of goods for sale as compared to demands for purchase.
We see that the market process always tends to eliminate such shortages and surpluses
and establish a price where demanders can find a supply and suppliers a demand.
It is important to realize that this process of overbidding of buyers and underbidding
Bidding of sellers always takes place in the market, even if the surface aspects of the
specific case make it appear that only the sellers or buyers are setting the price.
Thus, a good might be sold in retail shops with prices simply quoted by the individual
seller.
But the same process of bidding goes on in such a market as in any other.
If the sellers set their prices below the equilibrium price, buyers will rush to make
their purchases, and the sellers will find that shortages develop, accompanied by queues
of buyers eager to purchase goods that are unavailable.
Realizing that they could obtain higher prices for their goods, the sellers raise their quoted
prices accordingly.
On the other hand, if they set their prices above the equilibrium price, surpluses of
of Unsold Stocks will appear, and they will have to lower their prices in order to move
their accumulation of unwanted stocks and to clear the market.
The case where buyers quote prices and therefore appear to set them is similar.
If the buyers quote prices below the equilibrium price, they will find that they cannot satisfy
all their demands at that price.
As a result, they will have to raise their quoted prices.
On the other hand, if the buyers set the prices too high, they will find a stampede of sellers
with unsaleable stocks, and will take advantage of the opportunity to lower the price and
clear the market.
Thus, regardless of the form of the market, the result of the market process is always
is to tend toward the establishment of the equilibrium price via the mutual bidding of
buyers and sellers.
It is evident that if we eliminate the assumption that no preliminary sales were made before
the equilibrium price was established, this does not change the results of the analysis.
Even if, through ignorance and error, a sale was made at a price of $81 or $99, these prices
This still will be ephemeral and temporary, and the final price for the good will tend
to be the equilibrium price.
Once the market price is established, it is clear that one price must rule over the entire
market.
This has already been implied by the fact that all buyers and sellers will tend to exchange
at the same price as their marginal competitors.
There will always be a tendency on the market to establish one and only one price at any
time for a good.
Thus, suppose that the market price has been established at 89, and that one crafty seller
tries to induce a buyer to buy at 92.
It is evident that no buyer will buy at 92 when he knows that he can buy on the regular
market at 89.
Similarly, no seller will be willing to sell at a price below the market if he knows that
he can readily make his sale at 89.
If for example an ignorant seller sells a horse at 87, the buyer is likely to enter
the market as a seller to sell the horse at 89.
Such drives for arbitrage gains, buying and selling to take advantage of discrepancies
in the price of a good act quickly to establish one price for one good over the entire market.
Such market prices will tend to change only when changing supply and demand conditions alter the
equilibrium price and establish a condition of excess supply or excess demand where before
The market had been cleared. It is evident that as the price increases, new suppliers with higher
minimum selling prices are brought into the market, while demanders with low maximum buying prices
will begin to drop out. Therefore, as the price decreases, the quantity demanded must always
The tabulation of supply offered at any given price is known as the supply schedule. Similarly, the tabulation of demand is the demand schedule.
The direct determinants of the price are the marginal buyers and sellers, while the valuations
of the supermarginal people are important in determining which buyers and sellers will
be at the margin.
The valuations of the excluded buyers and sellers far beyond the margin have no direct
influence on the price.
Up to this point we have assumed for the sake of simplicity and clarity that each demander
as well as each supplier was limited to one unit of the good, the price of which we have
been concentrating on, the horse.
Now we can remove this restriction and complete our analysis of the real world of exchange
by permitting suppliers and demanders to exchange any number of horses that they may desire.
It will be seen immediately that the removal of our implicit restriction makes no substantial
change in the analysis.
Thus, let us revert to the case of Johnson, whose minimum selling price for a horse was
81 barrels of fish.
Let us now assume that Johnson has a stock of several horses.
He is willing to sell one horse, the first, for a minimum price of 81 barrels, since on
In his value scale, he places the horse between 81 and 80 barrels of fish.
What will be Johnson's minimum selling price to part with his second horse?
We have seen earlier in this chapter that according to the law of marginal utility,
as a man's stock of goods declines, the value placed on each unit remaining increases.
Conversely, as a man's stock of goods increases, the marginal utility of each unit declines.
Therefore, the marginal utility of the second horse, or strictly, of each horse after the first horse is gone,
will be greater than the marginal utility of the first horse.
This will be true even though each horse is capable of the same service as every other.
Similarly, the value of parting with a third horse will be still greater.
On the other hand, while the marginal utility placed on each horse given up increases,
the marginal utility of the additional fish acquired in exchange will decline.
The result of these two factors is, inevitably, to raise the minimum selling price for each successive horse sold.
Thus, suppose the minimum selling price for the first horse is 81 barrels of fish.
When it comes to the second exchange, the value foregone of the second horse will be
greater, and the value of the same barrels in exchange will decline.
As a result, the minimum selling price below which Johnson will not sell the horse will
increase, say, to 88.
Thus, as the seller's stock dwindles, his minimum selling price increases.
Johnson's value scale may appear as follows.
Johnson's highest value is 100 barrels of fish, followed by 99 barrels of fish, followed
by a fourth horse, followed by 98 barrels of fish, followed by 97 barrels of fish, followed
Followed by eighty-seven barrels, followed by eighty-six barrels, followed by eighty-five
barrels, followed by eighty-four barrels, followed by l
The selling prices are 81, 88, 95 and 99 barrels of fish.
On the basis of this value scale, Johnson's own individual supply schedule can be constructed.
He will supply 0 horses up to a price of 80, 1 horse at a price between 81 and 87, 2 horses
With the price between $88 and $94, three horses at a price of $95 to $98 and four horses
at a price of $99 and above.
The same can be done for each seller in the market.
Where the seller has only one horse to sell, the supply schedule is constructed as before.
It is clear that a market supply schedule can be constructed simply by adding the supplies
The Essentials of the Foregoing Analysis of Market Supply Remain Unchanged
9.
The fact that it is one man that is supplying the new units, rather than different men,
does not change the results of the analysis.
What it does is to reinforce the rule that the supply must always remain unchanged or
increase, with an increase in price.
For in addition to the fact that new suppliers will be brought into the market with an increase
The same supplier will offer more units of the good.
Thus the operation of the law of marginal utility serves to reinforce the rule that the supply cannot decrease at higher prices, but must increase or remain the same.
The exact converse occurs in the case of demand.
Suppose that we allow buyers to purchase any desired number of horses.
We remember that Smith's maximum buying price for the first horse was 100 barrels of fish.
If he considers buying a second horse, the marginal utility of the additional horse will
be less than the utility of the first one, and the marginal utility of the same amount
of fish that he would have to give up will increase.
If the marginal utility of the purchases declines as more are made, and the marginal utility
of the good given up increases, these factors result in lower maximum buying prices for
each successive horse bought.
Thus, Smith's value scale might appear as follows, Smith's highest value 102 barrels
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An individual demand schedule for Smith can be constructed.
Smith will demand four horses at a price of 83 and below,
three horses at a price of 84 to 89, two horses at a price of 90 to 94,
one horse at a price of 95 to 100, and zero horses at a price of 101 or over.
Such individual demand schedules can be made for each buyer on the market.
It is evident that the effect of allowing more than one unit to be demanded by each buyer brings in the law of marginal utility,
to reinforce the aforementioned rule that the demand must either increase or remain unchanged as the price decreases,
for added to the fact that lower prices bring in previously excluded buyers each
individual will tend to demand more as the price declines since the maximum
buying prices will be lower with the purchase of more units in accordance
with the law of marginal utility let us now sum up the factors determining
Making Prices in Interpersonal Exchange
One price will tend to be established for each good on the market, and that price will tend
to be the equilibrium price, determined by the intersection of the market's supply and
demand schedules.
Those making the exchanges at this price will be the supramarginal and marginal buyers and
and The Seller's, while the less capable or sub-marginal will be excluded from the sale
because their value scales do not permit them to make an exchange, their maximum buying
prices are too low, or their minimum selling prices too high.
The market supply and demand schedules are themselves determined by the minimum selling
prices and maximum buying prices of all the individuals in the market, the latter in total.
are determined by the placing of the units to be bought and sold on the individual's value scales, these rankings being influenced by the law of marginal utility.
In addition to the law of marginal utility, there is another factor influencing the rankings on each individual's value scale.
It is obvious that the amount that Johnson will supply at any price is limited by the stock of goods that he has available.
Thus, Johnson may be willing to supply a fourth horse at a price of 99, but if this exhausts his available stock of horses,
no higher price will be able to call forth a larger supply from Johnson.
At least this is true as long as Johnson has no further stock available to sell.
Thus, at any given time, the total stock of the good available puts a maximum limit on
the amount of the good that can be supplied in the market.
Conversely, the total stock of the purchasing good will put a maximum limit on the total
of the sale good that any one individual or the market can demand.
At the same time that the market's supply and demand schedules are setting the equilibrium
price, they are also clearly setting the equilibrium quantity of both goods that will be exchanged.
In our previous example, the equilibrium quantities exchanged are 5 horses and 5 x 89 or 445 barrels
Tools of Fish for the aggregate of the market.