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NOTE 4.04. The Gains of Exchange

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4. The Gains of Exchange

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As in the case considered in Chapter 2, the sellers who are included in the sale at the

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equilibrium price are those whose value scales make them the most capable, the most eager

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sellers. Similarly, it will be the most capable or most eager buyers who will purchase the

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The Good at the Equilibrium Price

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With a price of two and a half grains of gold per pound of butter, the sellers will be those

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for whom two and a half grains of gold is worth more than one pound of butter.

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The buyers will be those for whom the reverse valuation holds.

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Those who are excluded from sale or purchase by their own value scales are the less capable,

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for Less Eager Buyers and Sellers, who may be referred to as sub-marginal.

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The marginal buyer and the marginal seller are the ones whose schedules just barely permit

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them to stay in the market.

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The marginal seller is the one whose minimum selling price is just two and a half.

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A slightly lower selling price would drive him out of the market.

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The marginal buyer is the one whose maximum buying price is just two and a half.

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A slightly higher selling price would drive him out of the market.

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Under the law of price uniformity, all the exchanges are made at the equilibrium price

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once it is established, that is, between the valuations of the marginal buyer and those

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Those of the marginal seller, with the demand and supply schedules and their intersection

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determining the point of the margin.

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It is clear from the nature of human action that all buyers will benefit or decide they

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will benefit from the exchange.

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Those who abstain from buying the good have decided that they would lose from the exchange.

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These propositions hold true for all goods.

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Such importance has been attached by some writers to the psychic surplus gained through

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exchange by the most capable buyers and sellers, and attempts have been made to measure or

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compare these surpluses.

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The buyer who would have bought the same amount for four grains is obviously attaining a subjective

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benefit because he can buy it for two and a half.

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are purely ordinal, and there is no way whatever of measuring the distance between the rankings.

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Indeed, any concept of such distance is a fallacious one. Consequently, there is no way of making interpersonal comparisons and measurements,

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and no basis for saying that one person subjectively benefits more than another.

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We might in some situations make such comparisons as historians using imprecise judgment.

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We cannot, however, do so as praxeologists or economists.

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We may illustrate the impossibility of measuring utility or benefit in the following way.

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Suppose that the equilibrium market price for eggs has been established at three grains per dozen.

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The following are the value scales of some selected buyers and would-be buyers.

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At the top of buyer A's value scale is four grains of gold, followed by three and a half grains of gold,

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followed by one dozen eggs, followed by three grains of gold, followed by two and a half grains of gold.

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At the top of buyer B's value scale is five grains of gold, followed by one dozen eggs, followed by four and a half grains of gold, followed by four grains, followed by three and a half grains, followed by three grains, followed by two and a half grains.

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The value scale of buyer C is topped by three and a half grains of gold, followed by three grains of gold, followed by one dozen eggs, followed by two and a half grains of gold.

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The money prices are divided into units of one half grain. For purposes of simplification, each buyer is assumed to be considering the purchase of one unit, one dozen eggs.

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C is obviously a sub-marginal buyer. He is just excluded from the purchase, because three grains is higher on his value scale than the dozen eggs.

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A and B, however, will make the purchase.

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Now A is a marginal buyer. He is just able to make the purchase.

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In a price of three and a half grains, he would be excluded from the market, because

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of the rankings on his value scale.

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B, on the other hand, is a super marginal buyer.

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He would buy the dozen eggs even if the price were raised to four and a half grains.

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But can we say that B benefits from his purchase more than A?

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No, we cannot.

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Each value scale, as has been explained previously, is purely ordinal, a matter of rank.

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Even though B prefers the eggs to four and a half grains, and A prefers three and a half

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grains to the eggs, we still have no standard for comparing the two surpluses.

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All we can say is that above the price of three grains, B has a psychic surplus from

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Exchange, while A becomes sub-marginal with no surplus.

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But even if we assume for a moment that the concept of distance between ranks makes sense,

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for all we know, A's surplus over 3 grains may give him a far greater subjective utility

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than B's surplus over 3 grains, even though the latter is also a surplus over 4.5 grains.

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There can be no interpersonal comparison of utilities, and the relative rankings of money

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and goods on different value scales cannot be used for such comparisons.

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Those writers who have vainly attempted to measure psychic gains from exchange have concentrated

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on consumer surpluses.

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Most recent attempts try to base their measurements on the price a man would have paid for the

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for the Good if confronted with the possibility of being deprived of it.

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These methods are completely fallacious.

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The fact that A would have bought a suit at 80 gold grains as well as at the 50 grains

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market price, while B would not have bought the suit if the price had been as high as

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52 grains, does not, as we have seen, permit any measurement of the psychic surpluses,

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Nor does it permit us to say that A's gain was in any way greater than B's.

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The fact that even if we could identify the marginal and supramarginal purchasers, we

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could never assert that one's gain is greater than another's, is a conclusive reason for

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the rejection of all attempts to measure consumers or other psychic surpluses.

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There are several other fundamental methodological errors in such a procedure.

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In the first place, individual value scales are here separated from concrete action.

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But economics deals with the universal aspects of real action, not with the actor's inner

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psychological workings.

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We deduce the existence of a specific value scale on the basis of the real act.

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We have no knowledge of that part of a value scale that is not revealed in real action.

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The question how much one would pay if threatened with deprivation of the whole stock of a good

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is strictly an academic question with no relation to human action.

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Like all other such constructions, it has no place in economics.

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Furthermore this particular concept is a reversion to the classical economic fallacy of dealing

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with the whole supply of a good as if it were relevant to individual action.

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It must be understood that only marginal units are relevant to action, and that there is

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no determinate relation at all between the marginal utility of a unit and the utility

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of the Supply as a Whole.

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It is true that the total utility of a supply increases with the size of the supply.

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This is deducible from the very nature of a good.

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Ten units of a good will be ranked higher on an individual's value scale than four

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units will.

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But this ranking is completely unrelated to the utility ranking of each unit when the

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Total utility, indeed, makes sense as a real and relevant, rather than as a hypothetical concept, only when actual decisions must be made concerning the whole supply, in that case, it is still marginal utility, but with the size of the margin or unit now being the whole supply.

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The absurdity of the attempt to measure consumer's surplus would become clearer if we considered, as we logically may, all the consumer's goods at once, and attempted to measure in any way the undoubted consumer's surplus arising from the fact that production for exchange exists at all. This has never been attempted.

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It is interesting that those who attempt to measure consumer surplus explicitly rule out consideration of all goods or of any good that looms large in the consumer's budget.

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Such a course is convenient but illogical and glosses over fundamental difficulties in the analysis.

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It is, however, typical of the Marshallian tradition in economics.