Principles of Economics

Marshall, Alfred
(1842-1924)
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First Pub. Date
1890
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London: Macmillan and Co., Ltd.
Pub. Date
1920
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8th edition
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APPENDIX F

BARTER*63.

App.F.1

Let us consider the case of two individuals engaged in barter. A has, say, a basket of apples, B a basket of nuts; A wants some nuts, B wants some apples. The satisfaction which B would get from one apple would perhaps outweigh that which he would lose by parting with 12 nuts; while the satisfaction which A would get from perhaps three nuts would outweigh that which he would lose by parting with one apple. The exchange will be started somewhere between these two rates: but if it goes on gradually, every apple that A loses will increase the marginal utility of apples to him and make him more unwilling to part with any more: while every additional nut that he gets will lower the marginal utility of nuts to him and diminish his eagerness for more: and vice versâ with B. At last A's eagerness for nuts relatively to apples will no longer exceed B's; and exchange will cease because any terms that the one is willing to propose would be disadvantageous to the other. Up to this point exchange has increased the satisfaction on both sides, but it can do so no further. Equilibrium has been attained; but really it is not the equilibrium, it is an accidental equilibrium.

App.F.2

There is, however, one equilibrium rate of exchange which has some sort of right to be called the true equilibrium rate, because if once hit upon it would be adhered to throughout. It is clear that if very many nuts were to be given throughout for an apple, B would be willing to do but little business; while if but very few were to be given, A would be willing to do but little. There must be some intermediate rate at which they would be willing to do business to the same extent. Suppose that this rate is six nuts for an apple; and that A is willing to give eight apples for 48 nuts, while B is willing to receive eight apples at that rate; but that A would not be willing to give a ninth apple for another six nuts while B would not be willing to give another six nuts for a ninth apple. This is then the true position of equilibrium; but there is no reason to suppose that it will be reached in practice.

App.F.3

Suppose, for instance, that A's basket had originally 20 apples in it and B's 100 nuts, and that A at starting induced B to believe that he does not care much to have any nuts; and so manages to barter four apples for 40 nuts, and afterwards two more for 17 nuts, and afterwards one more for eight. Equilibrium may now have been reached, there may be no further exchange which is advantageous to both. A has 65 nuts and does not care to give another apple even for eight; while B, having only 35 nuts, sets a high value on them, and will not give as many as eight for another apple.

App.F.4

On the other hand, if B had been the more skilful in bargaining he might have perhaps induced A to give six apples for 15 nuts, and then two more for seven. A has now given up eight apples and got 22 nuts: if the terms at starting had been six nuts for an apple and he had got 48 nuts for his eight apples, he would not have given up another apple for even seven nuts; but having so few nuts he is anxious to get more and is willing to give two more apples in exchange for eight nuts, and then two more for nine nuts, and then one more for five; and then again equilibrium may be reached; for B, having 13 apples and 56 nuts, does not perhaps care to give more than five nuts for an apple, and A may be unwilling to give up one of his few remaining apples for less than six.

App.F.5

In both these cases the exchange would have increased the satisfaction of both as far as it went; and when it ceased, no further exchange would have been possible which would not have diminished the satisfaction of at least one of them. In each case an equilibrium rate would have been reached; but it would be an arbitrary equilibrium.

App.F.6

Next suppose that there are a hundred people in a similar position to that of A, each with about 20 apples, and the same desire for nuts as A; and an equal number on the other side similarly situated to the original B. Then the acutest bargainers in the market would probably be some of them on A's side, some of them on B's; and whether there was free communication throughout the market or not, the mean of the bargains would not be so likely to differ very widely from the rate of six nuts for an apple as in the case of barter between two people. But yet there would be no such strong probability of its adhering very closely to that rate, as we saw was the case in the corn-market. It would be quite possible for those on the A side to get in varying degrees the better of those on the B side in bargaining, so that after a time 6500 nuts might have been exchanged for 700 apples; and then those on the A side, having so many nuts, might be unwilling to do any more trade except at the rate of at least eight nuts for an apple, while those on the B side, having only 35 nuts apiece left on the average, might probably refuse to part with any more at that rate. On the other hand, the B's might have got in various degrees the better of the A's in bargaining, with the result that after a time 1300 apples had been exchanged for only 4400 nuts: the B's having then 1300 apples and 5600 nuts, might be unwilling to offer more than five nuts for an apple, while the A's, having only seven apples apiece left on the average, might decline that rate. In the one case equilibrium would be found at a rate of eight nuts for an apple, and in the other at the rate of five nuts. In each case an equilibrium would be attained, but not the equilibrium.

App.F.7

This uncertainty of the rate at which equilibrium is reached depends indirectly on the fact that one commodity is being bartered for another instead of being sold for money. For, since money is a general purchasing medium, there are likely to be many dealers who can conveniently take in, or give out, large supplies of it; and this tends to steady the market. But where barter prevails apples are likely to be exchanged for nuts in one case, for fish in another, for arrows in another, and so on; the steadying influences which hold together a market in which values are set in money are absent; and we are obliged to regard the marginal utilities of all commodities as varying. It is however true that, if nut-growing had been a chief industry of our barter-district, and all the traders on both sides had large stores of nuts, while only the A's had apples; then the exchange of a few handfuls of nuts would not have visibly affected their stores, or changed appreciably the marginal utility of nuts. In that case the bargaining would have resembled in all fundamentals the buying and selling in an ordinary corn-market.

App.F.8

Thus, for instance, let a single A with 20 apples, bargain with a single B. Let A be willing to sell 5 apples for 15 nuts, a sixth for 4 nuts, a seventh for 5, an eighth for 6, a ninth for 7 and so on; the marginal utility of nuts being always constant to him, so that he is just willing to sell the eighth for 6 and so on, whether in the earlier part of the trade he has got the better of the bargaining with B or not. Meanwhile let B be willing to pay 50 nuts for the first five apples rather than go without them, 9 for a sixth, 7 for a seventh, 6 for an eighth, and only 5 for a ninth; the marginal utility of nuts being constant to him, so that he will just give 6 nuts for the eighth apple whether he has bought the earlier apples cheaply or not. In this case the bargaining must issue in the transfer of eight apples, the eighth apple being given for six nuts. But of course if A had got the better of the bargaining at first, he might have got 50 or 60 nuts for the first seven apples; while if B had got the better of the bargaining at first, he might have got the first seven apples for 30 or 40 nuts. This corresponds to the fact that in the corn-market discussed in the text, about 700 quarters would be sold with a final rate of 36s.; but if the sellers had got the best of the bargaining at first, the aggregate price paid might be a good deal more than 700 times 36s.; while if the buyers had got the better of the bargaining at first, the aggregate price would be a good deal less than 700 times 36s. The real distinction then between the theory of buying and selling and that of barter is that in the former it generally is, and in the latter it generally is not, right to assume that the stock of one of the things which is in the market and ready to be exchanged for the other is very large and in many hands; and that therefore its marginal utility is practically constant. See Note XII. bis in the Mathematical Appendix.


Notes for this chapter


63.
See p. 336.

End of Notes


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