Chapter 62 Appendix VI Barter

In barter, market transactions are more volatile than where money is used; partly because one can generally give or get back a certain amount (not a percentage) of value in money without greatly Changing the marginal utility of money to him, which is not the case in the form of a single commodity. Let us consider the situation where two people barter.Suppose A has a basket of apples; B has a basket of walnuts; A needs some walnuts, and B needs some apples.B may gain more satisfaction from one apple than he loses by giving away twelve walnuts.And A may gain more satisfaction from three walnuts than he loses from ceding an apple.The exchange will start at some point midway between these two ratios.However, if the exchange continues, each apple ceded by A will increase its marginal utility to him and make him unwilling to cede any more apples, while each additional walnut he will decrease his marginal utility to him , and make him unwilling to ask for more walnuts; B's situation is just the opposite.In the end, A will no longer be more enthusiastic about walnuts than about apples; and the exchange must stop, because any conditions that one party is willing to offer are not beneficial to the other party.Up to this point, the exchange increases the satisfaction of both parties and cannot be increased any further.Equilibrium appears; but in fact it is not the only equilibrium, but a kind of accidental equilibrium.

There is, however, an equilibrium rate of exchange which may be called the true equilibrium rate, because once it is encountered it is maintained to the end.Obviously, if many walnuts are always exchanged for an apple, B is willing to exchange very little, and if few walnuts are to be exchanged for an apple, A is also willing to exchange very little.There must be an intermediate ratio at which both parties are willing to trade to the same extent.Suppose the ratio is six walnuts for one apple; A is willing to exchange eight apples for forty-eight walnuts, and B is willing to accept eight apples at that rate; however, A is unwilling to exchange the ninth apple for six more walnuts, while B is unwilling to exchange six walnuts for the ninth apple.This is the true equilibrium position then; however, there is no reason to assume that such an equilibrium will actually be reached.

Suppose, for example, that there were originally twenty apples in A's basket, and a hundred nuts in B's basket, and suppose that at first A induced B to believe that he would not want nuts; and thus managed to exchange forty apples for forty. Walnuts, later exchanged two apples for seventeen walnuts, and then exchanged one apple for eight walnuts.Assuming that an equilibrium has been reached at that time, further exchanges are unfavorable to both parties.A owns sixty-five walnuts, and is unwilling to exchange an apple or even eight walnuts; while B has only thirty-five walnuts, so he values ​​them very high, and is unwilling to exchange eight walnuts for an apple.

On the other hand, if B is a good trader, he might be able to induce A to exchange six apples for fifteen nuts, and then to exchange two apples for seven nuts.At that time, A gave up eight apples and got twenty-two walnuts.If the initial condition is six walnuts for one apple, and he obtains forty-eight walnuts with eight apples, he may refuse to exchange one apple or even seven walnuts.But, as he had so few nuts, he was anxious to get some more, and was willing to exchange two apples for eight more nuts, then two apples for nine nuts, and one apple for five nuts; so Equilibrium is again reached; since B has only thirteen apples and fifty-six nuts, he may not be willing to exchange more than five nuts for an apple, while A has few apples left and cannot exchange one apple for six nuts , maybe not.

In both cases the exchange, so far as it goes, increases the satisfaction of both parties; when it ceases, further exchange necessarily diminishes the satisfaction of at least one of the parties.In each case, an equilibrium is reached; but it is an arbitrary equilibrium. Next, assume that there are a hundred people in the same position as A, each of whom has about twenty apples, and who have the same desire for walnuts as A; .The most astute sellers in the market may be some on Party A and some on Party B.Whether or not there is communication in the market, the average number of transactions is likely not to be far from the ratio of six walnuts to an apple, as in the case of two-person transactions.However, there is probably no chance of sticking to the ratio as closely as we have seen in the grain market.During the transaction, the people of Party A are likely to beat the people of Party B to varying degrees. Therefore, they then exchanged 700 apples for 6,500 walnuts; The apples-for-eight-nuts ratio, perhaps unwilling to make any more trades.And the people of Party B may refuse to continue to sell according to that ratio because each person has an average of 35 walnuts left.On the other hand, the people of Party B may beat the people of Party A to varying degrees during the transaction. As a result, 4,400 walnuts were exchanged for 1,300 apples in a short time. Apples and 5,600 walnuts, except at the rate of five walnuts for one apple, may not be willing to sell more, and Party A may refuse that rate because each person has only seven apples left on average.On one occasion, the ratio of eight walnuts to one apple is reached, and on the other occasion, the ratio of five walnuts to one apple is reached.

The instability of the ratio by which equilibrium is attained depends indirectly on the fact that one commodity is exchanged for another, and not for money.Since money is the general means of purchase, there seem to be many people who can conveniently withdraw or throw large quantities of money; this has a tendency to stabilize the market.But where barter prevails, apples are likely to be exchanged sometimes for walnuts, sometimes for fish, sometimes for arrows, etc.; The marginal utility of various commodities is not regarded as variable.Indeed, if walnut cultivation is the main industry in our barter area, and all the buyers and sellers have large stocks of walnuts, and only the person of Party A owns apples, then the exchange of a few handfuls of walnuts will have no effect on their reserves. have a significant effect without significantly changing their marginal utility.

For example, assume that A has 20 apples and trades with B.Suppose A is willing to sell fifteen walnuts for five apples, four walnuts for the sixth apple, five walnuts for the seventh apple, six walnuts for the eighth apple, and seven walnuts for the ninth apple. And so on; because the marginal utility of walnuts to him remains unchanged, he is willing to sell six walnuts with the eighth apple, and so on, regardless of whether he took advantage of B in the previous transaction.Also assume that B would rather pay fifty walnuts for the first five apples than throw them away, nine walnuts for the sixth apple, seven walnuts for the seventh apple, and six walnuts for the eighth apple , he only pays five walnuts for the ninth apple; since the marginal utility of walnuts to him remains unchanged, he is willing to buy the eighth apple with six walnuts, no matter whether the apples he bought before are cheap or expensive.In this case, since the eighth apple sells only six walnuts, the transaction must end in the transfer of eight apples.Of course, if A took advantage of the transaction at first, he might buy fifty or sixty walnuts for the first seven apples; A walnut was exchanged for the first seven apples.This is consistent with the fact that the corn market sells about 700 quarts of wheat at a final price of thirty-six shillings; 700 x 36 shillings, and if the buyers had initially gained the upper hand, the total price would probably be much less than 700 x 36 shillings.The real difference between the theory of exchange and the theory of barter is that, in the theory of exchange, it is assumed that the stock of a commodity which is to be exchanged for another commodity in the market is large and in the hands of many persons; therefore its marginal utility In fact, it is constant; this assumption is generally true; in the theory of barter, this assumption is generally false.See Note 12(b) in the Mathematics Appendix.