The following conclusions emerge from these constructions: (a) If the transactions proceed by trial and error if, that is to say, the equilibrium process consists of successive bargains at rates of interchange which are revised after each transaction, the final equilibrium will lie somewhere on the contract curve. With the completion of each transaction O will vary and there will be a revision of the rate of interchange.
The market will close with a rate which will be given by the common tangent to a pair of indifference curves; for, outside it neither of the parties will be able to move without bringing the other down to a less preferred position. (b) If the bargain is made as a whole if, that is to say, the exchange takes place as a single transaction from the position O, then the range of contract will lie on the double curve QPQi, which is called the bargaining locus, Q and Qt being points which represent the extreme most favourable bargains for A and B respectively. If A is the stronger bargainer, he will be able to bring B over to a point near to Q. On the other hand, if B is the stronger bargainer, exchange will take place at a point nearer to 61- In either of the circumstances considered above, equilibrium is indeterminate. In either case, all we know is the range over which the equilibrium will lie; we cannot know its precise position.
However, in case (b), if at all the rate of interchange given by the relative bargaining strength of the two parties were known, the amounts of X and Y exchanged could be read off from the relevant offer curve. In so far as the whole transaction is completed in a single bargain, a definite volume of trade will be associated with a given rate of interchange. For example, taking the extreme most favourable rate for A to prevail, namely tan _QOX, it can be seen from Diagram II that the amount of X exchanged will be ON and the amount of Y exchanged will be QN. In case (a), on the other hand, even if the final rate of interchange were known, the other variables would still be unknown. Here the equilibrium process leads up through a series of exchanges to a final position. But the final rate does not provide a clue to the earlier rates, nor for the matter of that to amounts of X and Y exchanged. However and this is the crucial point if somehow the parties hit upon the rate represented by the co-ordinates of the point P where the two offer curves intersect, and if this rate were adhered to throughout the course of exchange, then the market would close at P and the volume of trade could be derived from the rate of interchange. So market analysis is important.
The same result would follow if the parties had equal bargaining strength and their pressure were such as to bring the equilibrium position over to P, In such circumstances tan Z_POX would be the rate of interchange and OM and PM would be the amount of X and Y exchanged respectively. So market analysis is important.
Edgeworth invokes the hypothesis of what he calls ‘recontract’ to explain determinateness of equilibrium. In so far as earlier contracts can be revised as equilibrium price is approached, no transaction need actually take place at prices other than the equilibrium price. And if the scope of recontract is so wide that the ultimate equilibrium takes place at P, then we have a situation which has just been contemplated, namely one in which the amount of A’ exchanged, the amount of Y exchanged and the price ratio between the two are all derived from the point of intersection of the offer curves. This condition, according to Edgeworth, is fulfilled under perfect competition. When there are a large number of buyers and sellers (holders of X and Y in our example), a large scope is opened up for recontract and the range of final contract is narrowed down, until in the limit it gets down to the point at which the offer curves interest.
So far so good. But is this a realistic hypothesis? Does it typify the operation of the market as we know it? Marshall does not believe it does, and would not dismiss the possibility of transactions at prices other than the equilibrium price. The device that Marshall employs in this connexion is well-known. He concentrates on each single money-commodity transaction and assumes that the marginal utility of money is constant. This means, when money is measured along the 7-axis and the commodity along the .Y-axis, that the contract curve is a vertical line passing through the point of intersection of the offer curves. On this assumption the final price of the commodity turns out to be determinate whatever the initial price and the intermediate prices at which transactions are held. Yet even here the equilibrium point gives us only the amount of the commodity bought and sold; it does not give us the amount of money that is transferred from the buyers to the sellers in the course of transactions. The situation still eludes the apparatus of our offer curves; we know the measure of X, but we do not know the measure of Y. So market analysis is important.
Let us examine this with reference to the famous corn-market example of Marshall. The table shows that for 700 quarters of corn the marginal rate of preference for corn in terms of money is the same for both the parties; and since the marginal utility of money is constant, this rate (1:36) is independent of the amount of money that the buyers part with and the sellers receive in the course of trade. Thus whatever route the market may take whether it starts with 35s per quarter or with 37s per quarter trading will stop at the 700th quarter and at that point the price will be 36s per quarter, any other price being unacceptable either to the buyers or to the sellers. We have the equilibrium price at 36s per quarter and the amount of corn bought and sold at 700 quarters. But our apparatus breaks down when we come to considering the other variable the amount of money that is transferred from the buyers to the sellers in the process of exchange; for that is something which in the circumstances cannot be read off from the demand and supply schedules.
Obviously more money will pass from the buyers to the sellers if the sellers are the shrewder bargainers and the market starts with a price nearer to 37s per quarter than if it were the other way about and the market started with a price nearer to 35s per quarter. What difference this makes depends upon how far away these ‘false’ prices (as Hicks would call them) are from the equilibrium price and how much trade takes place at these prices. So market analysis is important.