There is a striking passage in Marshall’s famous article on Distribution and Exchange: The fact is, that twenty years ago I abandoned the use of curves for market problems because they were not really wanted; and I found people would not heed the note of warning that the curves for the normal problem relate to rates of production and consumption and those for market curves (sic) to amounts bought and sold.’1 Marshall reiterates it in one of his letters to Edgeworth: ‘You know I never apply curves or mathematics to market values.
I found that, if I once got people to use Demand and Supply curves which discussed stocks along the axis of x, they could not easily be kept from introducing the notion of stock when flow was essential.’2 The object of this paper is to examine the implication of this note of warning. So market price is important.
Let us see what the curves usually employed for the purpose teach us. The problem, let us remind ourselves, relates to the formation of price in a daily market. Two persons (or two groups of persons), A and B, have in their possession fixed stocks of two goods X and Y respectively, and they come to the market to interchange them. The dealers have their individual preference systems regarding the two goods, which can be shown in terms of indifference curves. So market analysis is important.
From these indifference curves we can also derive their respective offer curves. What light do these curves throw on the determination of the equilibrium of exchange ? Do they tell us what price ratio would evolve as a result of the two parties and bargaining of the two parties and what amounts of the goods would be interchanged? Let us have a look into the relevant diagrams.3
A given stock OX of X, measured along the horizontal axis, is held by A; and a given stock O Y, measured along the vertical axis,
Note : Originally published in The Indian Economic Journal, July, 1954.
1 The Economic Journal, Vol. VIII, p. 46. Italics mine.
2 Memorials of Alfred Marshall, ed. Pigou, (London, 1925), p. 435.
3 The origin of the curves used here can be traced to Edgeworth’s Mathematical Psychics (Part I, section on Economical Calculus). So market analysis is important.
But a succinct account of the various implications of the curves is given by Bowley in Chapter I of his Mathematical Groundwork of Economics (Oxford, 1924), from where the diagrams used in the text are adapted is held by B. The indifference curves 70, 71; 2 etc., of A are superimposed upon the indifference curves /0, iltra etc., of B with reference to the same origin O; and their offer curves OA and OB are placed alongside of one another, so that they intersect at P. CClt called the contract curve, is the locus of points of tangency between ,4’s indifference curves and B’s indifference curves; the intersection of the offer curves, also a point where a pair of the indifference curves touch one another, thus lies on the contract curve.
Q is the point of tangency between B’s offer curve and one of the indifference curves of A, and Q1,is the point of tangency between A’s offer curve and one of the indifference curves of B. All this is shown on Diagram I. Diagram II just takes over the section relating to the offer curves. So market analysis is important.