The Theory of Reciprocal Demand

The Theory of Reciprocal Demand, John Stuart Mill

Mill extended his deep understanding of supply and demand into the area of international values. Citing Ricardo as the premier writer on the issue of comparative costs and advantage, Mill pro­ceeded to construct a model that included both cost and demand determinants of international values and the terms of trade. Again, Mill used merely verbal exposition (Edgeworth and Marshall once more provided the graphics), but there is perhaps no better evidence of his analytical powers than his model of the equation of international demand.

Mill set out his ideas on trade in his Essays on Some Unsettled Questions of Political Economy but repeated the essentials of his argument in his Principles . Abstracting from transport costs and technological change, Mill built a two-country (England and Germany), two-commodity (cloth and linen) model in order to investigate international price determina­tion. Mill stated his law of reciprocal demand concisely:

The produce of a country exchanges for the produce of other countries, at such val­ues as are required in order that the whole of her exports may exactly pay for the whole of her imports. This law of International Values is but an extension of the more general law of Value, which we called the Equation of Supply and Demand__The value of a commodity always so adjusts itself as to bring the de­mand to the exact level of the supply.

But all trade, either between nations or individuals, is an interchange of commod­ities, in which the things that they respectively have to sell constitutes also their means of purchase: the supply brought by the one constitutes his demand for what is brought by the other. So that supply and demand are but another expression for re­ciprocal demand: and to say that value will adjust itself so as to equalize demand with supply, is in fact to say that it will adjust itself so as to equalize the demand on one side with the demand on the other (Principles, pp. 592-593).

The Edgeworth-Marshall Exposition Mill amplified his theory with an elab­orate numerical example, but an economy of exposition may be achieved by utilizing a graphic interpretation of reciprocal demand popularized by Edgeworth and Marshall. In Figure 2 the lines OP, OP', etc., represent the alternative international price lines that might face England and Germany. They express the price of cloth in terms of linen or the price of linen in terms of cloth, i.e., the "terms of trade." The flatter the OP curve, the cheaper linen is in terms of a given quantity of cloth and the more dear cloth is in terms of linen. The point can easily be established with respect to Figure 2. Quantity OC0 of cloth will trade for quantity OL1 of linen assuming price line OP'_ i.e.,
at a ratio of OL1/OC0—but quantity OC0 will trade for OL0, a ratio of OL0/ OC0, given price line OP. Obviously, the line OP represents a lower price of linen in terms of cloth than price line OP' does, because a larger quantity of linen may be obtained for the same amount of cloth.


Now assume some fixed quantity of linen, say OL0. The price of cloth in terms of linen is given as a ratio OC0/OL0 along price line OP or as OC1/OL0 along OP'. Clearly the price of linen becomes dearer in terms of cloth (more cloth for a given amount of linen) as the price line becomes more vertical (a movement from OP to OP', for example). Thus it is clear that if England is trading the good on the vertical axis (cloth) for the German good (linen) on the horizontal axis, England would get better terms of trade with a clockwise ro­tation of the price line and Germany's position would improve with a counter­clockwise rotation. When England's terms of trade improve, Germany's dete­riorate, and vice versa. In other words, a lowering of the price of linen in terms of cloth raises the price of cloth in terms of linen. It should be clear that a movement along any given price line—say, at points A and B in Figure 2— connotes the same price ratio of cloth to linen and linen to cloth.
Mill Once Again With a concept of the price line in hand, we may now turn to Mill's analysis. Mill viewed the trading of goods as a "real-goods" trade. As he noted, "the supply brought by the one constitutes his demand for what is brought by the other. So that supply and demand are but another expression for reciprocal demand." Mill's statement may be illustrated in Figure 2. At price OP' of cloth/linen, Germany will demand OC2 of cloth but will simulta­neously supply OL2 of linen. At a lower price of cloth, represented by price line OP", Germany will increase its demand for cloth to 0C3. Simultaneously, Germany will supply an increased amount, OL3, of linen.

A demand for cloth is thus expressed by a supply of linen. By varying price and connecting such points as C and D, a curve OG can be traced out. It is called a reciprocal-demand curve, but it is not a demand curve constructed in the usual sense. That is, it does not relate prices of a good to the quantity of that good demanded. Rather, it expresses the international demand for a good in terms of the amounts of another good that a country would be willing to supply in trade. Manifestly, the amounts of linen that Germany would be will­ing to supply in trade depend upon the cost of producing linen in Germany, the cost of producing cloth in relation to the cost of producing linen in Germany,5 and the overall demand for linen and cloth in Germany. In short, many market factors lie behind Mill's reciprocal-demand functions.