## Mill’s Reciprocal Demand Theory

Mill's Reciprocal Demand Theory

A summary of Mill's theory requires a second figure, 3, which reproduces Germany's demand function of Figure 2 and also one for England, OE (constructed in the manner described for Germany). As Mill indicated, trade will take place at such prices as are required to make the value of imports equal the total value of exports, simultaneously, for each party to the trade. If the value of exports does not equal the value of imports to both England and Germany simultaneously, price adjustment will take place to bring the equilibrium about. This extension of the more general law of sup­ply and demand is graphically expressed in Figure 3. Given price OP', Germany would be willing to supply OLo linen for ALo cloth. But demand-and-supply conditions in England are such that the quantity OLO of linen would be demanded at a much lower price, OP", of cloth (higher price of linen). England, in other words, would be willing to supply LoB of cloth for OL0 linen. But at price OP", Germany would not be willing to give OLo of linen for LoB of cloth. Clearly, international demands and supplies are not irrequilibrium at ei­ther price OP' or price OP".

Figure

What happens? As Mill carefully noted, prices (international values) will ad­just so as to bring demands and supplies into equilibrium. Indeed, it is the disequilibrium of supply and demand that brings about the price adjustment. At price OP', for example, England would demand a greater quantity (repre­sented at point C) of linen than OLo or what Germany would be willing to sup­ply. Similarly at price OP", Germany would demand a larger quantity of cloth than LoB, the amount that England would supply. Thus demand-and-supply disequilibrium forces an adjustment.

Prices will adjust until the price line becomes OP in Figure 3. At point F, the reciprocal-demand curves OG and OE intersect. The economic meaning of the intersection is that at price OP of cloth/linen or linen/cloth, the quantity supplied of cloth by England, C*, equals the quantity of cloth demanded by Germany, C*. Simultaneously, the quantity of linen supplied by Germany, L*, equals the quantity of linen demanded by England, L*. The value of exports equals the value of imports for both nations. It is a price adjustment or alter­ation in the terms of trade that brings this equilibrium about.

General Equilibrium in Exchange

Figure 3 may also be used to demon­strate Mill's understanding of general equilibrium in exchange. The model de­scribed in Figure 8-3 is in fact a general equilibrium model not unlike that for­malized by Leon Walras more than two decades later. Mill's ingenuity can perhaps best be seen by converting the reciprocal demand curves of Figure 3 into more conventional demand and supply curves, as drawn in Figures 4a and 8b. Recall that the offer curves of Germany and England are both demand and supply curves. Consider Germany's curve, OG, in Figure 8-3. Offer curve OG traces out the amount of linen Germany would supply for given quantities of England's cloth at alternative given price ratios. As the price of linen rises (which is equivalent to a fall in the price of cloth), Germany is willing to give more linen for more cloth. In equilbrium at price P in Figure 8-3, Germany gives the quantity L* for quantity of cloth C*. At a higher price of linen (a lower price of cloth) given by price ratio P", Germany would supply more linen, L,, if it received a greater quantity of cloth, C1, in return.

Figure 4a summarizes these observations in terms of supply and demand curves expressed not in money prices but in the real prices designated by the ratios of exchange. At the high price P" for linen (expressed in terms of the ratio of cloth to linen) Germany would be willing to supply L, of linen but England would demand only L0 of linen. Clearly, at price P" there is an excess supply of linen in terms of the desires of demanders and suppliers of linen. Market pressures would then exist for the price of linen (in terms of cloth) to fall.

Viewed from a general equilibrium perspective, however, it is clear that Germany's supply of linen is also the mirror image of its demand for cloth. Similarly, England's demand for linen also represents its supply of cloth. These "mirror-image" relations are reproduced in Figure 4b, which con­trasts the demand and supply of cloth in terms of the real price of cloth. A high price of linen in terms of cloth means a low price of cloth in terms of linen. At the price ratio P", the quantity demanded of cloth in Germany is C1 while the quantity of cloth that England is willing to supply is C0. (All information may be transferred directly from Figure 3 to Figures 4a and 4b.) As previ­ously noted, the supply curve of cloth also summarizes the demand curve for linen, and the demand curve for cloth is the supply curve for linen. At the low price of cloth in terms of linen, pressure for a rise in price exists since the quantity demanded of cloth exceeds the quantity supplied. Thus, twin pres­sures exist simultaneously in the linen and cloth markets. Reduction in linen price means an increase in cloth prices. Price changes occur until both markets clear simultaneously. Excess demand in one market must imply excess supply in the other. This idea is the basis for understanding how markets are interre­lated in general equilibrium, i.e., simultaneous equilibrium in all markets of an exchange economy.