In what follows, I shall from time to time refer to this distinction. In my own exposition, I shall always use "value of money" in the absolute sense, as distinguished from the mere "reciprocal of the price level,"--a practice which I have sought to justify in the chapter on "Value," and in other places there referred to.[47] The modern theory of supply and demand, then, assumes money, and a fixed value of money. It is, therefore, obviously unfitted as an instrument to solve the problem of the value of money. If supply and demand concepts are to be applied to this problem, they must be of a different sort. This was pointed out by Cairnes[48] who criticised Mill's formulation, and pointed out that Mill departed from it in three capital doctrines: in the theory of the value of money, in the theory of wages, and in the theory of international values. By the demand for money, Mill means, not the amount of _money_ demanded, but the quantity of goods offered against money--a very different conception. (Mill, _Principles_, Bk. III, ch. viii, par. 2.) In what sense a quantity of goods can equal a quantity of money, or in what sense there can be a ratio between goods and money, (to recur to Mill's former problem as to the ratio between things not of the same denomination) Mill does not make clear, nor is it defensible to speak of either a ratio or an equation on the basis of Mill's system, since Mill had no absolute value concept. Cairnes seeks to reconstruct the notion of supply and demand, in such fashion as to make it possible to apply it universally, and takes up the question of the comparability of supply conceived as a quantity of goods, and demand, conceived, not as a quantity of goods, but as desire combined with the ability to pay. He concludes that in both supply and demand there is a physical, as well as a mental, element. Demand he defines as the desire for a commodity backed by general purchasing power; supply as the desire for general purchasing power, backed by the offer of a commodity. Thus he thinks he has made the two of the same denomination, so that comparison may be instituted between them, and the ideas of equation, ratio, and proportion made legitimate. By "general purchasing power," Cairnes seems to mean money and the representatives of money. It is not an abstract power, since it is the "physical" element in demand, comparable with, and of the same denomination with, the physical element in supply, a commodity. Cairnes' solution of Mill's difficulty seems to me to be merely verbal, however. First, in what way is the desire for general purchasing power in the mind of one man comparable with the desire for a commodity in the mind of another man? I pass over the supposed difficulty that knowledge of other men's emotions is impossible,[49] and emphasize simply the point that price offer, either by demander or supplier, is no test of the intensity of desire where there are inequalities in the distribution of wealth. But second: in