Cambridge Philosophical Society. 469 



blems which have been solved by Mr. J. S. Mill and others by 

 means of numbers, taken as examples ; the principles of these writers 

 "being taken for granted in the algebraical solution. Mr. Mill has 

 rightly observed, that instead of saying that prices are determined 

 by the ratio of demand and supply, we ought to say that they are 

 determined by the equation of demand and supply. This equation 

 may be thus stated. Let p be the price, and q the quantity bought 

 and sold at that price. When p becomes p', let q become q' ; and p' 

 being equal to p(\-\-n), let p' q' =pq(l +mn) : this is the equation 

 of demand and supply. For different commodities, we have different 

 values. There are such classes of commodities as these : (A.) Con- 

 ventional necessaries, for which m=l : of these the same quantity is 

 bought whatever be the price. (B.) Articles of fixed expenditure, 

 for which m=0 : on these the same sum is always expended, a 

 smaller quantity being bought in proportion as they are dearer. (C.) 

 Common necessaries, in which m is between 1 and : in these, when 

 the price falls, the consumption is increased, but the money ex- 

 pended diminished. (D.) Popular luxuries, in which m is negative : 

 in these, when the price falls, the consumption is so much increased 

 that the money expended on them is increased also. For corn, the 



mean value of m seems to be about - : on this supposition a failure 



of one-fourth in the supply would double the price. The quantity 

 m measures the susceptibility of the price to change when the supply 

 changes, and also the intensity of the demand. 



Another division of commodities is, according to the cost of pro- 

 duction. These are (a) commodities of fixed and limited supply ; 

 (/3) commodities of fixed cost ; (y) commodities of increasing cost 

 for increasing supply, as for instance corn in a given limited district. 

 The equation of price for the last case was given. 



The like methods were applied to solve certain problems concern- 

 ing international trade, treated by Mr. Mill. If the relative value 

 of two commodities, C and D, in England and Germany be different, 

 there will be a saving in exporting each from where it is cheaper to 

 where it is dearer ; and the question is, at what point prices will 

 settle. We must introduce here the principle of the uniformity of 

 international prices ; namely, that when the trade is established, the 

 relative prices of C and D will be the same in the two countries : 

 the principle of the equality of imports and exports in each country; 

 and the equation of demand and supply already stated. By combining 

 these principles, the problem of the resulting price is solved. But 

 it is found that there is no solution possible (that is, no solution in 

 which both countries gain by the trade), except the mutual demand 

 for the interchange of commodities be nearly equal. This limitation 

 of the solution is given by the algebraical method, and seems to have 

 been overlooked by previous writers. 



The same methods were extended to a greater number of ex- 

 ported and imported commodities ; and finally, it was remarked that 

 these calculations are all founded on principles of equilibrium, 

 whereas a state of equilibrium is never attained ; and thus the theory 



