138 Dr. WHEWELL, ON THE MATHEMATICAL EXPOSITION OF 



Suppose that in England p is the price of D in terms of C ; and let q be the quantity of 

 (/)) consumed (that is, bought) in England at that price. 



D 



Then D=pC, C = — in England. 

 P 



Suppose that in Germany P is the price of C in terms of D, and let Q be the quantity of 



(C) consumed in Germany at that price. 



C 



Then C = PD, D = - in Germany. 



Now D in England costs p C when there is no international trade ; but if obtained from 



C 



Germany by exporting C, would there cost — . 



Therefore there would be a gain for England in obtaining D by exporting C rather than 



Q 



producing it at home if pC > — ; that is, if Pp > 1 : for the cost would be less. 



In like manner, there would be a gain for Germany in obtaining C by exporting D rather 



D 



than by producing it at home, if PD > — ; that is, if Pp > 1 : for the cost would be less. 



Hence on the supposition that England exports C and imports D, and Germany exports 

 D and imports C, both countries gain. 



36. What will be the amount of the exports and imports, and the prices, when the inter- 

 national trade 6x5818? 



In order to solve this problem, we must introduce another principle; namely this: that 



in the long run, and in the permanent condition of the trade, the value of the exports of each 

 country must equal the value of its imports. For each country pays for its imports by 

 its exports. 



Under the trade let p, the price of D in terms of C, in England, become p' ; and q, the 

 quantity of (D) consumed in England, become q', the whole being imported from Germany. 

 And let P, the price of C in terms of D in Germany become P, and let Q, the quantity 

 of (C) consumed in Germany, become Q', the whole being imported from England. 



In England p'C = D, in Germany, P"D = C ; and since these equations express prices 

 under the trade, by the principle of uniformity of international prices, the relation of C and D 

 is the same in the two countries. Therefore multiplying together the two equations, 



Pp = 1, 

 which is the equation of uniformity of international prices. 



37. England exports Q' of (C) and imports q of (D) ; and of this last the value is p q 

 in terms of C : therefore, by (36) p'q'=* Q'. 



In the same manner Germany exports q of (D) and imports Q' of (C) ; and of this last 

 the value is P'Q' in terms of D: therefore PQ'= q. 



The equation p'q'=Q', or PQ' = q', is the equation of import and export. The two 

 equations are identical in virtue of the equation P'p' = 1. 



