/ 



SOME DOCTRINES OF POLITICAL ECONOMY. 145 



54. It is evident that if we had any other commodities (£,) (E 2 ) exported by England, 

 and any other commodities (Pi) (P 2 ) exported by Germany, we should have equations of the 

 same form, to any number of terms. 



55. If Pp be considerably greater than l (35), the range of values of n within which the 

 trade is possible with mutual advantage will be wider. 



Thus, let a yard of cloth (C) exchange for l bushel of corn (Z>) in England; but for 



113 1 



4 bushels in Poland. Here p = 1, P = 4. Pp = 4 ; .\ — = - , k = - . Let m = M = - . 



Pp 4 4 2 



, , 1 . 1 - mk , x , , 8,5 



Hence «, (3Q), which must be between — - and — , (48), must be between - and - . 



v ' 1 - Mk 1 - k 5 2 



■I h. (7? 1 



56. For instance, if n = 2, w = -, whence X = = - ; 



' 2 1 - a? 2 



and (38) q = , T — - = -,, Q= T — - = i Q, p - ^ P' - ^ 



Here, since PQ = nq, and P = 4, « <= 2, 2Q = §. 

 In this state of the trade, a yard of cloth will exchange for 2 bushels of corn. Poland will 



produce and export -q of corn, besides her own consumption. England will produce and 



3 3 



export -Q of cloth, which is -q, besides her own consumption. And in this case England has 



half as much more corn, Poland half as much more cloth, as before. 



57. But this mutual advantage arises from the mutual demand being nearly equal. 

 Poland is supposed to demand, at first, half as many yards of cloth as England demands 



bushels of corn, for Q = -q. 



2 



If this be otherwise : if, for example, Poland demand at first only one-fourth as many 



yards of cloth as England demands bushels of corn, or Q = -q : since P = 4, PQ = q ; there- 



4 



fore n = 1. 



In this case I supposing m and M each = - ) by (38) q' = q = q , Eng- 

 land's import, 



also P'Q' = England's export ; 



k _ x 3 — 4# 5 — 4* 5 — 4a? 

 and since X =- = , P'Q' = PQ (l - MX) = PQ - q . 



!_# 4 - 4a? 8 - 8a? *8-8a? 



And the export will be less than the import for every positive value of a? ; that is, there cannot 

 be any fall of the price of corn, with relation to cloth in England, so small as to make the 

 imports and exports equal. 



In this case the relative price of cloth and corn in England w^U under the trade be ulti- 

 mately what it was before the trade ; and therefore ultimately, the relation of the prices will 

 Vol. IX. Paet I. 19 



