SOME DOCTRINES OF POLITICAL ECONOMY. 139 



38. Now to find the quantities of the imports and the prices. 



The consumption of (D) in England varies with the price (22). When the price falls from 

 pC to p'C, let the quantity consumed be increased from q to q. Let p' = p (1 - x), and let the 



law of altered money demand be, as before, p'q 1 ' = pq(l - mx). Hence q = q . 



1 - x 



In like manner the demand for (C) in Germany varies with the price. Let P = P(l - X), 

 PQ' = PQ (l - MX) ; whence Q' = Q " 



1 -X 



Since p (l - x) = p\ P (l - X) - P, we have Pp (1 - Jf) (1 - a?) = Pp' = i, by (36). 

 Hence (l - X) (l - x) = -— - = l - A, suppose, A; being a fraction ; since by (36) Pp is 

 greater than 1. 



The equation (1 - X) (l - x) = 1 - k, gives X = — ^— . 



The equation 9 '= P'Q', (37), gives q ~ ™ X = PQ (l - 3f^). 



] — a? 



Put for .y its value , and solve the equation in x ; and we find 



PQ (1 - Mk) - q 

 X ~ PQ(l-M)-mq' 



39. The values of x and X depend upon the ratio existing between PQ and q originally, 

 before the trade : that is, upon the relative value of (C) consumed in Germany and of (D) 

 consumed in England : and also upon m and M, the specific rate of change of each com- 

 modity. 



In general let PQ = nq; and we have 



n (1 - Mk) - 1 1 - n (l - Mk) 



x = , or x = . 



n (1 - M) -m m - n(\ - M) 



40. I will apply these formula; to the numerical examples given by Mr. Mill, (Polit. 

 Econ. ii. 123). 



g 

 He supposes that originally, in England, C = -D, and in Germany, C = 22). Hence 



2 4 



p = - , P = 2, Pp = - which being > 1, the trade is advantageous ; 



3 3 



— - =i 1 — k : whence k = - . 

 Pp 4 4 



2 

 Let m and JW be each = - . Hence we have 



3 



6 - 5n 



x = . 



4 -2« 



18—2 



