SOME DOCTRINES OF POLITICAL ECONOMY. 143 



2 

 This is on the supposition that m =■ -. In general, since x must be less than k, and 



_ l - n(l - Mk) 

 ~ m-n{\ - M)' 



we must have 1 > n(l — Mk) in order that the numerator may be positive. And since 

 .r<A;, 1 - n (1 - Mk) <mk - nk{\ - M); whence 



1 — km l 



n > — , and n < 



1 - k ' l-Mk 



It « = -, m = -, this gives n > — and n < - as above. 

 4 3 & 9 5 



11 8 7 



48. If m = -, 3f = -. Then n > - and n < -. 



2 2 7 6 



In this case a?= — . Since n must be between - and -, that is, between — and — 



4 - 4>n 7 6 84 84' 



97 7 6 



let n = —. Then x = —, w = — . 

 84 52 45 



, 1 - raw I 1 \ . \ - Mx ( 2 \ 



Hence q' = q = 1 + - } g ; Q' = Q - 1 + - Q. 



1-a; V 21/^ l-« V 39/ 



Both q and Q are increased by a fraction, and both countries gain. 



8 . 7 



If n be less than -, England alone gains : if n be greater than -, Germany alone gains. 



49- If we have to use the formula x = — — - , 



w(l -M)~ 1 



1 - mk 1 



we must have n < - — — , and n > 



l - k ' l-Mk 



50. Let now England produce another exportable commodity (£), and let the price of 

 E, a unit of (£), be = rC in England. 



Let Germany produce another exportable commodity (F), and let the price of F be i?X) in 

 Germany ; and let S be the quantity of (E) required in Germany, and s the quantity of (F) 

 required in England at the original prices. 



It is required to find the amount and prices of the imports and exports. 



51. Let the trade be established: let (E) be exported and (F) imported by England. 

 In this case, when p becomes p = p (l — x), and P becomes P' — P(l — X), let r become 



r, and R become i?', * become s', and S become S'. 



If England be entirely supplied with (F) by Germany, and Germany entirely supplied 

 with (E) by England, the import of England is now q of (D) and s' of (F); and the export 

 of England is now Q' of (C) and & of (E). 



