142 Dr. WHEWELL, ON THE MATHEMATICAL EXPOSITION OF 



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 before. Also the q of (D) cost in Germany the same labour as -q of (C), that is, as -Q of (C). 



* o 



Therefore - of the labour at first employed in producing (C) is set free for any new 

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employment. 



England gains nothing, consuming, as before, q of (D) and a certain quantity of (C) : but 



2 

 the labour which produced q of (£>) is transferred to the production of -q of (C) for the 



German customer. 



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45. If n be > -, as, if n = -, PQ = -7, Q = -9. In this case, Germany wants Q of (C) 



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3 

 which she can procure in England by exporting -Q of (D) instead of producing it at home 



where it would cost 2Q of {D). Hence she gains -Q of (D), and this may be expended on 



(C), (D), or any new commodity. 



2 5 



England exports Q of (C), which requires as much cost as -Q, that is, — a, 01(D). Hence 



the labour or cost which produced — q of (D) is transferred to produce (C), and produces -q of 



(C), in addition to the quantity required for home consumption. And the production of (D) 



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in England is diminished by -Q or — q which is brought from Germany. 



46. The case in which x or X is negative by the formulae, is the case in which the inequality 

 of mutual demand is such that no relative value of C and D intermediate between that in 

 Germany and that in England will satisfy the equation of import and export (37). In that 

 case, the gain is all on one side, as in the case last examined. 



To determine this gain in general in such cases, we must consider that Germany wants 



Q 



Q of (C) which she can procure in England by exporting — of (D) instead of producing so 



much (C) at home, where it would cost PQ of (X)). Hence her gain is 



Q Pp-1 kQ 

 PQ -3 = _£ Q = — of (J>), or kQ of (C), 



P. P P 



which may be spent in adding to (C) or to (D), or on any other commodity. 



2 



47. It appears by what has been said that in the case supposed, where p = -, P = 2, 



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(Mr. Mill's example), there is no possibility of a trade in which both countries shall gain, except 



10 , ( 



n be between — and - 



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England alone gains. 



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n be between — and -. If n be greater than - , Germany alone gains : if n be less than — 



