Principles of Political Economy and Taxation. 191 



existing in the country. Hence prices will be altered, and with 

 them the quantity of exports. 



Let e u e„...e t be the exports in the 1st, 2d...?" 1 year, 

 p a p„...p t , the corresponding prices, 



g\> gz---gt> the quantity of gold (or other currency) in the 

 country at the beginning of these years, (the amount of the cur- 

 rency being supposed to change only in consequence of the im- 

 portation of gold). 



Also let it be supposed that the increase of price is in pro- 

 portion to the increase of the quantity of gold, (see Post. II.;) 



that is, p, =/», — . 



g> 



We have therefore, since gi +1 —gi is the gold imported in the t th 

 year, which must equal the excess of exports, Setpt—Si*=g t+1 —g„ 

 or, putting for p t its value, 



tML S e t -Sis=g t+1 -g t ; 

 therefore g t+l = (1 + ^~Se,)g t -Sis...(l). 



o 1 



If we know the law of the diminution of the annual exports 

 Se t , we have Se t in terms of t, and hence, by integrating this 

 equation of finite differences, we can easily find g, in terms of 

 t, and hence the quantity of gold in the country after any num- 

 ber of years. In practice (on the suppositions already made) g, 

 would tend rapidly to a limit, and the quantity of gold after a 

 few years would receive no sensible increase. If t be the num- 

 ber of years which gives the limit with sufficient accuracy, we 



have 



Se t p t -Sis = 0; 



Qg t Se t -Sis=0, p l Se t = &Sfis...{V}. 



gi gt 



