212 Professor Whewell on the Mathematical Exposition 



Also — TR = arpk (1 -u) (1 +w)- arp {w — u- uw) -acqv. 



Hence the tax falls on rent, except the portion arp {w-u - uw) 

 which falls in price, and acqv which falls on profit. 



20. Let price vary inversely as supply, and we have as before 

 by (c). Art. 18, 



— = , or (l+a)) (1 - m) = i. Hence equations (fi) give us 



— tR = arpk — acqv 



— tQ = acqv 

 tP=0 



T = arpk. 

 Therefore in this case the consumer pays no more than he did 

 before the tax. The tax is taken entirely from rent and profits. 

 The consumer however receives less for his money. 



21. Let the price be determined as in Axiom 5, by the 

 expense of production on the limiting soil, both before and 

 after the tax is imposed: a„, and a,,-, being the limiting soils in 

 the two cases. Therefore by equation (6), Art. 18, 



and by the substitution of this value equation {B) becomes 



— tR = arp |l } — acqv 



— tQ = acqv 



Hence, — tR = arp ^— acqv, 



„ k- p — u + kp 

 tF = arp - — — TT T • 



(C). 



