•208 Professor Whewell on the Mathematical Exposition 



a„ out of cultivation ; the rate of profits q is supposed to remain 

 the same as at first : if this vary however, the consequences of 

 its variation may be traced afterwards. 



Various suppositions may be made, of which our formulae 

 will give us the consequences. 



16. We may suppose that no land is thrown out of culti- 

 vation in consequence of the tax : that the demand increases, 

 and with it the price, so as to keep a„ in cultivation. That this 

 may be so, we must have 



P^'n — ^n? f^ot less than by the second Axiom, 

 and p'r„— t„ — c„q not less than 0, for the same reason. 



Suppose that we take the soil a„ to be exactly of the 

 limiting- quality, so that by the 5th and 6th Axioms, 



pr„ - c„q = 0, p'r„ - f„ - c^q = O, and let <„ = k„p'r„, 



.-. p'r„ (1 - k„) = c„q, pr„ = c„q, .-. p' (l - k„) = p, 



Here also u = o, and v = o, because no land is thrown out, 



therefore putting for />' its value, we have by the last Article 



. r ■ arp k„arp 



Increase ot price. . . , = - — -. arp = - — i-. 



1 - «•„ 1 - /fn 



1 — A- k — k 

 Diminution of rent. . = arp - ar j-p = "•'"'P • ^j rr- 



Diminution of profits = 0. 



karp 



Tax. 



1 -A„ 



If the tax bear a given ratio to the produce for all soils, 

 h„ - k, the diminution of rent is o, the increase of price and the 

 amount of the tax are equal, and the whole tax falls upon the 

 consumers. 



This is the case considered by the writers who follow Mr. 

 Ricardo, and the conclusion depends entirely, as appears from the 



