of some Doctrines of Political Economy. 221 



m 



Also —tQ = acnv = arpu = arpk -, -, 



^ -' ^ ^e + m(M-l) 



tP = arp {(1 + ty) (1 + m) - 1} 



= arp \{e— 1 ) m - eu" i 



_ , r (e—l)m ernJc | 



Hence the parts of the tax, which affect rent, profits and 

 price, are nearly as m(M— l) — e(m — i), m, and (e - !)/« respec- 

 tively. 



In the case where m, n, e have the values above-mentioned, 

 these parts are as 15, 4, 8. 



In general, the part which falls on rent will be the greatest. 



32. Let the tax be a certain portion of the rent, viz. a 

 fraction s of the rent which arose when there was no tax ; 



.•. t„ = s {pi\ — qc„) 

 .■. the rent under the tax — pr„ — s {pr„ - qc„) — qc„ by Ax. 6". 



= (1 - s) {pr„- qc„). 



In this ca.se the tax falls wholly upon rent. 



33. Let the tax be a tax on profits, viz. a fraction s of the 

 previous profit. Therefore 



t,n = *■(?-!) c,„, and a,„ t„, = s{q - l) a,„c,„. 



And if t be the average tax, «„ the land thrown out of cultivation 

 by it, 



the whole tax = (a - a„) t =^s(q — 1) (ac - a„c„), 

 and hence, by Article 15, 



— rR = arp — ar {l — u)2y + s{q-l) {ac — 'a„cj — acq v. 



As before, p' = {l+w)p, a„c„ = vac; 



and hence, since acqv = arpu, 



— rR=:arp {1 - (1 - u) {1 + w)] + asc (q — I) {I -v)-acqv 



