D. Hectob. — Political Economy. 517 



1 dV J_ dT _ J_ dV^' _ 



From this we may deduce a relation between property-values 

 and rate of interest (r). 



Let V = property-value. 



Integrating, we get — 



This assumes that r is constant, and that all the rent is 

 devoted to buying more land and the interest to increasing 

 capital. Neither of these assumptions is true, for evidently 

 a man who is both a landowner and a capitalist may be most 

 erratic in his investments; but it seems evident that, since the 

 area of land in use is limited, more rent will find its way to 

 capital than interest to land, so that capital will increase more 

 quickly than given above and lanl-values more slowly. We 

 may, however, deduce a formula free from both these objec- 

 tions by replacing dY/dt by R ; then V, R, and r are simul- 

 taneous values at any time, and therefore true for all time. 



R 



y = r. 



Since R is always greater than 0, we see that when r = 

 V = oo, and vice versa. There is one case in which R = : 

 that is at and below the margin of cultivation ; the formula 

 then gives V = 0. True, but of no importance. 



II. 



Rent is equal to production minus the marginal production. 



Let productiveness mean the production from unit-area of 

 ground, and let it be represented by y, and the marginal pro- 

 ductiveness by g. Further, let dR/dx = z. Then we may 

 write y = g + z -f- f(x), so that the profit after the rent has 

 been paid is gr -f- f(x) ; but at the margin no rent has to be 

 paid, so that the profit there is g. Now, if equal areas of land 

 be taken at the margin and at any other point, we have — 



1 dG 1 dG' 



~G ' ~di " G 7 ' ~at 



— here I use C and C to include not only capital, but also 

 labour — 



g + fix) _g • 

 G " C ' 



or (C-G')g=f{x)C. 



