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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28

TABLE IIT — Main relations

/ R= RU LE _ R,+:C
¥ dt
Ry=R, + R,
C,=C+C,

R,= Ce

(110-1) (110-2)
(110-3) (110-4)
(110-5)

(116-13)

Production function
By hypothesis, real consumed income is a functional of the
primary inputs
Ro(t)=a(t)F[R, (1) @ (4,017
k = coefficient of homogeneity of the production function
 (§ 117)

Case of a quasi-stationary process with p=p (t)
wo (i-p)e
Rel)R (0) ofan
I AR op 1 AC ç(t) (122-3) (123-2)
R, dt C dat
R-R Ÿ for : (123-4) (123-12
Clt)o 2c to ce Or 120 3-4
) 1-7 a (HP)
[° Gi-eis
5R, nv dp(6)e _
R,  f“,. (io
© / wlole "de
R, maximum for i(t)-p(¢)=0
— 4
Re oN —- p lize) 29 _[ig=0]
Kom 2 d(i-p)
R.,= maximum value of R

y

All these relations except (117-1) are accounting identities
[relations (110), (112), (123)] or simple consequences of a
Paretian optimality (relations 12%).