The name is absent

1-      Y₁  =  c_t+ι_l

2.      I_t^o  -  I_l(L_l, K_l, F,°)

3.     C_t^o = C_l(L_l, K_l, F°)

4∙     ς.₁ = f^c c_l

5∙    4ι  = f' A

6.     L₁  -  L₁

7∙      K_t  -  K₁ = I_{t λ}

8.     F₁  =  F_l(f^c,f')

We have a world economy in two periods—present (t) and future (t+l) with a global
factor (F) that can constrain world production of consumption goods (C) and investment
goods (I) by limiting the productivity of ordinary factors of production, say labour (L) and
capital (K). This is depicted in equations 1, 2 and 3. In Diagram 1, the transformation curve
EF in period t is not limited by any constraint posed by F, and solely reflects the given
endowments of labour and capital in equations 6 and 7.

Assuming that the world is interested in leaving an adequate bequest, it prefers to
consume a minimum, OB, in period t. Then OA is the investment good produced. ⁸
Combined with L_r+1, it yields the transformation curve GH in period (t+l), if unconstrained
by F. The community indifference curve UU' determines J as the equilibrium production-
consumption combination.

Given Q and J, quadrilateral ABCD is the equilibrium production-consumption
configuration for current and future generations.

OB plus OA yields Y_t at normalised prices.

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