# Full text: Study week on the econometric approach to development planning

```304 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28
traints. Condition 1 is specific to the consideration of unlimited
programs. We shall have occasions to see in the following
examples that it is not vacuous.
We may also observe that the equations «,=o0, §,=0 imply
together with the equilibrium condition at time # a set of dif-
ference equations which may usually be solved recursively for
all C,, K,, N, starting from any given allocation of S, between
Co and K,. Thus, the regular programs generate a one pa-
rameter family of programs, the parameter being C, (or equi-
valently Ko, S, being given). Typically, one and only one
program of this family will meet condition 1 and therefore be
optimal. A possible computational procedure would be first to
determine the regular program corresponding to any fixed
initial allocation, and then to find by trials and errors the initial
allocation that leads to fulfilment of condition 1.
Before turning to specific examples, we may look at the
economic interpretations of equations (22), stating that the «,’s
and §3,’s are all zero, and of condition 1.
The first equation (22) may be written as:
34) I+fæ = (1+e) (1+T,) (I+U,)
f= being the marginal productivity of capital, or the equili-
brium rate of interest, e the social rate of interest used for the
discount factor of the utility function, =, the rate of increase
of the population, and u, the rate of decrease of the marginal
ut'ity of consumption. This equation exhibits in a suggestive
way the three components which explain the equilibrium rate
of interest. It is similar to relations recently put forwards by
Sir Roy HARROD and Professor RAGNAR FRISCH.
Condition 1 implies that the equilibrium rate of interest be
larger than the rate of increase in the stock of good S,, and the-
refore that the present value of S, decreases to zero with £.
5] Malnvaud - pag.
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